Formula Sheet

Gases, Liquids, and Solutions

\( PV = nRT \)

\( PV = nRTP_{\mathrm{total}}=P_A+P_B+P_C+\cdots \)

\( \mathrm{Kelvin}=^{\circ}\mathrm{C}+273 \)

\( P_1 V_1 = P_2 V_2 \)

\( \frac{V_1}{T_1}=\frac{V_2}{T_2} \)

\( \frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2} \)

\( d=\frac{m}{V} \)

\( KE_{\mathrm{per\ molecule}}=\frac{mV^2}{2} \)

\( \frac{r_1}{r_2}=\frac{\left ( M_1 \right )^{\frac{1}{2}}}{\left ( M_2 \right )^{\frac{1}{2}}} \)

\( \begin{matrix} M \\ \mathrm{(molarity)} \end{matrix} = \frac{\mathrm{moles\ solute}}{\mathrm{liter\ of\ solution}} \)

\( P \) = pressure, \( V \) = volume, \( T \) = temperature, \( n \) = number of moles, \( d \) = density, \( m \) = mass, \( v \) = velocity, \( KE \) = kinetic energy, \( r \) = rate of effusion, \( M \) = molar mass, \( Q \) = reaction quotient, \( E^O \) = standard reduction potential, \( K \) = equilibrium constant

\( R\mathrm{,\ gas\ constant}=\frac{8.31\mathrm{\ joules}}{\mathrm{mole}\cdot\mathrm{kelvin}}=0.0821\frac{\mathrm{liter}\cdot\mathrm{atm}}{\mathrm{mole}\cdot\mathrm{kelvin}}=8.31\frac{\mathrm{volts}\cdot\mathrm{coulombs}}{\mathrm{mole}\cdot\mathrm{kelvin}} \)

Atomic Structure

\( \Delta E=hv \) or \( \Delta E=hf \)

\( c=v\lambda \) or \( c=f\lambda \)

\( E \) = energy, \( v \) = frequency or \( f \) = frequency, \( \lambda \) = wavelength, \( v \) = velocity, \( c \) = speed of light = \( 3.00 \times 10^8 \frac{\mathrm{m}}{\mathrm{s}} \)

Equilibrium

\( K_w=1\times10^{-14}\mathrm{\ at\ }25^{\circ}\mathrm{C} \)

\( \mathrm{pH}=-\mathrm{log}\left [ \mathrm{H}^+ \right ], \mathrm{\ pOH}=-\mathrm{log}\left [ \mathrm{OH}^- \right ] \)

\( \mathrm{pH\ +\ pOH}=14 \)

\( H^O \) = standard enthalpy, \( E^O \) = standard reduction potential, \( T \) = temperature, \( q \) = heat, \( c \) = specific heat capacity, \( c_{\mathrm{water}}=\frac{4.18\mathrm{\ joule}}{\mathrm{g\ K}} \), \( H_f=\frac{330\mathrm{\ joule}}{\mathrm{gram}} \) for water, \( H_v=\frac{2260\mathrm{\ joule}}{\mathrm{gram}} \) for water

Periodic Table of the Elements