CHEM101 Study Guide

Site: Saylor Academy
Course: CHEM101: General Chemistry I
Book: CHEM101 Study Guide
Printed by: Guest user
Date: Tuesday, May 11, 2021, 3:05 AM

Unit 1: Matter and Measurements

1a. Define chemistry

Matter describes everything around us that has mass; chemistry is the academic discipline that studies matter. This includes solid objects, such as the table where we sit, the liquid water we drink, and the air (a gas) we breathe. Chemistry is part of everything we touch, feel, see, and smell.

Chemistry studies the properties and structure of matter, including chemical reactions, which describe the transformation of matter. Many people call chemistry the "central science" because we use it in most science and technology fields.


1b. Distinguish between physical and chemical properties of matter

  • How do the physical and chemical properties of matter differ?
  • List some examples of physical properties.
  • List some examples of chemical properties.

We can describe matter by its physical and chemical properties.

Physical properties describe our observations about the properties of a substance in which the substance itself does not change during or after our observation. Examples of physical properties we use to describe a substance include its boiling point, melting point, appearance, and density.

Chemical properties describe our observations about the properties of a substance during or after its chemical transformation. Examples of chemical properties we use to describe a substance include its acidity and the types of chemical reactions it can withstand or perform.

To review, see the table in section three that compares the physical and chemical properties of the element sodium.


1c. Classify changes of matter as physical or chemical

  • How do physical and chemical changes differ?
  • List some examples of physical changes.
  • List some examples of chemical changes.

Matter can undergo two types of changes: physical and chemical.

Physical changes do not alter or change the identity of a substance. Examples of physical transformations include freezing, melting, or boiling.

For example, when a solid ice cube melts to become liquid water, the water's chemical identity does not change. The transformation is physical because the identity of the initial and final substance remains the same, in this case, water. Likewise, water vapor (gas) that results from boiling is still comprised of water molecules.

Chemical changes, on the other hand, which we also call chemical "transformations" and chemical "reactions", do alter the identity of the substance.

For example, a nail that rusts represents a chemical change because the rusting process creates a new substance with a different chemical composition than the original nail. The transformation is chemical because the identity of the substance has changed. Similarly, burning represents a chemical change because the chemical composition of the substance changes during the burning process.


1d. Explain the solid, liquid, and gas states in terms of particles

  • Describe and draw a picture of solid, liquid, and gas-phase particles.
  • Which state or phase of matter usually has the lowest density?
  • Which state or phase of matter is considered a "condensed" state?

We can describe three states or phases of matter: solid, liquid, and gas.

Molecules in solid state matter are arranged in an "ordered" fashion. The particles touch each other and are close together. Solid materials have a definite shape.

Molecules in liquid state matter are close together but are not ordered like a solid. The particles can move or "slip" around each other. The liquids flow and move. Liquid materials take the shape of their container.

Molecules in gas state matter are far apart from one another and usually do not touch or interact. The molecules are completely disordered. Molecules in a gas take up the entire space of their container.

Review this simple diagram of the three states of matter.

Density measures the mass of an object per unit volume. In other words, a "denser" object has a higher mass than a second object which shares the same volume. Most liquids and solids have significantly higher densities than gases.

We consider molecules in a liquid or solid phase condensed phase matter. This means the molecules are in direct contact with their neighboring molecules.


1e. Distinguish among a quantity, a unit, and a measurement standard

  • Define the following terms: quantity, unit, measurement standard.

In chemistry, we use a defined set of units when we make measurements – to ensure consistency, accuracy, and make comparisons. We base units of measurement on a commonly-accepted, standard scale, so we can describe and communicate the results of our measurements with other researchers.

Quantity describes the amount we measure in an experiment. For example, a quantity could describe the mass, volume, length, or another observable measure.

A unit relates to the standard measurement scale. A unit defines the amount of a quantity measured. For example, we use meters to measure length (50 meters), grams to measure mass (10 grams), and liters to measure volume (5 liters), according to the metric scale of measurement.

A measurement standard is a universally-agreed-upon object that defines a unit of measurement.

Measuring instruments are calibrated to match measurement standards scientists have agreed to follow. Think about the length of a ruler (how long is 12 inches or one meter?), a mutually-agreed-upon amount of water used to follow a recipe (how much is in a cup?), or a common temperature used to calibrate a thermometer (how cold is 20 degrees Celsius or Fahrenheit?).


1f. Name and use SI units for length, mass, time, and volume

  • What are the base SI units for length, mass, time, and volume?
  • You should be able to recognize and use the standard SI decimal prefixes to convert among different units of measure.

Systeme Internationale (SI) units describe the internationally-recognized set of units of measurement that are standard in all scientific fields.

The base SI units for length, mass, time, and volume are as follows:


SI Unit


meter (m)


kilogram (kg)


second (s)

Volume (not actually SI)

Liter (l)

Review the table of SI decimal prefixes in The SI Units.

We use SI prefixes to convert among units that have different orders of magnitude. For example, you should use millimeters to measure extremely short lengths, and centimeters, meters, or kilometers, to measure longer units of measurement or distances.

We use dimensional analysis to convert among units since it makes it easier to compare quantities in different units. For example, from the SI decimal prefixes table we see that one kilogram (1 kg) = 103 g, or 1 kg = 1,000 g.


1g. Determine the number of significant figures in measurements

  • Explain why you need to use significant figures when reporting measured quantities.
  • Determine the number of significant figures in a given measurement.
  • Properly round numbers to a given number of significant figures.

You should use significant figures when reporting a measurement to convey your level of confidence in your measurement.

Chemists consider the last digit in a measurement uncertain because it is an approximation. Significant figures tell us "how good" or "confident" your measurement is, according to the equipment you used to make the measurement.

For example, you usually have to make an approximation when you measure the distance between the smallest markings on a ruler. You might say the coin in the image below measures 2.7 centimeters, but you really have to make an educated guess about the last figure since it is not exact. Scientists recognize this last digit is often uncertain (in other words, you have less confidence in its accuracy).

Image of a coin and a measuring ruler: 2.7??? cm

Review these general rules for determining the number of significant figures in a measured quantity:

  1. Leading zeros (single zeros that appear to the left of a decimal point) are not significant (for example, 0.35).
  2. Zeros that appear to the right of a nonzero number, before the decimal point, are significant (for example, 50.35).
  3. Trailing zeros (any zeros that appear to the right of a decimal point) are significant (for example, .350.
  4. Trailing zeros without a decimal point are ambiguous (for example, 350).

Here is an example.

For the number 0.003900270, the leading zero (the single zero to the left of the decimal point) is not significant. The trailing zero is significant because it follows the decimal point. Therefore, this number has seven significant figures (indicated in red in the diagram below).

(Note that in this diagram, the "placeholder" zeros mean they are showing the order of magnitude of the number rather than an actual measured value. So, the leading zeros in this number indicate the order of magnitude of the number and are not significant measured numbers.)

For the number 9024000.0, all of the zeros are significant because all zeros are between nonzero numbers, between nonzero numbers and a decimal point, or trailing after a decimal point. This number has eight significant figures. The last example, 9024000, has ambiguous trailing zeros.

Image with Significant, Ambiguous Numbers

When working with measured quantities, you should round the numbers properly to avoid confusion about the confidence you have in the measurement.

Review the rules for rounding significant figures in the yellow boxes in Rules for Rounding.

When rounding, round down if the first insignificant digit is less than five. Round up if the first insignificant figure is greater than five.

For example, to round 45.556 to four significant figures, the number should become 45.56 because the first insignificant digit (the last digit, six, in this case) is greater than five.

When rounding the answer for a multi-step problem, it is important to keep track of significant figures, but you should not round your number until after you have completed all of your calculations.


1h. Perform mathematical operations involving significant figures

  • How do you perform addition and subtraction using significant figures?
  • How do you perform multiplication and division using significant figures?
  • How do you perform logarithm calculations using significant figures?

Chemists often need to perform calculations on the quantities they have measured. They use significant figures to convey their level of confidence (or level of accuracy) in their measurements and follow specific rules for adding and subtracting, multiplying, and dividing quantities with significant figures.

For addition and subtraction, we determine the answer's number of significant figures by decimal places. Look at your input quantities and identify the quantity that has the fewest number of decimal places.

Line your addition or subtraction up vertically, according to the decimal point, to make this more clear. Your answer should have the same number of decimal places as the input quantity that had the fewest number of decimal places.

Image of How to Line up Numbers by Decimal Point

For multiplication and division, your answer should have the same number of significant figures as the input quantity that had the fewest number of significant figures.

Image of How to Multiply and Divide Numbers

For base 10 logarithms, the answer will have the same number of significant figures as the normalized form of the logarithm. Normalized means the logarithm is given in scientific notation a x 10b, where a is a number greater than 1 and less than 10.

Image of Number of Digits and Normalized Form of Logarithm


1i. Convert measurements into scientific notation

  • How do you convert quantities into scientific notation?

Scientific notation allows scientists and mathematicians to express small and large numbers more succinctly because they do not include all of the zeros in their notations and conversions. For example, scientists frequently use scientific notation when making a dimensional analysis to convert measurements from one unit to another.

Scientific notation uses multipliers of a x 10n, where a represents the part of the number that includes non-zero numbers. The decimal point is moved to follow the first non-zero number, and n represents the number of zeros that precede or follow the first nonzero number.

For example, 15,000 in scientific notation is 1.5 x 104. In this case, we move the decimal point to follow the first non-zero digit. Then count the number of digits that follow the first nonzero digit to get 104.

Similarly, 0.0007005 in scientific notation is 7.005 x 10−4. In this case, we move the decimal point to follow the first nonzero digit to get 7.005. Count back to the original decimal point to determine the number of zero digits before the first nonzero number. Since you can count four digits until you hit the original decimal point, the multiplier is 10−4. Be sure to use a negative exponent when the original number is less than one.


Unit 1 Vocabulary

  • Central science
  • Chemical change
  • Chemical reaction
  • Chemical transformation
  • Chemical property
  • Chemistry
  • Condensed state of matter
  • Density
  • Dimensional analysis
  • Gas
  • Liquid
  • Mass
  • Measurement standard
  • Physical property
  • Physical change
  • Physical transformation
  • Quantity
  • Scientific notation
  • Significant figures
  • Insignificant figures
  • SI units
  • Solid
  • Unit

Unit 2: The Atom

2a. Define the atom

  • How do we define the atom?

All matter is made up of small particles known as atoms.

John Dalton (1766–1844), an English chemist and physicist, introduced the concept of atoms in the 1800s. Atoms are the fundamental unit of all matter. They consist of subatomic particles known as protons, neutrons, and electrons. However, we cannot break atoms apart, except during a nuclear reaction. During a chemical reaction, atoms are rearranged, but they are not destroyed or changed.

Note that an element is a specific type of atom that has a unique set of properties. The elements are what is found on the periodic table. For example, the elements hydrogen, helium, carbon all have different atom types.


2b. List the properties of protons, neutrons, and electrons

  • Describe the properties of protons, neutrons, and electrons.
  • Which subatomic particles exist in the nucleus of the atom?
  • Draw a simple diagram of the nuclear atom.
  • How are ions formed?
  • What is a quantum particle?

All atoms contain subatomic particles known as protons, neutrons, and electrons. These subatomic particles have different properties.

Scientists have identified three particles within an atom:

  1. Protons exist in the nucleus (or dense center) of the atom, where almost all of the mass of the atom is contained. Protons and neutrons have approximately the same mass. Protons have a positive charge. 
  2. Neutrons exist in the nucleus of the atom with the protons. Protons and neutrons have approximately the same mass. Neutrons have no charge.
  3. Electrons exist in the atom as an electron cloud that surrounds the nucleus of the atom. We consider electrons "quantum particles" because they have almost no mass. We also cannot determine an electron's exact location at any given time. We can only determine the probability of finding an electron at a given location at a given time. Electrons have a negative charge.

When atoms that have no charge, an equal number of protons and electrons exist to create a neutral charge.

Ions describe atoms that have a negative or positive charge. These ions, or "charged particles", have a negative charge when the number of electrons is greater than the number of protons, or a positive charge when their protons outnumber the electrons.


2c. Define isotopes and explain how they relate to naturally occurring element mass

  • Describe isotopes.
  • Use isotope notation to write the symbol for an isotope.
  • How do we determine average element mass based on isotopes?

Isotopes are atoms of the same element that have different masses.

We define an element by the number of protons it contains. For example, hydrogen atoms (represented by a capital letter "H") have only one proton.

However, atoms that are the same element (by definition, they have the same number of protons) can have different numbers of neutrons. Isotopes are atoms that are the same element but different numbers of neutrons. For example, you can have different isotopes of hydrogen, which will have a different mass due to the different numbers of neutrons.

We can write symbols isotopes in terms of two important quantities: atomic number (which scientists represent in their equations with the capital letter "Z") and mass number (which scientists represent in their equations with the capital letter "A").

  • The atomic number of an atom is the number of protons in the element (and defines the element). You can find the atomic number for every element listed on the periodic table.
  • The mass number of an isotope is the sum of the number of protons and neutrons.

We can calculate n + Z = A, with n being the number of neutrons (in other words, neutrons + atomic number = mass number). Turn this equation around and you can subtract the atomic number ("Z") from the mass number ("A") to determine how many neutrons exist in the isotope.

Scientists write the symbol for an isotope (with the mass number and atomic number) this way:

This image offers another example of how isotope symbols are written for the isotopes of hydrogen.

The atomic mass of an element, which you see on the periodic table, presents the weighted average of all of the masses for all of the isotopes of that element. When you take a sample of any given element, different types of isotopes occur in a certain percentage in nature. So, for example, the atomic weight of hydrogen (one) is based on the fact that scientists have discovered more protium in the world than tritium. Scientists call this the relative abundance of each isotope.

Based on this, we can calculate the average atomic mass for any element by calculating the weighted average of the masses of the different isotopes.

Review examples of how scientists calculate atomic mass from isotope masses and relative abundances in Problem Example 4 and Problem Example 5, and the "Average Atomic Masses" video in Relative Atomic Masses: The Atomic Weight Scale.


2d. Define atomic number and atomic mass and describe how they apply to isotopes

  • Define atomic number and atomic mass.
  • How do we determine atomic mass using isotopes?

We use the atomic number and atomic mass to describe different atoms. Review 2c above to respond to these questions.


2e. Define Avogadro's number and describe the mole quantification of matter

  • Define Avogadro's number.
  • Define a mole.
  • Use Avogadro's number to convert the number of atoms to the number of moles.
  • Why do we need to use moles to quantify matter?
  • Use density and molar mass to determine the molar volume of a substance.

Avogadro's number is essentially a counting number for atoms or molecules.

Avogadro's number is 6.022 x 1023. Avogadro's number of particles is one mole.

Think about a mole (mol) as if you have a dozen items: 12 eggs and 12 cars. While the size and mass of the eggs and cars differ tremendously, you still have a dozen. In this case, you have a mole (or 6.022 x 1023) of objects or particles (rather than a dozen). Because Avogadro's number is so large, we really only use it to describe quantities of atoms and molecules.

Review a brief explanation of Avogadro's number in the orange box at the end of Counting Atoms: Avogadro's Number.

Scientists use a mole, the SI (Systeme Internationale) unit, for chemical entities (Avogadro's number of particles). This commonly-agreed-upon unit of measure allows chemists to easily measure and discuss macroscopic (visible to the naked eye) amounts of atoms or molecules.

We can use Avogadro's number (a conversion factor) to convert among a number of particles (such as atoms) and a number of moles of a given substance.

Review Problem Example 3 in Moles and Their Uses.

The atomic masses listed in the periodic table also correspond to the molar mass of the element using the units, grams per mole (grams/mole or g/mol). For example, carbon has an atomic mass of 12.01 amu (atomic mass unit) and a molar mass of 12.01 g/mol. This correspondence allows us to convert among the macroscopic measurements we make (or the mass in terms of grams) to the microscopic (or the number of atoms) we cannot see. We can perform these conversions using the molar mass of an element and Avogadro's number.

To determine the molar mass of a molecule, simply add up the molar masses for each element in the compound.

Practice converting between grams, moles, and a number of particles in Problem Example 4 and Problem Example 5 in Moles and Their Uses.

The molar volume of a substance is the volume one mole of the substance occupies. To determine the molar volume of a substance, you need to use the molar mass and density. Be careful to make sure the units are the same.

Practice calculating molar volume in Problem Examples 6 and 7 in Moles and Their Uses.


2f. Discuss the wave-particle duality of light

  • Define quantum particle.
  • Describe Young's Double Slit Experiment.
  • How does light both exhibit wave and particle properties?
  • How do quantum particles exhibit both wave and particle properties?

The concept of "wave-particle duality of light" is a cornerstone of the field of quantum mechanics.

A quantum particle is a very small particle we can describe as a wave or a particle, depending on how we measure it. For example, under different experimental conditions, we can describe light as a wave or a particle. 

Young's Double Slit Experiment identified the wave properties of light and matter.

In this experiment, Thomas Young (1773–1829), a British physician, shined a beam of light through two small slits onto a detector. When the beam of light hit the double slit, it divided into two and then recombined. The light showed an interference pattern or diffraction pattern, which can only occur when the light has wave properties.

Albert Einstein (1875–1955), the famous German physicist, inferred the particle nature of light when he worked on the photoelectric effect. In his experiment, he shined a high-energy beam of light onto a metal surface, which caused an electron to eject from the metal. This led him to conceive of the idea of photons, or light particles with distinct energy.

We can describe the energy of a photon of light in mathematical terms as: 

 e = hv = \frac{hc}{\lambda}

(e is the energy of the photon, h is Planck's constant, and v is the frequency of the photon).

Quantum particles also exhibit both wave and particle properties. You can perform the double-slit experiment using particles instead of light. If you throw a non-quantum particle (such as a baseball) through the double-slit experiment, some particles will go through either slit, which will result in two spots on the detector at each slit.

However, when a scientist puts a quantum particle through the double-slit experiment, the particles will exhibit the same interference pattern Einstein observed for light. This demonstrates that quantum particles exhibit wave properties, in addition to the particle properties we would typically expect.


2g. Describe the Bohr model of the hydrogen atom

  • What was wrong with the initial planetary model of the atom?
  • How did the Bohr model differ from the planetary model of the atom?
  • What is meant by quantized energy states?

Niels Bohr (1885–1962), a Dutch physicist, introduced the idea of quantized states of motion for electrons, which became known as the Bohr model of the hydrogen atom. While we now consider this model incorrect, it provided an important step in the development of modern atomic theory.

The planetary model of the atom consists of a nucleus containing protons and neutrons, and the electrons spinning around the nucleus, much like planets orbiting the sun. The problem with this model lies with the electrostatics of the electrons in orbit around the nucleus. If the electrons in an atom followed an orbit around the nucleus, they would eventually spiral into the nucleus because they are attracted to the positive protons. 

Bohr altered the planetary model of the atom to limit electrons to specific energy states: they would not be able to spiral into the nucleus, based on their angular momentum. He determined electrons would remain in their orbits at specific radii, which he expressed in the following mathematical equation:

 r = \frac{nh}{2 \pi mv}

(r is the radius of the electron, h is Planck's constant, m is the mass of the electron, v is the orbital velocity of the electron, and n is an integer value. Note that you do not need to know the exact definition for Planck's constant for this course, for this level of chemistry. Just know that it is a constant.)

The value n is known as a quantum number. This quantum number defines where the electron exists, with respect to the nucleus. The larger the quantum number, the further away it is from the nucleus. In other words, the quantum number describes the specific distances where the electrons orbit the nucleus.

It is important to note that electrons can never exist between the n levels. In other words, the electron can be in the n = 1 orbit or the n = 2 orbit, but it can never be in between the two.

You can think about the orbits as energy levels. Energy levels that are further away from the nucleus are higher in energy. This result shows quantized energy states within the atom. Only specific, discrete energy states can exist.


2h. List the four quantum numbers and describe their significance

  • How does the modern atom model differ from the Bohr atom model?
  • List the four quantum numbers and describe what each quantum number tells us about the electron.

We can describe the electrons of an atom in terms of a set of four quantum numbers. These quantum numbers describe the energy and properties of each electron in the atom.

Modern quantum mechanics theory is based on the Schrodinger equation, in which a wave function for each electron describes all quantum mechanical information about that electron. Because electrons are quantum particles, we cannot define their exact location; rather, we can define a probability density region where we are likely to find them.

Bohr's electron orbits were not exactly correct because we cannot precisely define where an electron exists. In the modern model of the atom, we replace orbits with orbitals, or probability density regions where we are likely to find an electron within the atom. This level of uncertainty leads us to our concept of the electron cloud – the region around the nucleus where you are likely to find electrons.

We can describe each electron by a set of four quantum numbers.

The principal quantum number n describes the distance of the electron from the nucleus. As n increases, the distance from the nucleus increases, and the energy of the electron increases.

You can determine the potential energy of an electron based on its principal quantum number using an equation you can find under the heading "Physical Significance of N" in Section 2 of The Quantum Atom.

The principal quantum number shows the electron "shells" surrounding the nucleus where you are likely to find an electron. We denote the principal quantum number with integer values.

The angular momentum quantum number l describes the shape of the orbital that the electron is in. We denote the angular momentum quantum number with number and letter designations.

  • If l equals 0, we say it is an s orbital, and it is spherical.
  • If l equals 1, we say it is a p orbital, and it is dumbbell-shaped.
  • If l equals 2, we say it is a d orbital, and it is the shape of "double dumbbells".
  • For larger atoms, we also see l equals three orbitals, which are called f orbitals. 

The magnetic quantum number m denotes the orientation within space of the orbital containing the electron.

  • For s equals 0, the orbital is spherical. Therefore, it cannot be oriented in different directions in space. However, for the other l values, the orbitals can be oriented in different ways. 

The magnetic quantum number can assume 2l + 1 values from negative l (−l) to l.

  • For l equals 0 (s orbital), m equals 1.
  • For l equals 1 (p orbital), m can be −1, 0, or 1.
  • For l equals 2 (d orbital), m can be −2, −1, 0, 1, or 2. 

The final quantum number, called the spin quantum number s, is a result of the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of quantum numbers. Every orbital can contain two electrons. Therefore, two electrons can have the same n, l, and m quantum numbers. To distinguish the two electrons in a given orbital, we have s = +1 and s = −1 for the two electrons in a given orbital.


2i. Describe the structure and organization of the periodic table

  • Identify the periods and groups on the periodic table.
  • Identify the blocks on the periodic table.
  • Identify the families on the periodic table. 

The periodic table is one of the most important tools that chemists use. Its organization allows us to determine a great deal of information about the elements.

On the periodic table, the rows are called periods. The vertical columns are known as groups. Elements in a group share certain characteristic properties.

Chemists also define blocks on the periodic table, based on the outermost filled electron shell. Review "Section 3: The Aufbau Rules" from Electrons in Atoms.

The blocks are labeled in red in the periodic table:

Chemists have also named families in the periodic table for groups of elements that have similar properties. Many of these names have historical roots. The families labeled in the following chart include alkali metals, alkaline earths, transition metals, post-transition metals, noble gases, semimetals (metalloids), halogens, lanthanides, and actinides.


Unit 2 Vocabulary

  • Angular momentum quantum number
  • Atom
  • Atomic mass
  • Atomic nucleus
  • Atomic number (Z)
  • Atomic weight 
  • Avogadro's number
  • Bohr Model of the atom
  • Diffraction pattern 
  • Double Slit Experiment 
  • Electron
  • Electron cloud 
  • Interference pattern 
  • Ion
  • Isotope
  • Magnetic quantum number
  • Mass number (A)
  • Molar mass
  • Molar volume
  • Mole (mol)
  • Neutron
  • Orbital
  • Pauli exclusion principle
  • Periodic table
  • Periodic table (group, period, family) 
  • Photon
  • Planetary model 
  • Planck's constant 
  • Principal quantum number
  • Proton
  • Quantum number
  • Quantum particle
  • Schrodinger equation
  • Spin quantum number
  • Subatomic particle 
  • Systeme Internationale (SI) 
  • Wave-particle duality
  • Young's Double Slit Experiment

Unit 3: Bonding

3a. Define chemical bonds

  • Describe the nature of the chemical bond.

Chemical bonding is fundamental to the study of chemistry since chemical bonds describe how molecules and compounds are formed.

Chemical bonds describe an effect that occurs when one or more outer shell electrons are simultaneously attracted to two atomic nuclei. The forces holding a chemical bond together are electrostatic forces. A molecule is created when chemical bonds form. You can think about a molecule as an aggregate of atoms with distinct properties.


3b. Explain why most atoms form chemical bonds

  • Describe the energetics of bond formation.
  • Why is it often favorable to form a bond?

Most elements found on the periodic table readily form chemical bonds to create molecules.

Atoms often bond together chemically to form molecules. Since heat is released during this process, chemical bonding is an example of an exothermic reaction. The more exothermic the reaction, the more stable the product. Since the formation of chemical bonds creates a more stable product, there is a natural tendency toward bond formation. We describe the bonds as energetically favorable since energy is released.

In general, the more stable structure that results (molecules) also has lower potential energy than the original individual atoms. Remember their energy was released during the chemical bonding process.


3c. Describe ionic, covalent, and metallic bonding

  • Describe the ionic bond and the types of atoms that can form ionic bonds.
  • Describe the covalent bond and the types of atoms that can form covalent bonds.
  • Describe the metallic bond and the types of atoms that can form metallic bonds.

Chemical bonds can take three forms depending on the atoms involved: ionic, covalent, and metallic.

In an ionic bond, ions of opposite charge are attracted to each other via electrostatic forces: an electron is donated from the negative ions to the positive ion to form the bond.

Table salt, or sodium chloride (NaCl), is an example of a compound that has an ionic bond. In the case of NaCl, the chloride (Cl) ion donates its extra electron to the sodium ion (Na+) to form the bond. Ionic solids, such as NaCl are crystalline in form.

Image of an ionic bond: table salt, or sodium chloride (NaCl)

In a covalent bond, the electrons in the bond are shared. Covalent bonds generally form among nonmetal atoms: each atom in the bond usually contributes one electron to form the bonding electron pair.

Image of a covalent bond

We classify covalent bonds as nonpolar covalent bonds or polar covalent bonds. In a nonpolar covalent bond, the two atoms in the bond share the bonding electrons equally. In a polar covalent bond, the electrons are unevenly shared.

This means, there is a greater electron density near one of the atoms in the bond than the other. This is because one of the atoms has higher electronegativity than the other atom. Electronegativity is a measure of how much an atom pulls electrons toward itself in a covalent bond.

Metallic bonds form, not surprisingly, among metal atoms. Metal atoms have low electronegativities, and have empty, or near empty, outer electron shells. Consequently, metal atoms do not attract electrons, nor do they easily donate them.

A simple way to think about metal bonding is that positive metal ions are immersed in an electron fluid of free-flowing electrons. This leads to many properties of metals. For example, metals conduct electricity because the valence electrons are mobile throughout the material.

Image of atomic cores immersed in valence "electron fluid"


3d. Describe and give examples of Van der Waals forces as part of intermolecular forces

  • Describe how each type of Van der Waals force works and the types of molecules that can be affected by the type of Van der Waals force.

Intermolecular forces are the forces that hold molecules of the same type together in the condensed phase.

Van der Waals forces, also known as intermolecular forces, describe the forces that exist between molecules that hold molecules together in the liquid or solid state.

In dipole-dipole force interactions, molecules with permanent dipole moments interact. A molecule has a permanent dipole moment if it has an uneven distribution of negative charge within the overall neutrally charged molecule. We call molecules with a permanent dipole moment polar molecules. A polar molecule has a partially positive area and a partially negative area within the molecule.

Image of dipole-dipole force interactions

When two polar molecules come together, the partially positive area of one molecule lines up with the partially negative area of the other molecule. The weak electrostatic attraction among the molecules leads to dipole-dipole interactions.

Image of two polar molecules

In ion-induced dipole forces, an ion interacts with a nonpolar molecule. In this case, the electrostatic charge on the ion induces or forces the nonpolar molecule to momentarily develop a dipole. This is a weaker interaction because the nonpolar molecule does not have a permanent dipole, and is therefore not strongly attracted to the ion.

Image of ion-induced dipole forces

In ion-dipole forces, an ion interacts with a polar molecule. The polar molecule lines up, so the opposite partial charge is attracted to the ion. This is a stronger interaction than ion-induced dipole because the polar molecule has a permanent partially-positive and partially-negative charge.

Image of ion-dipole forces

In dipole-induced dipole interactions, a polar molecule interacts with a nonpolar molecule. The dipole in the polar molecule induces or causes a momentary dipole in the nonpolar molecule. The resulting interaction is weak because the nonpolar molecule only has a momentary and not a permanent dipole.

Image of dipole-induced dipole interactions

Finally, London forces describe the forces between two nonpolar molecules. A momentary dipole that randomly forms in one molecule induces an induced dipole in the other nonpolar molecule. This is a very weak intermolecular force.

Image of London Forces


3e. Explain VSEPR theory

  • Explain why chemists use VSEPR to describe the shapes of molecules.
  • What forces determine the shape of molecules?

First, review how to write electron configurations for atoms in Section 3: The Aufbau Rules, in Electrons in Atoms. This will help you understand how to draw a Lewis Dot structure to apply VSEPR theory.

Next, read Section 2: Lewis Dot Structures to understand how Lewis dot structures work and review how to use VSEPR theory.

Section 3: How to Draw Lewis Dot Structures, provides a step-by-step description of how to draw Lewis dot structures in The Shared-Electron Covalent Bond.

To write a Lewis dot structure, first write the symbols for the elements in a simple diagram to show how the elements will be connected.

For example, for ammonia, NH3, or hydroxylamine, you would write the following:

Image of Ammonia and Hydroxylamine

Then, using the Aufbau principle, draw electron dot structures for each of the elements. These drawings tell us how many valence shell electrons are in each atom, based on their group on the periodic table. The group number on the periodic table equals the number of valence electrons.

For example, hydrogen is in group 1A, so it has one valence electron. Nitrogen is in group 5A so it has five valence electrons, and oxygen is in group 6A so it has six valence electrons.

Image of Position of Valence Electrons

Finally, bring the atoms together in a way that places eight electrons around each atom wherever possible. Note that hydrogen is an exception to this rule and will only ever have two electrons.

Image of Position of Valence Electrons

After studying the basics of Lewis electron dot structures, we can begin to understand VSEPR Theory.

VSEPR Theory is an acronym for Valence Shell Electron Pair Repulsion Theory. It describes the three-dimensional shapes of molecules.

VSEPR Theory focuses on the valence electron pairs in the outermost electron shells of the atoms involved in bonding. These pairs are the electrons that can form chemical bonds.

We assume that electrons involved in bonding exist in between the two atoms being bonded. We also know that similar or "like" charges repel each other via electrostatic forces. Therefore, the lone pairs of electrons, or nonbonding valence electrons in the molecule are repelled by the bonding pair and by all of the other lone pairs of electrons in the molecule.

Because they are repelled, all of the valence electron pairs will adopt shapes that make them as far apart from each other as possible in a three-dimensional space. This description provides the basis of VSEPR Theory and predicts the shapes different molecules will take based on the number of bonding and nonbonding valence electron pairs.

Image that shows minimum repulsion between electron clouds


3f. Predict the shape of molecules or polyatomic ions using VSEPR theory

  • How can you use VSEPR to predict the shape of a given molecule or polyatomic ion?

Remember that we use VSEPR Theory to predict the shape molecules and polyatomic ions will take on based on their Lewis electron dot structure.

Again, it is important to have a strong foundation in Lewis electron dot structures, so be sure to review Sections 2 and Section 3, in The Shared-Electron Covalent Bond.

Molecules with the formula AX2 have two bonding electron pairs that are 180° apart to maximize the distance between them. We call them linear molecules.

Image of linear molecule showing 180 degree separationImage of a linear molecule

Molecules with the formula AX3 have three bonding electron pairs that are 120° apart to maximize the distance between them. We call them trigonal planar molecules.

Image of trigonal planar molecules showing 120 degree separation

The most common configuration we see in chemistry is the AX 4 molecule. These molecules have bonding electron pairs 109.5° apart in three-dimensional space. These molecules are called tetrahedral molecules.

Methane, CH4, is an example of a tetrahedral molecule.

Image of methane, a tetrahedral molecule, showing 109.5 degree bond angles

Sometimes, one or more of the valence electron pairs in a molecule are lone pairs of electrons. This alters the geometry of the molecule since the lone pairs take up a bit more space than bonding electrons do.

A molecule of the form AX3E is based in tetrahedral geometry, but has one lone pair of electrons (E). Ammonia, NH3, is an example of this type of molecule. Here, the molecule takes a trigonal pyramidal shape and the bonding angles are approximately 107°.

Image of ammonia, a trigonal pyramidal shape, showing 107 degree angle

Water, H2O, is an example of a molecule with AX> E2 geometry. In this molecule, there are two bonding pairs of valence electrons and two lone pairs. This molecule has a bent geometry with a bond angle around 104.5°.

Image of a molecule has a bent geometry, showing 104.5 degree angle

Occasionally, we see molecules with five or six valence electron pairs that adopt other, more complex geometric shapes.

To review how VSEPR theory describes different molecular geometries, see the descriptions in Molecular Geometry.


3g. Explain how the shapes of molecules are accounted for by hybridization theory

  • Explain why hybridization theory is needed.
  • Use a hybridization diagram to construct molecular orbitals for a tetrahedral compound.
  • Describe why hybridization theory gives us molecular shapes.

Hybridization theory accounts for molecular shapes that have been seen in experiments when combining atomic orbitals into molecular orbitals.

Hybridization theory presents the limitations of VSEPR theory. In VSEPR theory, we assumed the electrons were in their atomic orbitals. If this were the case, many molecules we know to exist should never form.

For example, beryllium hydride, BeH2, is a known compound, but beryllium (Be) has a set of paired electrons in its valence shell (the 2s atomic orbital). The paired electrons in the atomic orbitals are stable and should not combine with other atomic orbitals to form bonds.

However, we know beryllium hydride, BeH2, exists. The only way for this to happen is for an electron from the beryllium valence shell to move to the next energy level, 2p, so there are unpaired electrons. We know this does not happen because it would require too much energy. Therefore, a new model of bonding is needed to explain molecules such as BeH2 which cannot be explained by VSEPR.

In hybridization theory, the electrons from the atoms involved in the bond are hybridized or combined into new molecular orbitals which are combinations of the input atomic orbitals. This is a mathematical construct that gives us molecular orbitals that possess properties that are consistent with what we observe about molecules.

Hybrid orbitals are constructed by combining the wavefunctions, ψ, of the atomic orbitals involved in the bond. Because the wavefunction describes a wave, the wavefunctions interfere constructively and destructively, to create a new shape for the hybrid molecular orbital.

Images of wavefunctions

To use a hybrid orbital diagram, we first fill the electron configurations for the atomic orbitals.

Review how to write electron configurations for atoms in Section 3: The Aufbau Rules, in Electrons in Atoms.

Then, we combine the electrons from both atoms together to fill in the hybrid molecular orbitals created by the atomic orbitals. We always fill the molecular orbitals starting at the lowest energy level. For each energy level, we fill in one electron per molecular orbital at a time and then fill the second electrons per molecular orbital in the energy level before moving on to the next energy level.

In linear molecules, s and p atomic orbitals combine to form hybrid sp orbitals.

Image of the origin of an sp hybrid orbital

In our example of beryllium hydride, BeH2, we can use hybrid orbitals to explain why this molecule exists and has a linear shape. Two sp hybrid orbitals are formed in this molecule and overlap with the 1s orbitals of each hydrogen atom to form covalent bonds.

Image of beryllium hydride, and its two sp hybrid orbitals

We can use hybridization theory to explain larger molecules as well. Here we will look at a trigonal planar molecule, BF3. In this case, the atomic orbitals of B hybridize to become three sp2 hybrid orbitals. These sp2 hybrid orbitals have unpaired electrons that can combine with the unpaired electrons of fluorine to create covalent bonds.

Image of sp2 hybrid orbitals in BF3

When the sp2 hybrid orbitals are formed, they create trigonal planar geometry:

Image of the origin of sp2 hybrid orbitals, and trigonal planar molecular geometry

Finally, we will describe the most important geometry in chemistry, tetrahedral, and how hybridization theory predicts the molecular geometry. We will use methane, CH4, as our example.

Here, the electrons in carbon hybridize to form four sp3 hybrid orbitals. Each of the four sp3 hybrid orbitals contains an unpaired electron that can combine with a hydrogen electron to form a bond.

Image of sp3 hybrid orbitals

The sp3 orbitals form the expected tetrahedral molecular geometry.

Image of origin of sp3 hybrid orbitals, and tetrahedral molecular geometry


3h. Explain what determines molecular polarity

  • Define molecular polarity.
  • Define electronegativity.
  • Define dipole moment.
  • Determine if a molecule is polar or nonpolar.

Molecular polarity occurs in molecules where the electrons are not evenly distributed.

Electronegativity measures how well an atom attracts electrons toward itself in a bond.

An atom that is highly-electronegative attracts electrons toward itself more strongly. On the other hand, an atom that has low electronegativity and does not attract electrons toward itself.

When determining polarity, chemists examine the relative electronegativities of an atom in a bond. The location of each element in the periodic table indicates this trend.

Fluorine is the most electronegative atom. The elements that appear closest to fluorine in the periodic table (top right) are the most electronegative. Elements that are located far away from fluorine in the periodic table (bottom left) are the least electronegative and said to be electropositive.

Image of a graph that shows electronegativities of elements in the periodic table

A polar covalent bond occurs among atoms with different electronegativities. The electrons in the bond are more attracted to the more electronegative atom and therefore spend more time closer to that atom. So, in these bonds, the electrons are not evenly shared.

We say polar covalent bonds have a dipole moment, which is a vector that points from the less electronegative atom to the more electronegative atom.

A vector is a mathematical quantity that also has a direction associated with it. Because dipole moments are vectors, we can sum the vectors to determine if a molecule is polar. If the vectors do not cancel out, the molecule is polar because one area of the molecule has a higher electron density than the rest. If the vectors do cancel out, the molecule is nonpolar because the electron distribution in the molecule is even.

Review a mathematical treatment of dipole moments in Section 2: Molecular Dipole Moments in Polar Covalence.

In the figure below, we can see how dipole moments determine molecular polarity. The oxygen molecule, O2, is homonuclear, or made up of only one element type. Therefore, there cannot be a difference in electronegativity and it is a nonpolar molecule.

Carbon monoxide, CO, consists of two different types of atoms (carbon and oxygen). Oxygen is more electronegative and therefore the dipole moment goes from the carbon to the oxygen (Note that the figure from your text contains an error here). Because there is a dipole moment, carbon monoxide is a polar molecule.

Carbon dioxide, CO2, on the other hand, also contains carbon-oxygen bonds. However, the two dipole moments are 180 degrees opposite each other and cancel each other out. Consequently, CO2 is a nonpolar molecule that contains polar bonds.

Image of a homonuclear molecule, carbon monoxide, and carbon dioxide


3i. Draw resonance structures

  • Why are resonance structures necessary?
  • Draw resonance structures for a given molecule or polyatomic ion.

We create resonance structures for molecules in which some electrons are delocalized. In general, resonance structures describe a molecule or polyatomic ion in which we could write more than one equivalent Lewis electron dot structure.

First, review the rules for writing Lewis electron dot structures in Section 2: Lewis Dot Structures, and, Section 3: How to Draw a Lewis Dot Structure, in The Shared-Electron Covalent Bond.

Resonance structures are necessary when there are multiple equivalent Lewis electron dot structures that could be written for a given molecule or polyatomic ion. Generally, resonance structures involve double bonds.

Let's look at the example of the nitrate ion, NO3. In the nitrate ion Lewis electron dot structure, we make two single N−O bonds and one double N=O bond. When we draw this, it does not matter which nitrogen-oxygen bonds we make single or double. We say that all three possibilities are resonance structures and we denote these with double arrows between them:

Image of the Nitrate Ion, NO3

In reality, the true structure of the nitrate ion is a superposition, or a combination of all three of these resonance structures. Each bond is really about 1 ⅓ of a bond, or bond order.

Image of the Nitrate Ion as a superposition

We write resonance structures because we cannot accurately draw the true structure of compounds with resonance.

Review the section for more examples of molecules and polyatomic ions with resonance structures, Multiple Equivalent Structures: Resonance, in The Shared-Electron Covalent Bond.


Unit 3 Vocabulary

  • Bent geometry
  • Bond order
  • Chemical bond
  • Covalent bond
  • Dipole moment
  • Dipole-dipole force
  • Dipole-induced dipole force
  • Electron fluid
  • Electronegativity
  • Exothermic
  • Homonuclear
  • Hybrid (or molecular) orbital
  • Hybridization theory
  • Ion
  • Ion-dipole force
  • Ion-induced dipole force
  • Ionic bond
  • Lewis Dot structure
  • London force
  • Metallic bond
  • Molecular orbital
  • Molecular polarity
  • Molecule
  • Nonpolar molecule
  • Permanent dipole/polar molecule
  • Polar covalent bond
  • Polar molecule
  • Resonance structures
  • Sp hybrid orbital
  • Sp2 hybrid orbital
  • Sp3 hybrid orbital
  • Superposition
  • Tetrahedral molecules
  • Trigonal planar molecule
  • Valence
  • Valence electron pair
  • Valence shell electron
  • Van der Waals force
  • VSEPR theory
  • Wavefunction

Unit 4: Chemical Formulas and Equations

4a. List the rules for assigning most common electronic charge states (oxidation numbers) of compounds or elements

  • How do you assign oxidation numbers for a given element?

Oxidation numbers are used to assign the most common electronic charge for a given element. Here are the general rules:

  1. The sum of oxidation states in a molecule must equal the molecule's charge. The sum is zero for a neutral molecule.
  2. The atom that is more electronegative in a bond gets a negative oxidation state. The atom that is more electropositive gets a positive oxidation state.
  3. Certain elements always have the same oxidation state.

Review the table Determining Oxidation States, in Oxidation Numbers and Redox Reactions.


4b. Give oxidation numbers for each element in the formula of a compound

  • Determine oxidation states of all atoms in a compound.

Determining the oxidation number of elements in a formula gives us important information about the bonding and reactivity of the compound.

Here, we use the rules listed in the previous learning outcome to assign oxidation numbers for each atom in the compound. It is important to apply these rules systematically and be sure to note any exceptions to the rules that may apply.

For example, let's explore the nitrate ion NO3, which is in the text.

  • We know this compound is an ion with a −1 charge, so the overall oxidation numbers must add up to −1.
  • We know oxygen is more electronegative than nitrogen, so we know oxygen will have a negative oxidation number and nitrogen will have a positive one.
  • We know oxygen almost always has a −2 oxidation state (with a few exceptions).
  • Since this is not one of the exceptions, the oxidation state for each oxygen is −2.
  • Now we can determine the oxidation state of nitrogen.
  • There are three oxygen atoms, each with an oxidation state of −2.
  • So, the total oxidation state from the three oxygen atoms is −6.
  • To get the overall compound oxidation state to be −1, the oxidation state of nitrogen must be +5.

To review, see Oxidation Numbers and Redox Reactions.


4c. Explain the significance of a chemical formula

  • Given a chemical formula, determine the number of each type of atom in the compound.
  • Use the chemical formula to determine the molecular mass.
  • Use the chemical formula to determine the mole ratios of atoms in the compound.
  • Use the chemical formula to determine the percent composition of the compound.

The chemical formula specifies the types of atoms in a chemical compound and the number of each type of atom in the compound. The chemical formula defines the compound.

For example, let's look at ethanol, C2H6O, which is the type of alcohol found in alcoholic beverages. The formula tells us ethanol has two carbons, six hydrogens, and one oxygen.

When we know the chemical formula for a compound, we can determine its molecular mass and molar mass.

Molecular mass, or molecular weight, is the mass of the compound in atomic mass units (amu). This is also called formula mass or formula weight. We can use the chemical formula to determine molecular mass by adding up the atomic masses of all atoms in the compound.

The chemical formula for a compound also allows us to calculate the mole ratios of elements for the compound. The atomic ratios in a formula are also the mole ratios of the atoms in the formula.

For example, in methane, CH4, there are four hydrogen atoms for every carbon atom. There are also four moles of hydrogen for every one mole of carbon.

We can also use the chemical formula to determine the mass fraction or percent composition of the elements in a given compound.

Review the Examples in Chemical Formulas and their Arithmetic.


4d. Determine the formula of an ionic compound when given the name

  • Know the names and charges of the ions listed in the text.
  • Use the names and charges of the ions to determine the formula of an ionic compound when given the name.

Before you review ionic compound formulas, review Section 4: Naming the Chemical Ions in Naming Chemical Substances. It is essential to know the names and charges of the ions listed here to be able to name ionic compounds.

To determine the formula of an ionic compound from the name, you must have a strong command of the names and charges of single atom ions and polyatomic ions. It may help create flashcards of the ion symbols, with their charge and names, to learn them.

When given a chemical name for an ionic compound, the first name is the cation, or positive ion, and the second name is the anion, or negative ion.

First, write the formula of the cation, including charge, and then write the formula of the anion, including charge. For cations that can have different charges, the charge will be written as a Roman numeral in parentheses. Then, balance the charges. In other words, make sure the positive charge equals the negative charge in the compound. To do this, you may need to alter the number of each type of ion.

For example, let's look at the chemical copper (II) chloride. The cation is copper, and we are told it has a +2 charge by the (II). Therefore, the cation is Cu2+. The anion is chloride, which is Cl. Now, balance the charges. There is a +2 charge from the cation and a −1 charge from the anion. Therefore, we need two chloride ions to get a −2 charge. The formula for copper (II) chloride is CuCl2.

Review more examples in salts in Section 5: Names of Ion-Derived Compounds in Naming Chemical Substances.


4e. Name an ionic compound when given a formula

  • Know the names and charges of the ions listed in the text.
  • Given a formula of an ionic compound, write the name.

Before you review ionic compound formulas, review Section 4: Naming the Chemical Ions in Naming Chemical Substances. It is essential to know the names and charges of the ions listed here to be able to name ionic compounds.

Look at the formula to determine the name of an ionic compound. The first ion listed is the cation, or positive ion. The second ion listed is the anion, or negative ion. From the formula, write the name of the cation. Then, from the formula, write the name of the anion.

If the cation can have different charges, we must write the charge of the anion in the formula name. From the formula, determine the total negative charge from the anions. Then, determine the charge of the cation needed to balance out the total negative charge from the anions. Write the charge of the cation in Roman numerals in parentheses after the name of the cation.

For example, let's look at Fe2S3. The cation is iron, and the anion is sulfide. Iron can have different charges, so we will need to write the cation charge in the name. The sulfide ion has a −2 charge. However, there are 3 sulfide ions in this compound. Therefore, the total anion charge is −6. The cation charge must balance this with a total +6 charge. There are 2 iron ions in this compound, so each iron ion must have a charge of +3. The name for this compound is iron (III) sulfide.

Review more examples in salts in Section 5: Names of Ion-Derived Compounds in Naming Chemical Substances.


4f Name binary molecular compounds using prefixes

  • What are the prefixes for binary molecular compounds?
  • Given a formula, write the correct binary molecular compound name.
  • Given a name, write the correct binary molecular compound formula.

Many molecular compounds are binary, which means they consist of two types of atoms.

See the chart of numerical prefixes in Section 3: Naming the Binary Compounds in Naming Chemical Substances. Consider making flashcards to help you memorize the numerical prefixes and their numerical values.

To write the name of a binary molecular compound from the formula, you need to know the names of the atoms involved. Write the names of the elements in the order they appear in the formula. The second element should end in -ide rather than the element name. Sometimes these are polyatomic ions rather than elements. Then, add the numerical prefixes from the chart to the names of the elements.

For example, we can name P4S3. The first element is phosphorus and the second element is sulfur. We change the second element to sulfide. Now, we add the numerical prefixes. There are four phosphorus atoms, so it is tetraphosphorus. There are three sulfur atoms, so it is trisulfide. The name of the molecule is tetraphosphorus trisulfide.

Given the name of a binary compound, we can determine the formula. Consider dinitrogen tetroxide. Here, we use the prefixes and element names to determine the chemical formula. The first element is nitrogen, and from the di- prefix, we know there are two nitrogens. The second element is oxygen, and from the tetra- prefix, we know there are four oxygens. Therefore, the formula is N2O4.

Review more examples in Section 3: Naming the Binary Molecules in Naming Chemical Substances.


4g. Balance a chemical equation

  • Identify reactants and products in a chemical reaction.
  • Explain why chemical reactions must be balanced.
  • Balance a given unbalanced chemical equation.

Chemical equations express the net change of composition that occur during a chemical change. Understanding how chemists write chemical reactions is an important part of the language of chemistry.

In a chemical reaction, reactants are transformed into products. It is a convention in chemistry to write the reactants on the left side of the equation and the products on the right.

We write an arrow going from reactants to products to signify the chemical change:

Reactants → Products

We need to balance a chemical equation to comply with the Law of Conservation of Mass, which states that matter (mass) in a chemical reaction must be conserved. This means you cannot make or lose mass during a chemical reaction. Balancing a chemical equation ensures the amount of reactants equals the amount of products. You need to ensure an equal number of each type of atom appears on both sides of the equation (reactant and product).

Review balancing a chemical equation in Problem Examples 1 and 2 in Chemical Equations and Calculations.

Let's examine the reaction in Problem Example 1: the combustion of propane, C3H8. The unbalanced chemical equation for this reaction is:

C3H8+ O2 → H2O + CO2

To begin, you should tally up the number of each type of atom on each side of the equation.

  • Reactant side: three carbons (C), eight hydrogens (H), two oxygens (O);
  • Product side: one carbon (C), two hydrogens (H), and three oxygens (O).

Then, add whole number coefficients to the molecules to ensure the number of each type of atom on each side of the equation is equal. Note that you can only alter the number of molecules – you cannot change the formulas of the molecules by changing the number of individual atoms in the molecule.

Let's start by balancing carbon. To balance carbon, put a coefficient of three in front of CO2 in the products. Then re-tally the atom count.

C3H8+ O2 → H2O + 3CO2

Reactants: 3 C, 8 H, 2 O; Products, 3 C, 2 H, 7 O

*Note that since CO2 has two oxygen atoms, the three CO2 molecules have six oxygen atoms. There is also an oxygen in the water in the products.

Next, repeat the process of balancing a different atom and calculating a new atom tally. Continue until the number of each type of atom on the reactant side is the same as the product side.

Secondly, let's balance hydrogen. Since eight hydrogen atoms are on the reactant side and two are on the product side, you should put a coefficient of four in front of the water to make eight hydrogens on the product side.

C3H8+ O2 → 4H2O + 3CO2

Reactants: 3 C, 8 H, 2 O; Product: 3 C, 8 H, 10 O

Finally, let's balance oxygen. Since two oxygen atoms are on the reactant side and 10 are on the product side, you should put a coefficient of five in front of the oxygen on the reactant side to balance.

C3H8+ 5O2 → 4H2O + 3CO2

Reactants: 3 C, 8 H, 10 O; Products: 3 C, 8 H, 10 O

The equation is balanced.


Unit 4 Vocabulary

  • Balancing a chemical equation
  • Binary molecular compound
  • Chemical equation
  • Chemical formula
  • Formula mass/formula weight
  • Law of Conservation of Mass
  • Molar mass
  • Molecular mass/molecular weight
  • Oxidation number
  • Polyatomic ion
  • Product
  • Reactant

Unit 5: States of Matter

5a. Use kinetic-molecular theory to explain the relationships among gas volume, temperature, number of moles, and pressure

  • Describe the kinetic molecular theory of gases.
  • Define the pressure of a gas.
  • Explain how the Kinetic Molecular Theory of Gases gives relationships among volume, temperature, number of moles of gas, and pressure.

Chemists use the Kinetic Molecular Theory of Gases to explain the behavior of gases on a macroscopic (visible to the naked eye) scale. The Kinetic Molecular Theory of Gases describes how gases behave and can allow us to predict certain properties of gases. Review the basic rules in Section 1: The Basic Idea of Kinetic Molecular Theory in Gas Molecules in Motion.

Here are the five parts of the Kinetic Molecular Theory of Gases:

  1. Gas particles are in constant motion and separated from each other by large distances. Therefore, the volume of the gas molecules in a sample is extremely small compared to the overall volume of the gas. Most of the volume of a gas is empty space.
  2. Molecules of an ideal gas do not interact with each other or the walls of the container.
  3. Molecules of a gas are in constant random motion. This random motion is in straight lines.
  4. All collisions among gas molecules are elastic collisions. This means that there is no energy loss when gas molecules collide.
  5. The temperature of a gas is directly proportional to its average kinetic energy, or energy of motion.

Particles in a gas phase are in constant motion and fill the entire container they inhabit. The gas particles are constantly hitting the surface of the container they are in, and exert force on the container surface. We define the pressure of the gas as the amount of force the gas exerts on the container they inhabit per unit area.

Image of gas molecules in a container

The Kinetic Molecular Theory of Gases explains the basic properties of gases. Review Section 2: How Kinetic Molecular Theory Explains Gas Laws in Gas Molecules in Motion.

According to the Kinetic Molecular Theory of Gases, gas must have pressure because it is constantly in motion in its container. When gas particles hit the wall of the container, they exert a force. Force divided by area is defined as pressure.

We can express the kinetic energy, the energy of motion, mathematically as:


( \mathrm{ke} represents kinetic energy,  m represents mass,  v represents velocity).

Keep in mind that temperature corresponds directly with average kinetic energy. As temperature rises, the velocity (speed) of the gas particles, as per the equation above, also increases.

The pressure of a gas also corresponds directly with its kinetic energy. As kinetic energy rises, the force with which the gas particles hit the wall of the container increases. Consequently, the pressure also increases.

As we increase the number of moles of gas in a container at constant pressure, more gas particles will hit the walls of the container in a given amount of time. If the pressure is constant, this will force the volume of the container to increase.


5b. Perform dimensional analysis conversions for gas law calculations

  • Use the gas constant with proper units to complete gas law equation calculations.
  • Convert units given in a question to units consistent with the units of the gas constant.

Many gas laws describe the behavior of gases under specific sets of conditions. These mathematical relations allow us to perform calculations – to calculate properties, such as pressure, temperature, volume, and number of moles of a gas under given conditions.

We express the gas constant mathematically as:

R = 0.082 L atm/mol K

Keep in mind that for gas law calculations:

  • Measurements of volume must be in L (liters);
  • Measurements of pressure must be in atm (atmospheres);
  • Measurements of substance must be in moles; and
  • Measurements of temperature must be in K (the Kelvin temperature scale).

Review the Ideal Gas Law in Section 4: The Ideal Gas Equation of State in The Basic Gas Laws. See Problem Example 3 for an example of how to use the Ideal Gas Law.


5c. State the ideal gas law

The ideal gas law shows the relationship among pressure, temperature, volume, and number of moles of a gas in ideal conditions. We express the ideal gas law mathematically as:

PV = nRT

(P represents pressure in atm, or atmospheres; V represents volume in L, or liters; n represents the number of moles; R represents the gas constant, or 0.082 L atm/mol K; and T represents temperature, which is K or the Kelvin scale.)

Review the Ideal Gas Law in Section 4: The Ideal Gas Equation of State in The Basic Gas Laws. See Problem Example 3 for an example of how to use the Ideal Gas Law.


5d. Describe the motion of particles in liquids and the properties of liquids

  • Describe the properties of a liquid.
  • How do particles in a liquid move?

Liquids exist between a substance's melting and boiling point.

Liquids are mobile, or exhibit mobility, which means their molecules can move around and change shape according to the container they inhabit. Viscosity describes another property of liquids, which means their resistance to flow. A liquid with high viscosity flows slowly (think of maple syrup or molasses), while a liquid with low viscosity flows easily (such as water). Viscosity relates to the strength of the intermolecular forces within the liquid.

Liquids also exhibit surface tension, which results from the strength and types of intermolecular forces within the liquid. As its name suggests, surface tension occurs on the surface of the liquid.

Within the bulk of a liquid, a liquid particle interacts with all of its surrounding particles. However, a liquid particle on the surface can only interact with the particles next to and below it. In general, intermolecular forces work to minimize the amount of surface area of liquids, so the intermolecular forces are maximized. Consequently, liquids form drops.

Image of liquid molecules and surface tension

Review the properties of liquids in Section 1: What is a Liquid? in Liquids and their Interfaces.


5e. Discuss the process by which liquids can change into a solid or a gas

  • Define vapor pressure.
  • How does vapor pressure lead to phase change for liquids?
  • Define nucleation.
  • How does nucleation lead to phase change for liquids?

Phase changes occur when a substance changes between different states – solid, liquid, or gas. All substances have a property known as free energy, which describes the tendency of a substance's thermal energy to escape and disperse.

Image of escaping tendency

Equilibrium vapor pressure, or vapor pressure, measure the tendency of surface liquid molecules to escape into the gas phase.

Equilibrium vapor pressure

In the figure above, when the container of water is open, no pressure from water molecules that have gone into the gas phase exists (as they escape into the rest of the room).

We can express this statement mathematically as Pw = 0 (i.e., the pressure of water equals zero).

When the container is closed, the pressure of the water molecules in the gas phase directly above the liquid increases (since they can no longer escape the container). Some water molecules escape to the gas phase, and some go back into the liquid phase. This builds until an equilibrium is reached among particles going into the gas phase and particles going back into the liquid phase.

When the equilibrium is reached, the system is at its equilibrium vapor pressure. For a liquid to boil, the vapor pressure must equal the external pressure.

During freezing, liquids turn into solid: the vapor pressure of the liquid equals the vapor pressure of the solid. The liquid changes phase into a solid.


5f. Define the characteristics of bonding in ionic compounds

  • What types of elements are generally involved in making ionic compounds?
  • How does ionic bonding differ from covalent bonding?
  • What do ionic compounds look like? What are their properties?

Ionic solids form a lattice of oppositely-charged ions held together by Coulombic charges. Ionic compounds are composed of positively and negatively charged ions held together by Coulombic charges. In other words, opposite charges are attracted to each other and the ionic solids form crystal lattices with a regular, repeating structure. This is different from covalently bonded compounds which are held together by covalent bonds.

This figure displays the crystal lattice of sodium chloride (table salt):

The crystal lattice of sodium chloride (table salt)

Ionic compounds are hard. Hardness measures how resistant a substance is to being deformed. Ionic compounds are also brittle. Brittleness means that one layer of the crystal lattice can "slip" over another when it is hit with a physical stress, which can cause the substance to break.

How one layer of the crystal lattice can break

For more details and examples of ionic solid structure, review Section 1: Introducing Ionic Solids in Ionic and Ion-derived Solids.


5g. Interpret phase diagrams

  • Identify the parts of a phase diagram, including the critical point and triple point.
  • For a given temperature and pressure, determine the state of matter on a phase diagram.

A phase diagram details the phase a substance will be in at any temperature and pressure.

A phase diagram

This figure details a general phase diagram for a given substance.

  • The horizontal axis shows the temperature, and the vertical axis shows the pressure.
  • The lines or curves are phase boundaries or conditions where the substance exists in equilibrium between two phases.
  • The area on the left (colored in yellow) shows the set of temperature and pressure conditions where a solid exists.
  • The area in the top middle (in green) shows the set of temperature and pressure conditions where a liquid exists.
  • The area in the bottom to the right (in blue) shows the set of temperature and pressure conditions where a gas exists.
  • The triple point displays the point where all three states of matter (solid, liquid, and gas) are in equilibrium.
  • The critical point displays the point where you can no longer have a liquid or a gas. Rather, after the critical point, a form of matter called a supercritical fluid is formed. Supercritical fluids have a unique set of properties that are similar to both liquids and gases. Supercritical fluids flow through solids like gases and can dissolve substances like liquids.

A phase diagram of water

This graph shows the phase diagram of water. Look at the four numbered points to determine the phase or phases of matter present at those conditions.

  • At the pressure and temperature point labeled 1, the water is a solid, since the point is in the solid region of the diagram.
  • At point 2, the water is at a phase boundary (the liquid-solid phase boundary). This means the water is in equilibrium between its solid and liquid state.
  • At point 3, the water is in the gas or vapor state.
  • At point 4, the water is above the critical point, which means it is in the state of supercritical fluid.

Review more examples of phase diagrams in Section 3: Phase Maps in Phases, Changes of State.


5f. Describe and explain the processes of boiling, evaporation, freezing, melting, and sublimation

There are five common types of phase changes.

  1. Boiling describes the change from liquid to the gas phase. Boiling occurs when the vapor pressure of the liquid equals the vapor pressure of the external environment. At this point, surface liquid molecules can escape into the gas phase.
  2. Evaporation occurs when the liquid container is open and the vapor pressure of the liquid is sufficient for surface molecules to escape into the gas phase.
  3. Freezing occurs when the liquid particles do not have sufficient energy to remain in the mobile liquid phase. Freezing occurs when the vapor pressure of the liquid equals that of the solid.
  4. Melting occurs when the solid molecules gain sufficient energy to escape into the liquid phase.
  5. Sublimation occurs when the solid and gas phases are in equilibrium.


Unit 5 Vocabulary

  • Atmosphere
  • Boiling
  • Brittleness
  • Coulombic charge
  • Constant pressure
  • Critical point
  • Crystal lattice
  • Elastic collision
  • Equilibrium vapor pressure/vapor pressure
  • Evaporation
  • Free energy
  • Freezing
  • Gas constant
  • Hardness
  • Ideal gas
  • Ideal gas equation
  • Ideal gas law
  • Intermolecular forces
  • Ionic compound
  • Kelvin
  • Kinetic energy
  • The Kinetic Molecular Theory of Gases
  • Melting
  • Mobility
  • Nucleation
  • Phase boundaries
  • Phase change
  • Phase diagram
  • Pressure
  • Sublimation
  • Supercritical fluid
  • Surface tension
  • Triple point
  • Vapor pressure
  • Viscosity

Unit 6: Thermochemistry and Thermodynamics

6a Define temperature

While we talk about temperature nearly every day, it has a specific definition central to thermodynamics. To understand temperature, first we need to define different types of energy.

Kinetic energy is the energy of motion, related to an object's mass and velocity, or speed.

Potential energy is the energy an object has based on its location. If an object is in a location where it is subject to a restoring force, such as gravity, it has potential energy. Gravity is an example of a restoring force. Because energy is conserved, potential energy can be converted into other types of energy.

A bike rider on a hill: kinetic energy, energy in, potential energy, and energy out

Chemical energy is the energy stored between the chemical bonds of molecules. As we have discussed above, chemical energy relates to the potential electrostatic energy forces that exist between electrons and the atomic nuclei.

Thermal energy is a microscopic version of kinetic energy. When an event involving energy transfer occurs (for example, a chemical reaction, a ball being dropped from a high surface), some of the energy is dispersed into the surrounding atoms or molecules in a random manner. This is thermal energy. Temperature is the measure of thermal energy.


6b. Define heat and state its units

In thermodynamics, we use precise definitions for many words we use in our common language. It is important to know these definitions and use these words properly when describing thermodynamics.

In thermodynamics, we define heat as the process where an object acquires or loses energy because it has a different temperature than its surroundings. It is important to note that thermal energy can only flow from high temperature to low temperature.

Heat has the same units as other energies. The most common unit used in chemistry is the joule (J). We also use the energy unit calorie (cal). Note that one cal = 4.184 J.

Review a listing of different energy units in the table in Section 2: Energy Scales and Units in Chemical Energetics.


6c. Define and perform enthalpy change, enthalpy of reaction, enthalpy of combustion, and enthalpy of formation calculations

  • Define enthalpy.
  • Calculate the enthalpy change for a given system.
  • Determine the enthalpy of reaction for a given reaction.
  • Determine the enthalpy of combustion for a given system.
  • Calculate enthalpy using standard enthalpy of formation.

Before we can define enthalpy, you need to understand how to describe a thermodynamics problem. When discussing thermodynamics, we think of the system and the surrounding.

The system describes what we are interested in. The surroundings describe everything around the system that the system can interact with. A system is closed when a boundary prevents the matter in the system from entering the surroundings. In an open system, matter can flow from the system to the surroundings.

A system and its surroundings

We define enthalpy (ΔH) as the heat change in a system at constant pressure (note that Δ is the Greek symbol delta which means "change", so you can read ΔH as a change in heat).

We can express enthalpy mathematically as:

ΔH ≡ qP = ΔU + PΔV.

You must use this equation to calculate ΔH for a given system. Note that to calculate ΔH you will probably be given ΔU, P (pressure), and change of volume in the system.

Review Equation (4-3) under the heading Enthalpy Hides Work and Saves it Too in The First Law of Thermodynamics.

For this equation:

Make sure your units match so your final answer is in the same energy units. You may need to employ a unit conversion factor to convert the work term to an energy unit.

Review how to calculate enthalpy and use a unit conversion factor to ensure proper units in Problem Example 3 in The First Law of Thermodynamics.

Just as Problem Example 3 demonstrates how to calculate enthalpy for a simple system, we can also calculate enthalpy for a chemical reaction. We can write the thermochemical equation that describes the process, including the substances and their states.

For example, the thermochemical equation for boiling water at its normal boiling point is:

H2O (l, 373 K, 1 atm) → H2O (g, 373 K, 1 atm) ΔH = 40.7 kJ mol−1

Here, ΔH is known as the enthalpy of vaporization of water. It describes the change in heat at constant pressure for the vaporization process.

To determine the enthalpy of a reaction, we use the following equation:

ΔH = Hproducts − Hreactants

Review Section 2: Standard Enthalpy of Formation in The First Law of Thermodynamics.

Here, Hproducts represents the enthalpy of products. Hreactants represents the enthalpy of the reactants. The question remains, how do we know Hproducts and Hreactants?

We use the standard enthalpies of formation for each of the reactants and products. The standard enthalpy of formation for a compound is the heat associated with the formation of one mole of the compound from its elements in their standard states.

For example, the following equation describes the standard enthalpy of formation of water:

H2(g) + ½ O2(g)→ H2O(l) ΔH = −286 kJ

You can find tables of standard enthalpies of formation in chemistry texts and online.

Consequently, we can write the equation for enthalpy of reaction as:

ΔH°reaction = Σ ΔHf °products Σ ΔHf °reactants

Review Equation (2-1) in Thermochemistry and Calorimetry.

To calculate the enthalpy of reaction, add the sum of the standard enthalpies of formation of the products, and subtract the sum of the standard enthalpies of the reactants.

By definition, combustion is the burning of a substance in oxygen. Hence, the enthalpy of combustion is the enthalpy change associated with burning a substance in oxygen.

Combustion is a highly exothermic (or heat releasing) process so these are easily measurable quantities. The enthalpy of combustion for many compounds is readily available in texts and online, just like the enthalpies of formation. Consequently, we can use enthalpy of combustion in the same way we use enthalpy of formation to calculate the enthalpy of a reaction.


6d. Define entropy

  • What are spontaneous processes?

Processes that proceed in a definite direction without needing a "push" are called spontaneous processes. The direction of a spontaneous process is determined by the degree of change in the disorder around the system, not by changes in heat.

Changes that increase disorder are spontaneous; changes that decrease disorder are non-spontaneous. In a chemical process, a system can occupy many different levels or states of energy. A spontaneous process increases the number of states the system occupies and consequently increases the disorder of the system.

For example, let's look at heat flow. We stated above that heat flows from hot to cold. The hot state has more energy, and occupies more energy levels, than the cold system. When heat flows from hot to cold, as in this figure, energy is distributed, which increases the disorder within the cold system.

Heat flow: hot, cold and combined

Based on this concept, entropy (S), measures how much thermal energy spreads in a chemical or physical change. Spreading energy can be based on the available space, such as a gas that expands, or on the energy states available, such as in the above heat flow example.


6e. Describe the driving force of a chemical reaction and relate it to Gibbs free energy

  • Define Gibbs Free Energy.
  • Use Gibbs Free Energy to explain the driving force of a chemical reaction.

We can express Gibbs Free Energy (ΔG) mathematically as ΔG = ΔH − T ΔS

(ΔH represents the enthalpy change of the reaction, T represents temperature, and ΔS represents the change in entropy of the system.)

Review Equation (4-2) in Free Energy: The Gibbs Function (Gibbs Energy).

Gibbs Free Energy combines important information from enthalpy and entropy to determine the extent and direction of a chemical change. The sign of ΔG determines the direction of spontaneity of a chemical reaction.

Review this chart:

ΔG < 0

Spontaneous to the right (products)

ΔG > 0

Spontaneous to the left (reactants)

ΔG = 0

System at equilibrium

Review details on the interplay between the enthalpy and entropy terms in the Gibbs Free Energy equation in cases one to four in Section 2: Gibbs Energy and Chemical Change, in Free Energy: The Gibbs Function (Gibbs Energy).


6f. define Hess' law and state its functions

State functions are mathematical functions that always give the same result, regardless of the steps taken to get there. Many thermodynamic functions are state functions, including enthalpy.

Imagine you want to take an elevator from the second to fifth floor. The elevator could take you directly to the fifth floor, or take you down to the first floor and up to five. The net change remains the same: you went from the second to the fifth floor, regardless of the path you took to get there.

Hess' Law states that the enthalpy of a chemical reaction is constant, regardless of the path taken. In other words, the net enthalpy of a reaction will always be the same regardless of how many steps it took for the net reaction to occur.

Hess' Law is extremely useful because it allows us to calculate the enthalpy for almost any reaction based on known quantities. Since we have calculated the standard enthalpies of formation for most compounds used in chemical reactions, we can determine the enthalpy of reaction.

Review a description Hess' Law from the beginning of Section 3: Hess' Law and Thermochemical Calculations in Thermochemistry and Calorimetry.


6g: use Hess' law to solve thermodynamic problems.

To use Hess' law, you must find enthalpy of formation and/or combustion reactions that can be added up to create the chemical reaction you are interested in.

  • If you flip the enthalpy of formation/combustion reaction, you must flip the sign of ΔHf.
  • If you multiply a reaction by a coefficient to get the right number of reactants and products, you must multiply ΔHf by the same coefficient.
  • After you find the set of enthalpy of formation/combustion reactions that add up to the reaction you want and you alter the ΔHf terms appropriately, you simply add the ΔHf terms up to get ΔHreaction.

Review how to use Hess' law in Problem Example 1 in Thermochemistry and Calorimetry. Review additional examples of using Hess' law in Hess' Law of Constant Heat Summation: Using Two Equations and their Enthalpies.


Unit 6 Vocabulary

  • Calorie (cal)
  • Chemical energy
  • Closed system
  • Combustion
  • Constant pressure
  • Enthalpy
  • Enthalpy of combustion
  • Enthalpy of formation
  • Enthalpy of reaction
  • Enthalpy of vaporization
  • Entropy
  • Entropy S
  • Exothermic
  • Gibbs Free Energy
  • Gravity
  • Heat
  • Hess' Law
  • Internal energy
  • Joule (J)
  • Kinetic energy
  • Nonspontaneous process
  • Open system
  • Potential energy
  • Restoring force
  • Spontaneous process
  • Standard enthalpy of formation
  • State function
  • Surroundings
  • System
  • Temperature
  • Thermal energy
  • Thermochemical equation
  • Thermodynamics

Unit 7: Acid-Base and Oxidation-Reduction Reactions

7a. Use the Arrhenius and Brønsted-Lowry definitions to identify acids and bases

  • Define Arrhenius acids and bases
  • Use the Arrhenius definition to identify acids and bases
  • Define Bronsted-Lowry acids and bases
  • Use the Bronsted-Lowry definition to identify acids and bases

There is more than one definition of acids and bases that can be useful in different situations. An Arrhenius acid is a substance with at least one hydrogen that can dissociate or ionize when dissolved in water. This produces a hydrated hydrogen ion and a counter ion. An Arrhenius base is a substance that has at least one hydroxide (OH) group that can dissociate or ionize when dissolved in water. Examples of Arrhenius acids include hydrochloric acid, HCl, sulfuric acid, H2SO4, and acetic acid (vinegar), CH3COOH.

Review the table in Section 2: Acids and the Hydrogen Ion in Acids and Bases: An Introduction for the dissociation reactions of these Arrhenius acids in water. You will clearly see the dissociated hydrogen ion in the products. Examples of Arrhenius bases include sodium hydroxide (also known as lye), NaOH, and ammonia, NH3.

To review the dissociation reactions of these bases see Equations (3-1) and (3-3) in Section 3: What is a Base? in Acids and Bases: An Introduction. You will clearly see the dissociated hydroxide ion in the products.

The Bronsted-Lowry definition of acids and bases is more general than the Arrhenius definition.

  • A Bronsted-Lowry acid is a proton (hydrogen ion) donator.
  • A Bronsted-Lowry base is a proton (hydrogen ion) acceptor. This definition is important because it shows that acids and bases must exist together. An acid cannot donate a proton without a base to accept it. Consequently, acids and bases always exist in pairs.

In cases of an acid, such as HCl in water, the HCl acts as the acid and the water acts as the base.

HCl(aq) + H2O → Cl(aq) + H3O+(aq)

Here, HCl is the acid because it gives a proton to the water, and becomes a Cl ion in the products. The water is the base because it accepts the proton and becomes H3O+, which is called the hydronium ion.

In cases such as NH3 in water, the NH3 acts as the base and the water acts as the acid.

NH3(aq) + H2O → NH4+(aq) + OH(aq)

Here, NH3 is the base because it accepts a proton from the water to become NH4+ in the products. The water is the acid because it donates a proton to the ammonia and becomes the hydroxide ion, OH.


7b. Write and balance equations for neutralization reactions

Neutralization reactions are the simplest type of acid base reaction. In this type of reaction, an acid and a base react with each other to form water and a salt. An acid and base will react to form water and a salt. A salt is an ionic compound, containing the cation of the base and the anion of the acid. To write a neutralization reaction, begin by writing the molecular reaction. For an example, let's write the neutralization reaction of HCl and NaOH.

We put the acid and base on the reactant side, with their states of matter.

HCl(aq) + NaOH(aq) →

We know that HCl is the acid because it has a proton that can dissociate. We know NaOH is the base because it has the OH that can dissociate. Therefore, we know the H+ from the HCl will dissociate and the OH from the NaOH will dissociate. When H+ and OH come together, they form water. The leftover parts are the Cl from the acid and the Na+ from the base. These come together to form NaCl.

HCl(aq) + NaOH(aq) → NaCl(aq) + H2O

Now, we can convert our reaction to what we call a net ionic equation. In a net ionic equation we eliminate ions that appear on both sides of the equation, so we only see the net change in the reaction. Here, all aqueous (aq) substances are known to dissociate into their ions in solution. Note that "aqueous substances" are substances that are dissolved in water.

First, we write a total ionic equation which includes each individual ion in the equation:

H+(aq) + Cl(aq)+ Na+(aq)+ OH(aq)→ Na+(aq)+ Cl(aq)+ H2O

We can see that Cl and Na+ appear on both sides of the equation. Just like in math, that means we can cancel them. This gets us to our net ionic equation for this reaction:

H+(aq) + OH(aq) → H2O

Review a step-by-step example of how to balance an acid-base neutralization reaction in Section 4: Neutralization: The Simplest Acid-Base Reaction in Acids and Bases: An Introduction.


7c. Explain the process of self-ionization of water molecules

  • Write an equation for the self-ionization or autoprotolysis of water.
  • How is water both an acid and a base?

Water is a unique molecule in many ways. One of its important properties that we saw above is that it can behave as either an acid or a base. In the reaction of HCl with water, we saw that water acted as a base, accepting the proton from HCl to form the hydronium ion.

HCl(aq) + H2O → Cl(aq) + H3O+(aq)

In the reaction of ammonia with water, we saw that water acted as an acid, donating a proton to the ammonia to form the hydroxide ion.

NH3(aq) + H2O → NH4+(aq) + OH(aq)

Notice that, since water can be both an acid and a base, water can react with itself in an acid-base reaction to form hydronium ion and hydroxide ion.

This is called the self-ionization of water or the self-protolysis of water:

H2O + H2O → H3O+(aq) + OH(aq)

In the self-ionization of water, one water molecule in the reactants serves as an acid, or proton donor. The other water molecule acts as a base, or proton acceptor. Note that the proton from the water always has become the hydronium ion rather than the H+ ion in solution.

Review a detailed description of this important ion in Section 2: The Hydronium Ion in Proton Donors and Acceptors: Acid-base Reactions à la Brønsted.


7d. Conduct pH calculations and use pH scale to classify solutions as acidic, basic, or neutral

  • Write the ion product of water.
  • Describe acidic, basic, and neutral solutions based on the [H3O+] and [OH].
  • Determine the concentration of [H3O+] or [OH] for a given solution.
  • Calculate pH for a given solution.
  • Use pH to classify a solution as acidic, neutral, or basic.

The pH scale gives us information about how acidic or basic a solution is. Water self-ionizes or dissociates into the hydronium ion and hydroxide ion. This only occurs to a small extent. The majority of water stays as water, but a small percent does dissociate.

We can write this as the ion product of water, Kw: [H+][OH] = 1.00 x 10−14, where the amounts in the square brackets are concentrations of the ions.

We can use the ion product of water to determine if a solution is acidic, neutral, or basic:


[H+] > [OH]


[H+] = [OH]


[H+] < [OH]

If we know the concentration of acid or base in a solution, we can determine the concentration of the H+ and OH ions by using the Kw expression.

Review the example involving HCl at the end of, Section 1: The Dissociation of Water in pH and Titration.

Using Kw, we can derive the equation for pH: the common scale used to determine if a solution is acidic, neutral, or basic.

There are two important equations from pH that you should know (see Equations 2-1a and 2-1b in pH and Titration.):

pH = −log [H+] and [H+] = 10−pH

If we know the [H+], we can easily determine pH. If we know the pH, we can easily determine [H+].

Another important scale is the pOH scale. This is analogous to the pH scale, except with hydroxide ions:

pOH = −log [OH] and [OH] = 10−pOH

Importantly, based on the relationship between [H+] and [OH], we know:

pH + pOH = 14

Therefore, just by knowing one piece of information (pH, pOH, [H+] or [OH]), we can determine all other values.

Review an example of using pH and pOH to determine ion concentrations in Problem Example 2 in pH and Titration.

Finally, you must be able to determine if a solution is acidic, neutral, or basic from its pH value:


pH < 7


pH = 7


pH > 7


7e. Explain the process of titration

Titrations are practical experiments to determine the concentration of an unknown sample of an acid or base. Titrations are experiments we conduct to determine the concentration of an acid or base by reacting it with a known concentration of acid or base until it is neutralized. By determining the number of moles of acid or base required to neutralize the unknown sample, you can determine the number of moles and concentration in the unknown sample.

We will use an example to explain how a titration experiment works. Assume we want to determine the concentration of an unknown solution of HCl. Begin with a known volume of your HCl solution. Then, you will titrate the HCl solution with a solution of NaOH of known concentration. You slowly add NaOH solution to the HCl until the neutralization reaction has completed.

By knowing the volume of NaOH you added, you can determine the number of moles of NaOH added. Then, based on the mole ratio of the neutralization reaction, you can determine the number of moles and therefore the molarity, or concentration, of the HCl solution. The point at which the neutralization reaction has completed is called the equivalence point. Generally, the equivalence point is found using color-changing indicator solutions, which change color when the equivalence point is reached.

Review a worked example of a titration problem in Problem Example 3 in pH and Titration.

We can interpret a titration using a titration curve. The titration curve shows the pH of the solution as moles of the titrant, or solution of known concentration, are added. When the curve rises vertically, you have reached the equivalence point of the titration.

A titration curve


7f. Explain the relationship between conjugate acids and bases

  • Define conjugate acid and bases.
  • For a given reaction, identify the conjugate acid-base pairs.

From the Bronsted-Lowry definition of acids and bases, we saw that acids and bases must exist together. Review Section 1: Proton Donors and Acceptors, in Proton Donors and Acceptors: Acid-base Reactions à la Brønsted.

In any acid-base reaction, the acid donates a proton and the base accepts a proton. The products of the reaction are the "leftover" parts of the acid and base. For example, in a generic acid dissociation reaction:

HA + B → A+ HB+

HA is the acid and B is the base. The product A is what the acid becomes, and the product HB+ is what the base becomes. We say that A is the conjugate base of the acid HA. HA and A are a conjugate acid-base pair. Likewise, we say that HB+ is the conjugate acid of B. B and HB+ are a conjugate acid-base pair.

We can summarize this as:

Conjugate base and conjugate acid


7g. Compare and contrast the processes of oxidation and reduction

  • Define oxidation.
  • Define reduction.
  • For a given reaction, determine if it is oxidation or reduction.

Oxidation-reduction reactions, or redox reactions, are an important class of chemical reactions. Redox reactions involve two half-reactions: an oxidation reaction and a reduction reaction.

Consider this (unbalanced) reaction:

Cu(s) + 2Ag+(aq) → Cu2+(aq) + Ag(s)

We can think of this reaction in terms of electron transfer. Electrons from the solid copper must be removed to form the positive copper ion. We can think of this half-reaction as:

Cu(s) → Cu2+(aq) + 2e− where e is an electron.

Likewise, we can think of the half-reaction involving the silver. Here, the silver ion gains two electrons from the copper to form silver solid:

2Ag+(aq) + 2e → Ag(s)

An oxidation reaction is a reaction in which electrons are lost. In this case, the copper is oxidized. A reduction reaction is a reaction in which electrons are gained. In this case, silver is reduced. We say copper is a reducing agent in this reaction because it causes the reduction reaction of silver. We say silver is an oxidizing agent in this reaction because it causes the oxidation reaction of copper.

Review how to write half reactions from a redox reaction in Example 11.14.1 in Redox Reactions.


7h. Write and balance equations for oxidation-reduction reactions

In writing and balancing redox reactions, we need to use a different set of rules from general balancing rules. This is because we need to account for the electrons being transferred in the reaction. First, we will describe the rules for writing a redox reaction in an acidic solution. The first step is to write the oxidation numbers for each element in each compound in the reaction. Review the rules for determining oxidation numbers in the section Determining Oxidation States, in Oxidation Numbers and Redox Reactions.

Secondly, write the unbalanced half-reactions for oxidation and reduction. Note which elements are being oxidized or reduced.

Then, balance each half-reaction. First, balance the elements being oxidized or reduced in each half-reaction. Balance oxygen atoms by adding water as needed to either side of the half-reactions. This is okay to do because water is the solvent in these reactions, so there is water present. Lastly, balance the hydrogen atoms by adding H+ ions as needed. This is okay to do because, in an acidic solution, there are extra H+ ions in solution. Lastly, balance electronic charge by adding electrons as needed to the half-reactions.

When you add the balanced half-reactions up, cross out any terms that appear on both sides, and ensure that the number of atoms and the charges balance.

Now, we will describe the rules for writing a redox reaction in a basic solution. As above, the first step is to assign oxidation states to each atom in the compounds in the reaction.

The second step is to write the unbalanced half-reactions for oxidation and reduction. Note which elements are being oxidized or reduced.

Then, balance the half-reactions. First, balance the elements being oxidized or reduced in each half-reaction. Balance oxygen by adding hydroxide, OH as needed. This is acceptable because a basic solution has excess OH in solution. Then, balance the hydrogen atoms by adding water as needed. Lastly, balance electronic charge by adding electrons as needed to the half-reactions.

When you add the balanced half-reactions up, cross out any terms that appear on both sides, and ensure that the number of atoms and the charges balance.

Review detailed, step-by-step examples of balancing redox reactions in acidic and basic solutions in the section Balancing Redox Reactions, in Balancing Redox Equations.


7i. Identify common oxidizing agents, common reducing agents, and substances that can act both as oxidizing and reducing agents

Oxygen is the most common oxidizing agent. Oxygen readily oxidizes metals, creating metal oxides. Most metals exist as oxides in nature because of the abundance of oxygen in the air. This picture shows a common example we are familiar with, rust, which is a hydrated iron oxide.

A rusty pipe

Metals, particularly those on the left of the periodic table, are strong reducing agents. Water and hydrogen peroxide, H2O2, can act as both oxidizing agents and reducing agents.


Unit 7 Vocabulary 

  • Arrhenius acid
  • Arrhenius base
  • Aqueous
  • Bronsted-Lowry acid
  • Bronsted-Lowry base
  • Conjugate acid
  • Conjugate base
  • Conjugate base pair
  • Equivalence point
  • Half reaction
  • Hydronium ion
  • Hydroxide ion
  • Indicator solution
  • Ion product of water
  • Net ionic equation
  • Neutralization
  • Oxidation reaction
  • Oxidizing agent
  • pH
  • pOH
  • Redox
  • Reducing agent
  • Reduction reaction
  • Salt
  • Self-ionization/self protolysis of water
  • Titrant
  • Titration
  • Titration curve

Unit 8: Nuclear Chemistry

8a. Distinguish different types of nuclear decay

  • Define the characteristics of an alpha particle.
  • Define the characteristics of a beta particle.

There are two main types of nuclear decay. An alpha particle is a type of nuclear decay that is equivalent to a helium nucleus: 42He. When this type of decay occurs, the atomic number of the product will be reduced by two. A beta particle is a high energy electron. During beta particle decay, the neutron decomposes into a beta particle and a hydrogen nucleus, 11H. When this type of decay occurs, the atomic number of the product is increased.

Review examples of alpha particle emission in Alpha-Decay. Review examples of beta particle emission in Beta-Decay.


8b. Balance nuclear equations

To balance a nuclear equation, we must account for how the emission of nuclear particles changes the nucleus of the atom. Alpha particle decay will reduce the mass number of the product by four and the atomic number by two. Beta particle decay will keep the mass number constant but will increase the atomic number by one.

Review examples of Alpha particle decay in Alpha-Decay. Review examples of Beta particle decay in Beta-Decay.


8c. Explain the process of radioactive dating

  • What is half-life?
  • How does radioactive dating work?

Radioactive dating is an important technique that takes advantage of the known half-lives and natural abundances of radioisotopes.

All radioactive isotopes decay in a predictable pattern. We define the term half-life as the time it takes for half of a sample of a radioactive isotope to decay to its daughter element. Half-lives are known and are constant for different isotopes. This decay occurs in a predictable pattern, as seen below.

A graph that depicts half-life in terms of the number of atoms of a specific isotope and time

We can write a rate equation for the rate of radioactive decay:


( \mathrm{k} is called the rate constant, and  t_{1/2} is the half-life of the isotope)

From this equation, we can determine the ratio of the concentration of the isotope at a certain time, Ct, to the initial concentration of the isotope, C0, by the equation:

 \ln \frac{C_0}{C_t}=\mathrm{kt}

This allows us to determine how much of a radioactive isotope will remain after a certain amount of time has passed. Review a detailed description of the half-life rate equations in Half-Life.

The most common type of isotope dating is carbon dating, which is used for determining the age of archeological and other artifacts. In carbon dating, the age of carbon-containing material is determined by comparing the decay rate of that material with living material.

Carbon-14 decays by the following reaction:

 ^{14}_{6}\mathrm{C}\rightarrow ^{14}_{7}\mathrm{N} + ^{0}_{-1}e with a half-life of 5.73 x 103 years

Review an example of how carbon dating was used to determine the age of the dead sea scrolls in Carbon Dating.


8d. Describe the processes of nuclear fission and fusion

The two types of nuclear reactions are nuclear fission and nuclear fusion. In nuclear fission, a large nucleus is split by being “hit” by a high energy neutron. This creates two new atoms, which each continue to form new atoms and neutrons if there is sufficient energy. This is known as a chain reaction, which produces an immense amount of energy. Nuclear fission reactions were what was used in the atomic bombs.

Diagram of nuclear fission, a chain reaction

Nuclear fusion, by contrast, is the process of combining small nuclei to form a larger nucleus.

The simplest example of this is combining two deuterium (hydrogen isotope) atoms to form helium:

 ^{2}_{1}\mathrm{H}+^{2}_{1}\mathrm{H}\rightarrow ^{4}_{2}\mathrm{He}

This produces significantly more energy than nuclear fission. Nuclear fusion is what takes place in the sun and other stars because they have sufficient hydrogen reserves to sustain the reaction.

Review background on nuclear reactions in Transmutation of the Elements, and The Mass Defect.


8e. Explain how radioactive decay is used as a source of energy

Nuclear power is a source of energy for many people all over the world. In nuclear power plants, a nuclear fission chain reaction takes place to produce energy. The reaction rate is controlled by control rods that absorb excess neutrons produced in the chain reaction without undergoing nuclear fission reactions themselves. These control rods are made of different metals and alloys. The nuclear material is kept in fuel rods that are placed between the control rods. By moving the control rods, the rate of nuclear reaction in the fuel rods can be controlled. The energy from the nuclear reaction is put through a heat exchanger to create steam to turn a turbine. The most-used radioactive material is uranium.

Review a description of some of the considerations in using nuclear power in Nuclear Energy.


Unit 8 Vocabulary

  • Alpha particle
  • Beta particle
  • Carbon dating
  • Chain reaction
  • Control rod
  • Daughter element
  • Fuel rod
  • Half-life
  • Nuclear decay
  • Nuclear fission
  • Nuclear fusion
  • Radioactive dating
  • Rate equation