CHEM101 Study Guide

Site: Saylor Academy
Course: CHEM101: General Chemistry I
Book: CHEM101 Study Guide
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Date: Saturday, May 25, 2024, 4:11 PM

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Study Guide Structure

In this study guide, the sections in each unit (1a., 1b., etc.) are the learning outcomes of that unit. 

Beneath each learning outcome are:

  • questions for you to answer independently; and
  • a brief summary of the learning outcome topic with linked resources.

At the end of each unit, there is also a list of suggested vocabulary words.


How to Use this Study Guide

  1. Review the entire course by reading the learning outcome summaries and the linked resources.
  2. Test your understanding of the course information by answering questions related to each unit learning outcome and defining and memorizing the vocabulary words at the end of each unit.

By clicking on the gear button on the top right of the screen, you can print the study guide. Then you can make notes, highlight, and underline as you work.

Through reviewing and completing the study guide, you should gain a deeper understanding of each learning outcome in the course and be better prepared for the final exam!

Unit 1: Matter and Measurements


1a. Classify properties of matter and changes of matter as physical or chemical

  • How do physical and chemical changes differ?
  • What are some examples of physical changes?
  • What are some examples of chemical changes?

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 water (a liquid) 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.

Scientists classify properties of matter as physical or chemical. Physical properties are those we can observe without altering the identity of the substance. For example, the melting or boiling point of a substance is a physical property because they do not alter the identity of the substance.

We can only observe chemical properties when we alter the identity of the substance. Rusting is an example of a chemical property because it is a chemical reaction that changes the composition of the substance.

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 composed 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 that has 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.

Review this material in Physical and Chemical Properties and Physical and Chemical Changes.


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

  • Can you list the base SI units for length, mass, time, and volume?
  • Can you 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)

We use SI prefixes to convert among units that have different orders of magnitude. For example, you should use millimeters to measure lengths that are extremely short, 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) = 10^{3} g, or 1 kg = 1,000 g.

Review this material in Units of Measure and Units and Dimensions in Chemistry.


1c. Perform mathematical operations involving significant figures

  • Can you add and subtract using significant figures?
  • Can you multiply and divide using significant figures?
  • Can 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.

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. Notice how the leading zeros in front of the nonzero digits are insignificant figures. This is shown in the 0.000029 example below.

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\times 10^{b} where a is a number greater than one, and less than 10.

Review this material in Significant Figures, Using Significant Figures and Significant Figure Practice.


1d. 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\times 10^{n}, 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 non-zero number.

For example, 15,000 in scientific notation is 1.5\times 10^{4}. 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 non-zero digit to get 10^{4}.

Similarly, 0.0007005 in scientific notation is a\times 7.005\times 10^{-4}. In this case, we move the decimal point to follow the first non-zero digit to get 7.005. Count back to the original decimal point to determine the number of zero digits before the first non-zero 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.

Review this material in Introduction to Scientific Notation.


1e. Perform dimensional analysis conversions between different units of measure

  • Can you convert feet to inches?
  • How many minutes are in one day?

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 above we see that one kilogram (1 kg) = 10^{3} g, or 1 kg = 1,000 g.

Dimensional analysis allows chemists to convert from a given unit of measurement to a desired unit of measurement. For example, if you are given 12 inches and want to convert inches to meters, you would use the following dimensional analysis conversion:

Review this material in Convert Units.


1f. Perform calculations involving density

  • What is the density of an object having a volume of 100 mL and a mass of 10 g?
  • What is the density of water at 4°C?

Density measures how tightly packed the particles in a substance are.

We define density (d) as the mass or volume of a substance at a given temperature. We write d = m/v where d is density, m is mass, and v is volume. If we know two of the variables in this equation, we can solve for the third algebraically. The units for density are a mass unit divided by a volume unit. The units used to describe density often differ for the phases of matter: solids (g/cm3), liquids (g/mL), and gases (g/L).

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

Review this material in Density and Its Uses and Calculations Using Density.


Unit 1 Vocabulary

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

Unit 2: The Atom


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

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

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 are found on the periodic table. For example, the elements hydrogen, helium, carbon all have different atom types.

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

Ions are 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.

Review this material in Atoms, Elements, and the Nucleus and The Nuclear Atom.


2b. Define isotopes and use isotopic abundance data to calculate the average atomic mass for a given element

  • What are isotopes?
  • Can you 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. We call atoms that are the same element but have different numbers of neutrons "isotopes". So 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 for 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 that exist 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 shows how to write isotope symbols for the isotopes of hydrogen.

When you take a sample of any given element, different types of isotopes occur in a certain percentage in nature. 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. 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.

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 The Nuclear Atom and Atomic Mass.


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

  • What are 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 how to respond to the questions in this learning outcome in learning outcome 2b above.


2d. Use Avogadro's number to convert between the number of particles and moles

  • What is Avogadro's number?
  • What is a mole?
  • Can you use Avogadro's number to convert a number of atoms to a 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: 6.0022\times 10^{23}. Avogadro's number of particles is one mole.

You can think about a mole (mol) as if you have a dozen items: 12 eggs or 12 cars. While the size and mass of the eggs and cars differ tremendously, you still have a dozen. In our case here, we have a mole (or 6.0022\times 10^{23}) 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.

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.

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.

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.

Review this material in Avogadro's Number and the Mole and the two videos in Atom to Moles. Review Problem Example 4 Number of Moles in N Particles. Practice calculating molar volume in Problem Example 7 Molar Volume of a Liquid and Problem Example 8 Radius of a Strontium Atom. Practice converting between grams, moles, and the number of particles in Problem Example 5 Boron Content of Borax and Problem Example 6 Magnesium in Chlorophyll.


2e. Explain the wave-particle duality of light

  • What are quantum particles?
  • Can you 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 the 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:


Note that E is the energy of the photon, h is Planck's constant (6.626 × 10-34 J-s), 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 (like a baseball) through the double-slit experiment, some particles (baseballs) 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.

Review this material in Quanta and Light, Particles and Waves.


2f. 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. Although we now consider this model to be incorrect (see learning outcome 2g), 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}

Note that 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. 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.

Review this material in The Bohr Model.


2g. 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.

  1. 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.

  1. 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 zero, we say it is an s orbital and it is spherical.

  • If l equals one, we say it is a p orbital and it is dumbbell-shaped.

  • If l equals two, 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.

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

  • For s equals zero, the orbital is spherical shaped. 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 zero (s orbital), m equals one.

  • For l equals one (p orbital), m can be negative one, zero, or one.

  • For l equals two (d orbital), m can be negative two, negative one, zero, one, or two.

  1. 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. So, to distinguish the two electrons in a given orbital, we have s=+1 and s=-1 for the two electrons in a given orbital.

Review this material in The Quantum Mechanical Model of the Atom and The Quantum Atom.


2h. 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, we call the rows periods. We call the vertical columns groups. Elements in a group share certain characteristic properties.

The blocks are labeled in red in the periodic table:

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

Review this material on electron configurations in Valence Electrons and Periodic Properties of the Elements.


Unit 2 Vocabulary

  • Albert Einstein
  • 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 dumbbell
  • Electron
  • Electron cloud
  • Electron shell
  • Interference pattern
  • Ion
  • Isotope
  • John Dalton
  • Magnetic quantum number
  • Mass
  • Mass number (A)
  • Molar mass
  • Molar volume
  • Mole (mol)
  • Niels Bohr
  • 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
  • Relative abundance
  • Schrodinger equation
  • Spin quantum number
  • Subatomic particle
  • Systeme Internationale (SI)
  • Thomas Young
  • Valence electrons
  • Wave-particle duality
  • Young's Double Slit Experiment

Unit 3: Bonding


3a. Compare and contrast ionic, covalent, and metallic bonding

  • Can you describe the nature of a chemical bond?
  • Can you describe the energetics of bond formation?
  • Why is it often favorable to form a bond?
  • What is an ionic bond? What types of atoms can form ionic bonds?
  • What is a covalent bond? What types of atoms can form covalent bonds?
  • What is a metallic bond? What types of atoms can form metallic bonds?

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

Chemical bonds result when one or more outer valence 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.

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 can describe the bonds as energetically favorable since energy is released.

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

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.

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 a higher electronegativity than the other atom. Electronegativity is a measure of how much an atom pulls electrons toward itself in a covalent bond.

Not surprisingly, Metallic bonds form 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.

Review this material in What are Covalent and Ionic bonds? and Ionic, Covalent and Metallic Bonds.


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

  • Why do chemists use VSEPR to describe the shapes of molecules?
  • What forces determine the shape of molecules?
  • How can you use VSEPR to predict the shape of a given molecule or polyatomic ion?

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

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

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.

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.

After you study the basics of Lewis electron dot structures, you 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 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.

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

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.

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.

The most common configuration we see in chemistry is the AX4 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.

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 a 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°.

Water (H2O) is an example of a molecule with AX2E2 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°.

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

To review, you should first read about how to write electron configurations for atoms in Electron Configurations. This will help you understand how to draw a Lewis Dot structure to apply VSEPR theory. Then, 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: Lewis Dot-Structures and the Octet Rule. To review how VSEPR theory describes different molecular geometries, see the descriptions in Molecular Geometry. For more, see VSEPR practice.


3c. Use hybridization theory to determine the shapes of molecules or polyatomic ions

  • Why is hybridization theory needed?
  • Can you use a hybridization diagram to construct molecular orbitals for a tetrahedral compound?
  • Why does hybridization theory give us molecular shapes?

Hybridization theory accounts for the molecular shapes we see in experiments that combine 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.

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

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.

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.

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

The sp3 orbitals form the expected tetrahedral molecular geometry.

Review how to write electron configurations for atoms in Electron Configurations and The Hybrid Orbital Model.


3d. Use molecular shape to determine a molecule's polarity

  • What is molecular polarity?
  • What is electronegativity?
  • What is a dipole moment?
  • Can you 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.

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 them. Because dipole moments are vectors, we can sum the vectors to determine if a molecule is polar (polar molecule). 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.

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: 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.

Review this material in Polar Covalence and Predicting Bond Type.


3e. Determine if a given compound or polyatomic ion has resonance structures, and draw them

  • Why are resonance structures necessary?
  • Can you 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.

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:

In reality, the true structure of the nitrate ion is a superposition, or combination of all three of these resonance structures. Each bond is really about 1\frac{1}{3} of a bond, or bond order.

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

First, review the rules for writing Lewis electron dot structures The Shared-Electron Covalent Bond: Lewis Dot-Structures and the Octet Rule. Review The Shared-Electron Covalent Bond: Lewis Dot-Structures and the Octet Rule for more examples of molecules and polyatomic ions with resonance structures. Finally, review Resonance Hybrids.


3f. List the different types of intermolecular forces and determine the type(s) of intermolecular forces present for a given molecule

  • How does each type of Van der Waals force work?
  • Which types of molecules can be affected by each 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.

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.

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.

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.

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 momentary and not permanent dipole.

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.

Review this material in Interactions Between Molecular Units.


Unit 3 Vocabulary

  • Bent geometry
  • Bond order
  • Chemical bond
  • Covalent bond
  • Dipole moment
  • Dipole-dipole force
  • Dipole-induced dipole force
  • Electron fluid
  • Electronegativity
  • Electrostatic force
  • Endothermic
  • Energetically favorable
  • Exothermic
  • Homonuclear
  • Hybrid (or molecular) orbital
  • Hybridization theory
  • Ion
  • Ion-dipole force
  • Ion-induced dipole force
  • Ionic bond
  • Lewis Dot structure
  • Like charge
  • 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
  • Trigonal pyramidal
  • Valence
  • Valence electron pair
  • Valence shell electron
  • Van der Waals force
  • VSEPR theory
  • Wavefunction

Unit 4: Chemical Formulas and Equations


4a. Determine the formula of an ionic compound when given the name, and name the ionic compound when given a formula

  • Do you know the names and charges of the most common ions listed in this course?
  • Can you 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 Chemical Nomenclature. 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 be helpful to 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 this material in Chemical Nomenclature.


4b. Use mass percent data and formula mass to determine empirical and molecular formulas

  • Can you use a chemical formula to determine mole ratios of atoms in a compound?
  • Can you use a chemical formula to determine the percent composition of a compound?
  • Can you calculate the percent composition of carbon in C10H16?
  • Can you determine the molecular formula of glycoaldehyde given the following information?
    • Its molar mass is 60 g/mol
    • Its percent composition is 40% C, 6.71% H, and 53.28% O

A list of the percent by mass of each element in a compound is known as the percent composition. As an example, calculate the mass percent of carbon in CH4. To perform this calculation you need the number of carbons present (1C) times the mass of carbon (12 amu) and then you divide the number by the molar mass of the compound (CH4 = 16 amu). Since it is a percentage, you will then multiply by 100%. Here is an example:

[(1C) × (12 amu)] / (16 amu) × 100% = 75% C in CH4

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

After knowing the percent composition of a molecule, we can use it to calculate the empirical formula and molecule formula.

For more examples of percent composition, review Calculating Mass Percent, Chemical Formulas and their Arithmetic, and Molecular and Empirical Formulas from Percent Composition.


4c. Name binary molecular compounds using prefixes.

  • What are the prefixes for binary molecular compounds?
  • Given a formula, can you write the correct binary molecular compound name?
  • Given a name, can you 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 the section Naming the Binary Molecules, in Chemical Nomenclature. 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 a 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 this material in Chemical Nomenclature.


4d. Balance a chemical equation

  • Can you identify reactants and products in a chemical reaction?
  • Why must chemical reactions be balanced?
  • Can you balance a chemical equation?

Chemical equations express the net change of composition that occurs 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 convention in chemistry that we 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).

Let's examine 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: 3C, 8H, 2O; Products, 3C, 2H, 7O

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

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

The equation is balanced.

Review balancing a chemical equation in Combustion of Propane and Combustion of Ethane. For more review, see Balancing Chemical Reactions.


4e. Use molar mass or formula mass in conversions between grams and moles

  • Given a chemical formula, can you determine the number of each type of atom in the compound?
  • Can you use the chemical formula to determine molecular mass?
  • Can you convert the molecular mass of a compound to moles?

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.

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.

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. To identify the molecular mass, we multiple the number of each element by the mass on the periodic table.

2 mol C = 2 × 12 g/mol = 24g of C

6 mol H = 6 × 1 g/mol = 6g of H

1 mol O = 1 × 16 g/mol = 16g of O

Molar mass of C2H6O is equal to 24 + 6 + 16 = 46 g/mol.

Now that we know the molar mass of a molecule, we can use it to convert grams of a molecule to moles of a molecule. Here is an example of determining the number of moles of ethanol in 10g of ethanol.

To solve this problem, start with the 10g of ethanol and divide it by the molar mass of ethanol (46 g/mol):

10g ethanol × 1 mol ethanol/46 g ethanol = 0.22 mol of ethanol.

Can you determine the number of moles in 16g of ethanol?

To review, see Formula Weight and Molar Mass, Mole Ratio Calculation, Mole Fraction, and Mole Percent. For more information, review Calculating Molar Mass and Number of Moles and Chemical Formulas and their Arithmetic.


4f. Perform stoichiometry calculations, including stoichiometry calculations when there is a limiting reactant

  • Can you convert nomenclature into a chemical reaction?
  • Can you balance a chemical reaction?
  • Can you identify the limiting reactant in a balanced chemical reaction?
  • Can you perform stoichiometry using a limiting reactant?

When we write a chemical equation, we are showing how elements or compounds react to form new compounds. We must make sure the number of each element on the reactant side equals the number of each element on the product side. This is called balancing a chemical equation, and it ensures that the Law of Conservation of Mass is not violated.

When chemical reactions occur, the reactants react in whole-number mole ratios with each other. Products are formed in whole-number mole ratios. We read the equation for the hydrolysis of water (2H2O → 2H2 + O2) as "two moles of water react to yield two moles of hydrogen and two moles of oxygen".

The coefficients before each formula are called stoichiometric coefficients. These coefficients are the mole ratios in the balanced equation. When we have a balanced equation, we can use the mole ratios of a balanced chemical equation to determine the amount of product that can be produced. These are called stoichiometry calculations.

Review this material in Stoichiometry and Stoichiometry Example Problems. For additional information on limiting reactants, review Calculating Amounts of Reactants and Products.


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
  • Polyatomic ion
  • Product
  • Reactant

Unit 5: States of Matter


5a. Use the ideal gas law to calculate the properties of a gas

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

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

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

Chemists use the Kinetic Molecular Theory of Gases to explain the behavior of gases on a macroscopic scale (that is, visible to the naked eye). The Kinetic Molecular Theory of Gas describes how gases behave and can allow us to predict certain properties of gases.

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

  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.

The Kinetic Molecular Theory of Gas explains basic properties of gases. According to the Kinetic Molecular Theory of Gas, 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. We define force divided by area as pressure.

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


(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 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.

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.

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 Kinetic Molecular Theory and The Basic Gas Laws. See Problem Example 3 for an example of how to use the Ideal Gas Law. Also, review The Ideal Gas Equation and Gas Molecules in Motion.


5b. Compare the motion of particles in a solid, liquid, and gas

  • What are the properties of a liquid?
  • How do particles in a liquid move?
  • Define vapor pressure.
  • How does vapor pressure lead to phase change for liquids?
  • Define nucleation.
  • How does nucleation lead to phase change for liquids?

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

Liquids exhibit mobility, which means they are "mobile" and 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.

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.

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

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 the statement mathematically as P_{w}=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.

Review this material in Liquids and Their Interfaces and Vapor Pressure.


5c. 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):

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 physical stress, which can cause the substance to break.

For more details and examples of ionic solid structure, review Ionic and Ion-derived Solids. Then, review Cubic Crystal Lattices and Close-Packing, and Ionic and Ion-derived Solids.


5d. Interpret phase diagrams

  • Can you identify the parts of a phase diagram, including the critical point and triple point?
  • For a given temperature and pressure, can you 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.

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 (the solid area colored in yellow) shows the set of temperature and pressure conditions where a solid exists.

  • The area in the top middle (the liquid area colored in green) shows the set of temperature and pressure conditions where a liquid exists.

  • The area in the bottom to the right (the gas area colored 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.


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 number one, the water is a solid, since the point is in the solid region of the diagram.

  • At point two, 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 three, the water is in the gas or vapor state.

  • At point four, the water is above the critical point, which means it is in the state of supercritical fluid.

Review this material in Phase Diagrams and Phases, Changes of State.


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

  • Can you describe 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.

Review this material in States of Matter, Specific Heat, Heat of Fusion and Vaporization, Chilling Water Problem, Change of State Example, Phase Diagrams, and Phases, Changes of State.


Unit 5 Vocabulary

  • Atmosphere
  • Boiling
  • Brittleness
  • Coulombic charge
  • 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
  • Kinetic molecular theory of gas
  • Melting
  • Mobility
  • Nucleation
  • Phase boundaries
  • Phase change
  • Phase diagram
  • Pressure
  • Sublimation
  • Supercritical fluid
  • Surface tension
  • Triple point
  • Vapor pressure
  • Velocity
  • Viscosity

Unit 6: Thermochemistry and Thermodynamics


6a. Define temperature and heat, and state the units used for each

  • What is temperature?
  • What is the definition of heat?
  • What units are used to describe heat?

While we talk about temperature nearly every day, it has a specific definition central to thermodynamics. To understand temperature, we first 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.

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.

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 this material in Energy, Heat, and Work and Molecules as Energy Carriers.


6b. Perform enthalpy change, enthalpy of reaction, enthalpy of combustion, and enthalpy of formation calculations

  • What is enthalpy?
  • Can you calculate the enthalpy change for a given system?
  • Can you determine the enthalpy of reaction for a given reaction?
  • Can you determine the enthalpy of combustion for a given system?
  • Can you 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.

We define enthalpy (\Delta H) as the heat change in a system at constant pressure.

Note that \Delta is the Greek symbol delta which means change, so you should read the expression \Delta H as a change in heat.

We can express enthalpy mathematically as: \Delta H\equiv q_{p}=\Delta U+P\Delta V .

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

For this equation:

  • q_{P} represents heat at constant pressure

  • \Delta U represents the change in internal energy

  • P \Delta V represents pressure-volume work

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.

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, \Delta H 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 reaction, we use the following equation:

\Delta H=H_{products}-H_{reactants}

Here, H_{products} represents the enthalpy of products. H_{reactants} represents the enthalpy of the reactants.

The question remains, how do we know the H_{products} and H_{reactants}?

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:

H_{2}(g)+\frac{1}{2}\:O_{2}(g)\rightarrow H_{2}O(l)\:\Delta H=-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:

\Delta H^{\circ}_{reaction}=\Sigma \: \Delta H{_{f}}^{\circ}_{products}\: \Sigma \Delta H{_{f}}^{\circ}_{reactants}

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 are 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 enthalpy of reaction.

Review this material in Enthalpy, Heat of Formation, Calculate Standard Enthalpy of Reaction, Thermochemistry and Calorimetry, and The First Law of Thermodynamics.


6c. Define entropy

  • What are spontaneous processes?
  • What is entropy?

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 nonspontaneous.

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.

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.

Review this material in What is Entropy? and the Availability of Energy.


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

  • What is Gibbs Free Energy?
  • Can you use Gibbs Free Energy to explain the driving force of a chemical reaction?

We can express Gibbs Free Energy (\Delta G) mathematically as \Delta G=\Delta H - T \Delta S

(\Delta H represents the enthalpy change of the reaction, T represents temperature, and \Delta S represents the change in entropy of the system.)

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 the spontaneity of a chemical reaction.

Review this chart:


\Delta G < 0

Spontaneous to the right (products)

\Delta G > 0

Spontaneous to the left (reactants)

\Delta G = 0

System at equilibrium


Review this material in Free Energy: The Gibbs Function (Gibbs Energy), Gibbs Free Energy and Spontaneity, and Gibbs Free Energy Example.


6e. Use Hess' Law to solve thermodynamic problems

  • What is a state function?
  • What is Hess' Law?
  • How is Hess' law used?
  • Can you use Hess' law to determine the enthalpy of a reaction from enthalpies of formation and/or combustion?

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 the 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 the reaction.

To use Hess' law, you must find the 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 \Delta H_{f}.

  • If you multiply a reaction by a coefficient to get the right number of reactants and products, you must multiply \Delta H_{f} 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 \Delta H_{f} terms appropriately, you simply add the \Delta H_{f} terms up to get \Delta H_{reaction}.

Review this material in Hess' Law Example and Hess' Law and Thermochemical Calculations.


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 S
  • Exothermic
  • Gibbs Free Energy
  • Gravity
  • Heat
  • Heat flow
  • Hess' Law
  • Internal energy
  • Joule (J)
  • Kinetic energy
  • Nonspontaneous
  • 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

  • What are Arrhenius acids and bases?
  • Can you use the Arrhenius definition to identify acids and bases?
  • What are Brønsted-Lowry acids and bases?
  • Can you use the Brønsted-Lowry definition to identify acids and bases?
  • Can you write an equation for the self-ionization or autoprotolysis of water?
  • How is water both an acid and a base?
  • What are conjugate acids and bases?
  • For a given reaction, can you identify the conjugate acid-base pairs?

There is more than one definition of acids and bases which 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 are hydrochloric acid, HCl, sulfuric acid, H2SO4, and acetic acid (vinegar), CH3COOH. Examples of Arrhenius bases are sodium hydroxide (also known as lye), NaOH, and ammonia, NH3.

The Brønsted-Lowry definition of acids and bases is more general than the Arrhenius definition. A Brønsted-Lowry acid is a proton (hydrogen ion) donator. A Brønsted-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-.

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)

Note 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 (a proton acceptor). Note that the proton from the water always has become the hydronium ion rather than the H+ ion in solution.

From the Brønsted-Lowry definition of acids and bases, we saw that acids and bases must exist together. 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:

Review this material in Acids and Bases: An Introduction, What are Acids and Bases?, Arrhenius Definition of Acids and Bases, Brønsted-Lowry Definition of Acids and Bases, Proton Donors and Acceptors: Acid-base Reactions à la Brønsted, and Conjugate Acids and Bases.


7b. Write and balance equations for neutralization reactions

  • Can you write and balance a neutralization reaction for a given acid and base?
  • What is a salt?

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. 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 those that are dissolved in water.

So, we first write a total ionic equation in which we write 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 Acids and Bases: An Introduction. Also, review Acid-Base Neutralization Reaction.


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

  • Can you write the ion product of water?
  • What are acidic, basic, and neutral solutions based on the [H3O+] and [OH-]?
  • Can you determine the concentration of [H3O+] or [OH-] for a given solution?
  • Can you calculate pH for a given solution?
  • Can you 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. As we learned above, 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 × 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 K_{w} expression. Using K_{w}, 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:

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.

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

Review this material in Aqueous Solution, pH, and Titration and Definition of pH.


7d. Contrast strong acids and bases with weak acids and bases

  • Can you identify the strong acid or base in a reaction?
  • Can you write the neutralization reaction between a strong acid and a strong base?
  • How would you organize acids based on their strengths?

Acids and bases are either strong or weak. Strong acids are good at donating protons because of the stability of the anions they form. In each strong acid, the proton is bonded to a very strong electronegative atom (O, Cl, Br, I). When the proton is donated, the leftover bonding electrons remain on the electronegative atom.

There are 7 strong acids: HCl, HBr, HI, HNO3, HClO3, HClO4, and H2SO4.

There are 8 strong bases: LiOH, NaOH, KOH, RbOH, CsOH, Ca(OH)2, Sr(OH)2, and Ba(OH)2.

Any other acid or base is considered weak.

Strong acids completely ionize in solution, whereas weak acids only partially ionize. Notice the difference between the reaction arrows used here:

Strong bases will also completely ionize in solution. Weak acids and bases have much smaller ionization constants (Ka) than their stronger counterparts.

Review this material in Strong Acids and Bases and Ka and Acid Strength.


7e. Perform calculations for a titration of a strong acid with a strong base

  • What is titration?
  • What are the steps of a titration?

Titrations are practical 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 the 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.

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.

Review this material in Titration Introduction.


7f. Compare and contrast processes of oxidation and reduction

  • What is oxidation?
  • What is reduction?
  • For a given reaction, can you 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 Redox Reactions.


7g. Calculate oxidation numbers for each element in a given compound

  • How do you assign oxidation numbers for a given element?
  • How do you determine the oxidation states of all atoms in a compound?

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.

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

  • 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.

Review this material in Oxidation Numbers and Redox Reactions.


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

  • Can you write and balance redox reactions in an acidic solution?
  • Can you write and balance redox reactions in a basic solution?

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.

Second, 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 the 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 basic solutions. 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 the rules for determining oxidation numbers in Oxidation Numbers and Redox Reactions. Review detailed, step-by-step examples of balancing redox reactions in acidic and basic solutions in Balancing Redox Equations and Write a Balanced Redox Reaction.


Unit 7 Vocabulary

  • Arrhenius acid
  • Arrhenius base
  • Aqueous
  • Aqueous substance
  • Brønsted-Lowry acid
  • Brønsted-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 of water
  • Self-protolysis of water
  • Titrant
  • Titration
  • Titration curve

Unit 8: Nuclear Chemistry


8a. Distinguish different types of nuclear decay

  • What are the characteristics of an alpha particle?
  • What are 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:  ^4 \, _2He . 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,  ^1 \, _1H . When this type of decay occurs, the atomic number of the product is increased.

Review this material in Radioactive Decay, Alpha Decay, Beta Decay, and Types of Decay.


8b. Balance nuclear equations

  • Can you 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.

_{92}^{238}\textrm{U}\;\rightarrow \;_{90}^{234}\textrm{Th}\;+\; _{2}^{4}\textrm{He}

When balancing a nuclear equation, be sure that the mass number and the atomic number sum to the same amount on both sides of the equation arrow. For example, identify the missing species when isotope 212-Po decays to isotope 208-Pb.

212-Po has a mass of 212 and an atomic number of 84.
208-Pb has a mass of 208 and an atomic number of 82.

The mass and atomic numbers must sum to the same amount on both sides of the equation arrow. Thus, the product side is missing a mass of 4 (208 + 4 = 212) and an atomic number of 2 (82 + 2 = 84). If an alpha particle is added to the product side, this will balance the nuclear equation.

_{84}^{212}\textrm{Po}\;\rightarrow \;_{82}^{208}\textrm{Pb}\;+\; _{2}^{4}\textrm{He}

Beta particle decay will keep the mass number constant but will increase the atomic number by one.

_{53}^{131}\textrm{I}\;\rightarrow \;_{54}^{131}\textrm{Xe}\;+\; _{-1}^{0}\textrm{ }\beta

Review this material in Alpha-Decay, Beta-Decay, and Writing Nuclear Equations.


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.

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

k=\frac{In\left [ 2 \right ]}{t_{1/2}}=\frac{0.693}{t_{1/2}}

(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, C_{0} by the equation:

In\: \frac{C_{0}}{C_{1}}=kt

This allows us to determine how much of a radioactive isotope will remain after a certain amount of time has passed.

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:

_{6}^{14}\textrm{C}\rightarrow _{7}^{14}\textrm{N}+_{-1}^{0}\textrm{e} with a half-life of 5.73 \times 10^{3} years

Review this material in Half-Life and Carbon Dating.


8d. Contrast the processes of nuclear fission and fusion

  • What is nuclear fission?
  • What is nuclear 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 used in the atomic bombs.

Nuclear fusion, by contrast, is the process of combining small nuclei together to form a larger nucleus. The simplest example of this is combining two deuterium (hydrogen isotope) atoms to form helium:

_{1}^{2}\textrm{H}+_{1}^{2}\textrm{H}\rightarrow _{2}^{4}\textrm{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 this material in Transmutation of the Elements, Mass Defect, Nuclear Fission, and Nuclear Fusion.


8e. Explain the risks and benefits of nuclear energy

  • How is nuclear chemistry used to produce 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 which 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 common radioactive material used in nuclear reactors is the isotope uranium-235.

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