Chemical Equilibrium (NCERT)

Cheatsheet Content

1. Introduction to Equilibrium Reversible Reactions: Reactions that proceed in both forward and backward directions. Example: $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$ Chemical Equilibrium: The state where the rate of forward reaction equals the rate of backward reaction. Concentrations of reactants and products remain constant over time. Dynamic in nature (reactions continue, but no net change). Physical Equilibrium: Equilibrium involving physical processes (e.g., solid-liquid, liquid-gas). Example: $H_2O(l) \rightleftharpoons H_2O(g)$ (at constant temperature and pressure) 2. Law of Chemical Equilibrium & Equilibrium Constant Law of Mass Action: At a given temperature, the rate of a chemical reaction is directly proportional to the product of the molar concentrations of the reactants, each raised to the power equal to its stoichiometric coefficient in the balanced chemical equation. For a general reversible reaction: $aA + bB \rightleftharpoons cC + dD$ Rate of forward reaction: $R_f = k_f [A]^a [B]^b$ Rate of backward reaction: $R_b = k_b [C]^c [D]^d$ Equilibrium Constant ($K_c$): At equilibrium, $R_f = R_b$, so $k_f [A]^a [B]^b = k_b [C]^c [D]^d$. $K_c = \frac{k_f}{k_b} = \frac{[C]^c [D]^d}{[A]^a [B]^b}$ (for concentrations in mol/L) Equilibrium Constant ($K_p$): For gaseous reactions, expressed in terms of partial pressures. $K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$ Relationship between $K_p$ and $K_c$: $K_p = K_c (RT)^{\Delta n_g}$ $\Delta n_g = (\text{sum of stoichiometric coefficients of gaseous products}) - (\text{sum of stoichiometric coefficients of gaseous reactants})$ $R$ = Gas constant, $T$ = absolute temperature (in Kelvin) Units of $K_c$ and $K_p$: $K_c$ has units of $(\text{mol L}^{-1})^{\Delta n}$. $K_p$ has units of $(\text{atm})^{\Delta n_g}$ or $(\text{bar})^{\Delta n_g}$. For reactions where $\Delta n = 0$, $K_c$ and $K_p$ are dimensionless. 3. Characteristics of Equilibrium Constant It is constant for a given reaction at a particular temperature. Its value indicates the extent of the reaction: $K_c > 10^3$: Products largely favored. $K_c $10^{-3} If the reaction is reversed, the new equilibrium constant is $K_c' = 1/K_c$. If the equation is multiplied by 'n', the new equilibrium constant is $K_c^n$. If the equation is divided by 'n', the new equilibrium constant is $K_c^{1/n}$. If a reaction is the sum of two reactions, its $K_c$ is the product of their individual $K_c$ values. 4. Predicting the Direction of Reaction (Reaction Quotient, Q) Reaction Quotient ($Q_c$): Calculated using non-equilibrium concentrations. $Q_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$ (at any given time 't') Comparison with $K_c$: If $Q_c If $Q_c > K_c$: Net reaction proceeds in the backward direction. If $Q_c = K_c$: Reaction is at equilibrium. 5. Le Chatelier's Principle "When a system at equilibrium is subjected to a change in temperature, pressure, or concentration, the system will readjust itself to counteract the effect of the change and establish a new equilibrium." Effect of Concentration Change: Adding reactant: Equilibrium shifts forward (to consume added reactant). Adding product: Equilibrium shifts backward (to consume added product). Removing reactant: Equilibrium shifts backward. Removing product: Equilibrium shifts forward. Effect of Pressure Change: (Applicable only for gaseous reactions with $\Delta n_g \neq 0$) Increasing pressure: Equilibrium shifts towards the side with fewer moles of gas. Decreasing pressure: Equilibrium shifts towards the side with more moles of gas. If $\Delta n_g = 0$, pressure change has no effect. Effect of Temperature Change: Endothermic Reaction ($\Delta H > 0$): Increase in T: Equilibrium shifts forward (to absorb heat). $K_c$ increases. Decrease in T: Equilibrium shifts backward. $K_c$ decreases. Exothermic Reaction ($\Delta H Increase in T: Equilibrium shifts backward (to consume heat). $K_c$ decreases. Decrease in T: Equilibrium shifts forward. $K_c$ increases. Effect of Inert Gas Addition: At constant volume: No effect on equilibrium position (partial pressures and molar concentrations remain unchanged). At constant pressure: Volume increases, so partial pressures of reactants/products decrease. Equilibrium shifts to the side with more gaseous moles. Effect of Catalyst: A catalyst increases the rate of both forward and backward reactions equally. It helps in achieving equilibrium faster but does not change the equilibrium position or the value of $K_c$. 6. Heterogeneous Equilibria Equilibrium involving reactants and products in different physical states. Concentrations of pure solids and pure liquids are considered constant and are not included in the equilibrium constant expression. Example: $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$ $K_c = [CO_2]$ or $K_p = P_{CO_2}$ 7. Free Energy and Equilibrium Constant Gibbs Free Energy Change ($\Delta G$): $\Delta G = \Delta G^\circ + RT \ln Q$ At equilibrium, $\Delta G = 0$ and $Q = K_c$. So, $0 = \Delta G^\circ + RT \ln K_c$ $\Delta G^\circ = -RT \ln K_c$ Relationship between $\Delta G^\circ$ and $K_c$: If $\Delta G^\circ 1$ (products favored). If $\Delta G^\circ > 0$, $K_c If $\Delta G^\circ = 0$, $K_c = 1$ (equilibrium).