Chemical equilibrium is a dynamic state where the rates of forward and reverse reactions are equal, and macroscopic properties (concentration, pressure, colour) remain constant. The equilibrium constant $K_c = \dfrac{[C]^c[D]^d}{[A]^a[B]^b}$ for $aA + bB \rightleftharpoons cC + dD$. Key properties of equilibrium: (1) Dynamic: both reactions continue at equal rates. (2) Concentrations constant but not zero. (3) Only achievable in closed system. (4) $K$ depends only on temperature. (5) $K$ is independent of: initial concentrations, pressure changes, addition of catalyst, presence of inert gas. (6) $\Delta G = 0$ at equilibrium. If $\Delta G < 0$: forward reaction spontaneous. If $\Delta G > 0$: reverse reaction spontaneous. $\Delta G^\circ = -RT\ln K$. $\Delta G = \Delta G^\circ + RT\ln Q = RT\ln(Q/K)$.

If a system at equilibrium is subjected to a change, it will respond to partially oppose that change and re-establish equilibrium. Changes and responses: (1) Increase in concentration of reactant: equilibrium shifts right (produces more product). (2) Decrease in concentration of product: equilibrium shifts right. (3) Increase in pressure (by reducing volume): shifts to side with fewer moles of gas. Decrease in pressure: shifts to side with more moles of gas. (4) Increase in temperature: shifts in endothermic direction (forward if $\Delta H > 0$, reverse if $\Delta H < 0$). Decreases exothermic reaction's K. Increases endothermic K. (5) Catalyst: no shift; reaches equilibrium faster. (6) Adding inert gas at constant volume: no shift (partial pressures unchanged). (7) Adding inert gas at constant pressure: volume increases → mole fractions decrease → partial pressures decrease → shifts to side with more gas moles. Key distinction: constant volume vs constant pressure matters for inert gas addition!

$K_c$ uses molar concentrations (mol/L). $K_p$ uses partial pressures (atm or Pa). Relation: $K_p = K_c(RT)^{\Delta n_g}$ where $\Delta n_g$ = moles of gaseous products - moles of gaseous reactants and $R = 0.0821$ L·atm/(mol·K). When $\Delta n_g = 0$: $K_p = K_c$. When $\Delta n_g > 0$: $K_p > K_c$ (at $T > 1/R = 12.2$ K, i.e., always). When $\Delta n_g < 0$: $K_p < K_c$. $K_c$ and $K_p$ have units depending on $\Delta n_g$ but are often treated as dimensionless (using standard concentration 1 M or standard pressure 1 bar). If equation multiplied by $n$: $K_{new} = K^n$. If equation reversed: $K_{new} = 1/K$. Overall $K$ for stepwise reactions = product of individual $K$ values.

$Q$ has same form as $K$ but uses non-equilibrium concentrations/pressures. Comparing $Q$ and $K$: $Q < K$: reaction proceeds forward (towards products) to reach equilibrium. $Q > K$: reaction proceeds reverse (towards reactants). $Q = K$: system is at equilibrium. $Q$ helps predict: direction a reaction will shift, whether precipitation will occur ($Q > K_{sp}$), which direction a buffer will respond. Example: $N_2 + 3H_2 \rightleftharpoons 2NH_3$, $K_c = 10^5$ at 25°C. If $[N_2]=1, [H_2]=0.5, [NH_3]=0.1$: $Q = (0.1)^2/((1)(0.5)^3) = 0.01/0.125 = 0.08 << K$. Reaction proceeds forward to produce more NH₃.

Temperature: ONLY factor that changes $K$. Endothermic forward ($\Delta H > 0$): increase T → K increases (more product at equilibrium). Exothermic forward ($\Delta H < 0$): increase T → K decreases (less product). Van't Hoff equation: $\dfrac{d\ln K}{dT} = \dfrac{\Delta H^\circ}{RT^2}$. Concentration: changes $Q$ but not $K$. Adding reactant: $Q < K$ → forward shift. Pressure (for gases): changes $Q$ if $\Delta n_g \neq 0$. For $N_2 + 3H_2 \rightleftharpoons 2NH_3$ ($\Delta n_g = -2$): increase pressure → $Q > K$ → reverse shift initially... wait: if all concentrations increase equally (volume decrease), then $Q$ changes depending on $\Delta n_g$. For this reaction, increasing pressure shifts forward (towards fewer gas moles). Catalyst: does not change $K$, $Q$, or concentrations at equilibrium. Only changes rate of approach to equilibrium.

Strong acids (HCl, H₂SO₄, HNO₃, HClO₄, HBr, HI): fully dissociated. $[H^+] = C$ (for monoprotic). pH $= -\log[H^+]$. Strong bases (NaOH, KOH): $[OH^-] = C$. pOH $= -\log[OH^-]$. pH $= 14 -$ pOH at 25°C. Weak acid (HA): $K_a = [H^+][A^-]/[HA]$. $[H^+] = \sqrt{K_a C}$ (if $\alpha << 1$). Weak base (B): $K_b = [BH^+][OH^-]/[B]$. $[OH^-] = \sqrt{K_b C}$. Buffer: Henderson-Hasselbalch: pH $= pK_a + \log\dfrac{[A^-]}{[HA]}$. Maximum buffer capacity when $[A^-] = [HA]$ → pH $= pK_a$. Buffer range: $pK_a \pm 1$. Common buffers: phosphate (pH 7.2), bicarbonate (pH 6.1), acetate (pH 4.75), ammonia (pH 9.25).

$K_{sp}$ = solubility product. For $M_aX_b \rightleftharpoons aM^{n+} + bX^{m-}$: $K_{sp} = [M^{n+}]^a[X^{m-}]^b$. If molar solubility $= s$: $K_{sp} = (as)^a(bs)^b = a^a b^b s^{a+b}$. For 1:1 electrolyte (AgCl): $K_{sp} = s^2$, $s = \sqrt{K_{sp}}$. Common ion effect: adding common ion suppresses solubility. AgCl in 0.1 M NaCl: $s = K_{sp}/[Cl^-] = 1.8\times10^{-10}/0.1 = 1.8\times10^{-9}$ M. Compare pure water: $s = \sqrt{1.8\times10^{-10}} = 1.34\times10^{-5}$ M. Reduction by factor 7400. Simultaneous equilibria: precipitation of one ion while another remains in solution (selective precipitation). Temperature effect: for most salts, Ksp increases with T (endothermic dissolution). CaSO₄, Li₂SO₄: exceptions (decreases with T).

Complex ions form by coordination of ligands to metal ions. Formation constants $K_f$ (also called stability constant): $Ag^+ + 2NH_3 \rightleftharpoons [Ag(NH_3)_2]^+$, $K_f = 1.7\times10^7$. Large $K_f$ means complex is very stable. Effect on solubility: forming a complex with the ion increases solubility of sparingly soluble salt. AgCl (Ksp $= 1.8\times10^{-10}$) dissolves in NH₃ because Ag⁺ is removed as $[Ag(NH_3)_2]^+$ → $Q < K_{sp}$ → more AgCl dissolves. Stepwise formation constants: $\beta_1, \beta_2,...$ are stepwise; $\beta_n$ (overall) $= \beta_1 \times \beta_2 \times ... \times \beta_n$. Applications: EDTA titrations (EDTA has large $K_f$ for metal ions), photography ($[Ag(S_2O_3)_2]^{3-}$ fixing), cyanide process for gold extraction ($[Au(CN)_2]^-$, $K_f = 2\times10^{38}$).