Equilibrium Constants

$K_c = \frac{[\text{products}]^{\text{coeff}}}{[\text{reactants}]^{\text{coeff}}} \qquad K_p = K_c(RT)^{\Delta n}$

$\Delta n = n_{\text{gaseous products}} - n_{\text{gaseous reactants}}$

$\Delta G^\circ = -RT \ln K = -2.303\,RT\log K$

Ionic Equilibrium

$K_w = [H^+][OH^-] = 10^{-14} \text{ at 25°C}$

$pH = -\log[H^+] \qquad pOH = -\log[OH^-] \qquad pH + pOH = 14 \text{ (25°C)}$

$[H^+]_{\text{weak acid}} = \sqrt{K_a \cdot C} \qquad K_a \times K_b = K_w \text{ (conjugate pair)}$

$pH_{\text{buffer}} = pK_a + \log\frac{[\text{salt}]}{[\text{acid}]} \qquad pOH_{\text{buffer}} = pK_b + \log\frac{[\text{salt}]}{[\text{base}]}$

Salt Hydrolysis

$\text{WA + SB:} \quad pH = 7 + \tfrac{1}{2}pK_a + \tfrac{1}{2}\log C$

$\text{SA + WB:} \quad pH = 7 - \tfrac{1}{2}pK_b - \tfrac{1}{2}\log C$

$\text{WA + WB:} \quad pH = 7 + \tfrac{1}{2}pK_a - \tfrac{1}{2}pK_b$

Ksp

$K_{sp}(\text{AgCl}) = s^2 \Rightarrow s = \sqrt{K_{sp}} \qquad K_{sp} = 1.8 \times 10^{-10}$

$K_{sp}(\text{Ag}_2\text{CrO}_4) = 4s^3 \Rightarrow s = \left(\frac{K_{sp}}{4}\right)^{1/3} \qquad K_{sp} = 1.1 \times 10^{-12}$

$K_{sp}(\text{Ca(OH)}_2) = 4s^3 \qquad K_{sp} = 5.5 \times 10^{-6}$

Key Constant Values