Ionic Equilibrium - Formula Sheet

Self-Ionization of Water

\(K_w = [H_3O^+][OH^-]\)
At 298 K, \(K_w = 1 \times 10^{-14}\)

pH Scale

\(pH = -\log_{10}[H_3O^+]\)
\(pOH = -\log_{10}[OH^-]\)
\(pH + pOH = pK_w\) (equal to 14 at 298 K)

Ostwald's Dilution Law

\(K_a = \frac{\alpha^2 C}{1 - \alpha}\)
For weak electrolytes (\(\alpha \ll 1\)): \(K_a \approx \alpha^2 C\) or \(\alpha = \sqrt{\frac{K_a}{C}}\)
\([H_3O^+] = \sqrt{K_a \cdot C}\)

Henderson-Hasselbalch Equation

Acidic Buffer: \(pH = pK_a + \log \frac{[Salt]}{[Acid]}\)
Basic Buffer: \(pOH = pK_b + \log \frac{[Salt]}{[Base]}\)

Salt Hydrolysis

Strong Base + Weak Acid: \(pH = 7 + \frac{1}{2} pK_a + \frac{1}{2} \log C\)
Strong Acid + Weak Base: \(pH = 7 - \frac{1}{2} pK_b - \frac{1}{2} \log C\)
Weak Acid + Weak Base: \(pH = 7 + \frac{1}{2} pK_a - \frac{1}{2} pK_b\)

Solubility Equilibria

For salt \(A_mB_n\): \(K_{sp} = [A^{n+}]^m [B^{m-}]^n\)
Relationship with molar solubility (\(s\)): \(K_{sp} = m^m \cdot n^n \cdot s^{m+n}\)

Symbol Definitions

• \(K_a, K_b\): Acid and base dissociation constants
• \(K_w\): Ionic product of water
• \(K_h\): Hydrolysis constant
• \(\alpha\): Degree of dissociation
• \(h\): Degree of hydrolysis
• \(C\): Molar concentration
• \(s\): Molar solubility
• \(K_{sp}\): Solubility product constant