## Section 6: Chemical Equilibrium - 4: Homogeneous Equilibria Homogeneous equilibria occur when all reactants and products exist in the **same physical phase** – either entirely as gases or entirely dissolved in a single solution. This uniformity simplifies the mathematical treatment of equilibrium compared to heterogeneous systems. The **equilibrium constant expression** for a homogeneous reaction is written using the concentrations (for solutions, denoted as K_c) or partial pressures (for gases, denoted as K_p), with each term raised to the power of its stoichiometric coefficient. For the general reaction: $$ a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D} $$ The equilibrium constants are: * K_c = $\frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b}$ (Concentrations in mol/L) * K_p = $\frac{(P_\text{C})^c (P_\text{D})^d}{(P_\text{A})^a (P_\text{B})^b}$ (Partial pressures in atm, bar, etc.) **Crucially, pure liquids and solids are excluded from equilibrium constant expressions, but since homogeneous systems involve only gases or solutes, all species are included.** For reactions involving **ideal gases**, K_c and K_p are related by: $$ K_p = K_c (RT)^{\Delta n} $$ where: * $R$ is the ideal gas constant (use 0.0821 L·atm·mol⁻¹·K⁻¹ for atm). * $T$ is the absolute temperature in Kelvin. * $\Delta n$ is the change in the number of moles of gas (products minus reactants: $\Delta n = (c + d) - (a + b)$). * Note: If $\Delta n = 0$, then $K_p = K_c$. **Examples:** 1. **Gas-Phase:** The decomposition of dinitrogen tetroxide: $$ \text{N}_2\text{O}_4(g) \rightleftharpoons 2\text{NO}_2(g) $$ K_c = $\frac{[\text{NO}_2]^2}{[\text{N}_2\text{O}_4]}$ ; K_p = $\frac{(P_{\text{NO}_2})^2}{P_{\text{N}_2\text{O}_4}}$ ; $\Delta n = 2 - 1 = 1$ → $K_p = K_c (RT)$ 2. **Solution-Phase:** The ionization of acetic acid (a weak acid): $$ \text{CH}_3\text{COOH}(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_3\text{O}^+(aq) + \text{CH}_3\text{COO}^-(aq) $$ K_c = $\frac{[\text{H}_3\text{O}^+][\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COOH}]}$ (Water concentration is constant and absorbed into K_a, the acid dissociation constant). The **reaction quotient (Q)** for a homogeneous reaction has the exact same form as K_c or K_p, but uses the instantaneous concentrations or partial pressures *before* the system reaches equilibrium. Comparing Q to K determines the direction the reaction will proceed to achieve equilibrium.

1: Matter and measurement

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