Class 11 Chemistry: Equilibrium

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1. Equilibrium: Introduction Definition: A state in a reversible process where the rates of forward and reverse reactions are equal, and the concentrations of reactants and products remain constant over time. Types: Physical Equilibrium: Equilibrium between different physical states (e.g., solid-liquid, liquid-gas). Chemical Equilibrium: Equilibrium between reactants and products in a chemical reaction. Dynamic Nature: Equilibrium is dynamic, meaning reactions continue in both directions at equal rates, not that they stop. 2. Physical Equilibrium 2.1. Solid-Liquid Equilibrium Rate of melting = Rate of freezing. Example: Ice $\rightleftharpoons$ Water at 0°C and 1 atm. 2.2. Liquid-Gas Equilibrium Rate of vaporization = Rate of condensation. Example: Water $\rightleftharpoons$ Water vapour at 100°C and 1 atm. Vapour Pressure: Pressure exerted by the vapours in equilibrium with the liquid at a given temperature. 2.3. Solid-Gas Equilibrium Rate of sublimation = Rate of deposition. Example: Iodine solid $\rightleftharpoons$ Iodine vapour. 2.4. Solution Equilibrium Solid in Liquid: Rate of dissolution = Rate of crystallization. (Saturated solution) Gas in Liquid: Rate of dissolution = Rate of escape of gas from solution. Governed by Henry's Law: $P = K_H \cdot C$, where $P$ is partial pressure of gas, $C$ is concentration, $K_H$ is Henry's constant. 3. Chemical Equilibrium 3.1. Law of Chemical Equilibrium & Equilibrium Constant For a general reversible reaction: $aA + bB \rightleftharpoons cC + dD$ Law of Mass Action: At a given temperature, the ratio of product of molar concentrations of products to that of reactants, each raised to the power of their stoichiometric coefficients, is constant. Equilibrium Constant ($K_c$): $$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$ where $[X]$ denotes molar concentration of X at equilibrium. Equilibrium Constant ($K_p$): For gaseous reactions, in terms of partial pressures: $$K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$$ where $P_X$ denotes partial pressure of X at equilibrium. 3.2. Relationship between $K_p$ and $K_c$ $K_p = K_c (RT)^{\Delta n_g}$ $\Delta n_g = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants})$ $R$ = gas constant ($0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1}$), $T$ = temperature in Kelvin. 3.3. Characteristics of Equilibrium Constant Its value is constant at a given temperature. Independent of initial concentrations. For reverse reaction, $K'_c = 1/K_c$. If reaction is multiplied by 'n', $K'_c = (K_c)^n$. If reactions are added, their equilibrium constants are multiplied. Pure solids and liquids are excluded from the equilibrium constant expression (their concentrations are considered constant). 3.4. Reaction Quotient ($Q$) Expression for $Q$ is same as $K_c$, but concentrations are not necessarily at equilibrium. Predicting direction: If $Q_c If $Q_c > K_c$: Net reaction proceeds in reverse direction. If $Q_c = K_c$: Reaction is at equilibrium. 4. Le Chatelier's Principle "If a system at equilibrium is subjected to a change in temperature, pressure, or concentration of a reactant or product, the equilibrium will shift in a direction that tends to counteract the change." Effect of Concentration: Increase in reactant concentration: Equilibrium shifts forward. Increase in product concentration: Equilibrium shifts backward. Effect of Pressure (for gaseous reactions): Increase in pressure: Equilibrium shifts towards fewer moles of gas. Decrease in pressure: Equilibrium shifts towards more moles of gas. If $\Delta n_g = 0$: Pressure has no effect. Effect of Temperature: Exothermic Reaction ($\Delta H Increase temperature shifts equilibrium backward. Endothermic Reaction ($\Delta H > 0$): Increase temperature shifts equilibrium forward. Effect of Inert Gas Addition: At constant volume: No effect on equilibrium position. At constant pressure: Shifts equilibrium towards more moles of gas. Effect of Catalyst: Increases rate of both forward and reverse reactions equally. Helps attain equilibrium faster, but does NOT change the equilibrium position or $K_c$. 5. Ionic Equilibrium Equilibrium involving ions in aqueous solutions. Electrolytes: Substances that dissociate into ions in solution. Strong Electrolytes: Almost completely dissociate (e.g., HCl, NaOH, NaCl). Weak Electrolytes: Partially dissociate (e.g., $\text{CH}_3\text{COOH}$, $\text{NH}_4\text{OH}$). Degree of Dissociation ($\alpha$): Fraction of total molecules that dissociate. $$\alpha = \frac{\text{number of molecules dissociated}}{\text{total number of molecules}}$$ 5.1. Acids and Bases Arrhenius Concept: Acid: Substance that produces $H^+$ ions in water. Base: Substance that produces $OH^-$ ions in water. Brønsted-Lowry Concept: Acid: Proton ($H^+$) donor. Base: Proton ($H^+$) acceptor. Conjugate Acid-Base Pairs: Formed by the gain or loss of a proton. Acid $\rightleftharpoons$ Conjugate Base + $H^+$ Base + $H^+ \rightleftharpoons$ Conjugate Acid Lewis Concept: Acid: Electron pair acceptor. Base: Electron pair donor. 5.2. Ionization of Acids and Bases Weak Acid ($HA$): $HA_{(aq)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + A^-_{(aq)}$ $$K_a = \frac{[H_3O^+][A^-]}{[HA]}$$ Weak Base ($B$): $B_{(aq)} + H_2O_{(l)} \rightleftharpoons BH^+_{(aq)} + OH^-_{(aq)}$ $$K_b = \frac{[BH^+][OH^-]}{[B]}$$ Ostwald's Dilution Law: For a weak electrolyte, $\alpha = \sqrt{K/C}$ (where $K$ is $K_a$ or $K_b$, $C$ is initial concentration). Valid for dilute solutions. 5.3. Ionic Product of Water ($K_w$) $H_2O_{(l)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + OH^-_{(aq)}$ $K_w = [H_3O^+][OH^-]$ At 25°C, $K_w = 1.0 \times 10^{-14}$. $K_w$ increases with temperature. 5.4. pH Scale $pH = -\log[H^+]$ or $pH = -\log[H_3O^+]$ $pOH = -\log[OH^-]$ $pH + pOH = 14$ (at 25°C) Acidic solution: $pH Basic solution: $pH > 7$ Neutral solution: $pH = 7$ 5.5. Common Ion Effect The suppression of the dissociation of a weak electrolyte by the addition of a strong electrolyte containing a common ion. Example: Adding $\text{CH}_3\text{COONa}$ (strong electrolyte) to $\text{CH}_3\text{COOH}$ (weak acid) suppresses the dissociation of $\text{CH}_3\text{COOH}$. 5.6. Buffer Solutions Solutions that resist changes in pH upon addition of small amounts of acid or base. Types: Acidic Buffer: Weak acid + its salt with a strong base (e.g., $\text{CH}_3\text{COOH} + \text{CH}_3\text{COONa}$). Basic Buffer: Weak base + its salt with a strong acid (e.g., $\text{NH}_4\text{OH} + \text{NH}_4\text{Cl}$). Henderson-Hasselbalch Equation: For acidic buffer: $pH = pK_a + \log \frac{[\text{Salt}]}{[\text{Acid}]}$ For basic buffer: $pOH = pK_b + \log \frac{[\text{Salt}]}{[\text{Base}]}$ 5.7. Hydrolysis of Salts Reaction of cations or anions of a salt with water to produce acidity or alkalinity. Salt of Strong Acid & Strong Base: No hydrolysis, $pH = 7$. (e.g., NaCl) Salt of Strong Acid & Weak Base: Cationic hydrolysis, solution is acidic ($pH Salt of Weak Acid & Strong Base: Anionic hydrolysis, solution is basic ($pH > 7$). (e.g., $\text{CH}_3\text{COONa}$) Salt of Weak Acid & Weak Base: Both cation and anion hydrolyze. pH depends on relative strengths of acid and base. 5.8. Solubility Product ($K_{sp}$) For a sparingly soluble salt $A_xB_y$: $A_xB_y(s) \rightleftharpoons xA^{y+}(aq) + yB^{x-}(aq)$ $K_{sp} = [A^{y+}]^x [B^{x-}]^y$ Solubility ($S$): Molar concentration of the salt in a saturated solution. Condition for Precipitation: If Ionic Product ($Q_{sp}$) If Ionic Product ($Q_{sp}$) > $K_{sp}$: Solution is supersaturated, precipitation occurs. If Ionic Product ($Q_{sp}$) = $K_{sp}$: Solution is saturated, equilibrium exists. Common Ion Effect on Solubility: Addition of a common ion decreases the solubility of a sparingly soluble salt.