# General Chemistry/Useful Equations

 General Chemistry

### General

 Density $\displaystyle \frac{mass}{volume}$ Moles $\displaystyle \frac{given~mass~(g)}{gram~formula~mass}$ Percent Error $\displaystyle \frac{measured - accepted}{accepted} \times 100%$ Percent Composition (by mass) $\displaystyle \frac{mass~of~part}{mass~of~whole} \times 100%$ Molarity $\displaystyle \frac{moles~of~solute}{volume~of~solution}$ Molality $\displaystyle \frac{moles~of~solute}{mass~of~solvent~in~kg}$ Rate of Reaction $\displaystyle \frac{Difference~in~quantity}{Difference~in~time}$ de Broglie's law $\displaystyle \lambda$ = $\displaystyle \frac{h}{mv}$

### Atomic Structure

Symbol Meaning Symbol Meaning
$\displaystyle E$ energy $\displaystyle c$ speed of light
$\displaystyle v$ frequency $\displaystyle \lambda$ wavelength
$\displaystyle Q$ charge $\displaystyle r$ distance
$\displaystyle k_e$ Coulomb's constant $\displaystyle h$ Plank's constant H/nkne
 Energy of Wave $\displaystyle E = h v$ Wave Relation $\displaystyle c = \lambda v$ Coulomb's Law $\displaystyle F_e = k_e\frac{Q_1Q_2}{r^2}$

### Solutions, Liquids, and Gases

Symbol Meaning
$\displaystyle P$ pressure
$\displaystyle V$ volume
$\displaystyle n$ number of moles
$\displaystyle T$ temperature (in Kelvin)
$\displaystyle K_f$ molal freezing point constant
$\displaystyle K_b$ molal boiling point constant
$\displaystyle \chi$ mole fraction
$\displaystyle m$ molality
$\displaystyle M$ molarity
$\displaystyle c$ specific heat capacity
$\displaystyle M_w$ mass of water (Kg)
$\displaystyle E_h$ heat energy released

 Rauolt's Law $\displaystyle P_{solution} = P_{1} \chi_{1} + P_{2} \chi_{2} + \dots$ Boiling Point Elevation $\displaystyle \Delta T_{solution} = K_b \cdot m_{solute}$ Freezing Point Depression $\displaystyle \Delta T_{solution} = K_f \cdot m_{solute}$ Ideal Gas Law $\displaystyle PV = nRT$ Combined Gas Law $\displaystyle \frac{P_1 V_1}{n_1 T_1} = \frac{P_2 V_2}{n_2 T_2}$ Titration $\displaystyle M_A V_A = M_B V_B$ Dilution $\displaystyle M_1 V_1 = M_2 V_2$ Heat released by burning $\displaystyle E_h = cM_w\Delta T$

### Equilibrium

Symbol Meaning
$\displaystyle K_{eq}$ equilibrium constant (general)
$\displaystyle K_p$ pressure equilibrium constant
$\displaystyle K_c$ concentration equilibrium constant
$\displaystyle R$ gas law constant
$\displaystyle T$ temperature (in Kelvin)
$\displaystyle \Delta n$ moles of product – moles of reactant
 pH $\displaystyle \mathrm{pH} = - \log{[\mathrm{H^+}]}$ pOH $\displaystyle \mathrm{pOH} = - \log{[\mathrm{OH^-}]}$ (for water) $\displaystyle \mathrm{pH} + \mathrm{pOH} = 14$ Pressure/Concentration $\displaystyle K_p = K_c(RT)^{\Delta n}$ Equilibrium,for a reaction $\displaystyle a\mathrm{A} + b\mathrm{B} \rightarrow c\mathrm{C} + d\mathrm{D}$ $\displaystyle K_{eq} = \frac{[\mathrm{C}]^c [\mathrm{D}]^d}{[\mathrm{A}]^a [\mathrm{B}]^b}$

### Thermochemistry

Symbol Meaning
$\displaystyle q$ heat energy
$\displaystyle m$ mass
$\displaystyle c$ specific heat
$\displaystyle T$ temperature (in Kelvin)
$\displaystyle S$ entropy
$\displaystyle H$ enthalpy
$\displaystyle G$ Gibbs free energy
 Heat Transfer $\displaystyle q = m c \Delta T$ Enthalpy $\displaystyle \Delta H = H_{products} - H_{reactants}$ Entropy $\displaystyle \Delta S = S_{products} - S_{reactants}$ Free Energy $\displaystyle \Delta G = \Delta H - T \Delta S$