## 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