Summary

Dynamic equilibrium: In a closed system, the forward and reverse reaction rates become equal — the system appears static but is microscopically active. For a general reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant $K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$ (concentrations in mol/L). $K_p$ uses partial pressures: $K_p = K_c (RT)^{\Delta n_g}$, where $\Delta n_g = (c+d) - (a+b)$.

$K$ tells the story: $K \gg 1$ → products favoured; $K \ll 1$ → reactants favoured. $K$ changes only with temperature — never with concentration, pressure, or catalyst. For the reverse reaction, $K' = 1/K$; if you multiply the equation by $n$, $K_{\text{new}} = K^n$.

Reaction quotient $Q_c$: Same expression as $K_c$ but for any instant. Compare $Q$ with $K$: $Q < K$ → forward direction; $Q > K$ → reverse direction; $Q = K$ → equilibrium.

Le Chatelier’s principle: If a system at equilibrium is disturbed, it shifts to partially counteract the change.

• Concentration: Adding a reactant shifts right; removing a product shifts right.
• Pressure/volume: For gases, increasing pressure (decreasing volume) favours the side with fewer moles of gas. No effect if $\Delta n_g = 0$.
• Temperature: Exothermic reactions ($\Delta H < 0$) shift left on heating; endothermic ($\Delta H > 0$) shift right on heating. Catalyst does not shift equilibrium — it only helps reach it faster.

Ionic equilibrium in water: Water autoionises: $2H_2O \rightleftharpoons H_3O^+ + OH^-$, $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}$ at 25°C. Pure water: $[H_3O^+] = [OH^-] = 10^{-7}$ M. $pH = -\log[H_3O^+]$, $pOH = -\log[OH^-]$, $pH + pOH = 14$.

Acid–base strength: $K_a$ (acid dissociation constant) and $K_b$ (base dissociation constant). Strong acids/bases have $K_a$ or $K_b \gg 1$; weak ones have small $K$. For a conjugate pair: $K_a \times K_b = K_w$. $pK_a = -\log K_a$, $pK_b = -\log K_b$.

pH of weak acids/bases: Use the approximation $[H_3O^+] \approx \sqrt{K_a C}$ (valid when $C/K_a > 10^3$). Similarly, $[OH^-] \approx \sqrt{K_b C}$ for weak bases. For a salt of weak acid + strong base, $pH = 7 + \frac{1}{2}pK_a + \frac{1}{2}\log C$; for weak base + strong acid, $pH = 7 - \frac{1}{2}pK_b - \frac{1}{2}\log C$. …