Chapter: Equilibrium

• 1. Physical Equilibrium

  • Types
    • Solid-Liquid: Ice $\rightleftharpoons$ Water (at melting point)
    • Liquid-Vapour: Water $\rightleftharpoons$ Steam (in closed vessel)
    • Solid-Vapour: Camphor $\rightleftharpoons$ Vapour
    • Dissolution Equilibrium:
      • Solid in Liquid (Saturated solution)
      • Gas in Liquid (Henry's Law: $C \propto P$)
  • General Characteristics
    • Occurs only in a closed system
    • Dynamic nature: Forward rate = Reverse rate
    • Measurable parameters (pressure, concentration) remain constant

• 2. Chemical Equilibrium

  • Dynamic Nature
    • Reactants $\rightleftharpoons$ Products
    • Rates of forward and backward reactions are equal
  • Law of Mass Action
    • Reaction rate $\propto$ Product of active masses of reactants
  • Equilibrium Constant ($K$)
    • Concentration Basis ($K_c$): Ratio of molar concentrations of products to reactants
    • Pressure Basis ($K_p$): For gaseous reactions using partial pressures
    • Relationship: $K_p = K_c(RT)^{\Delta n_g}$
  • Reaction Quotient ($Q_c$)
    • $Q_c < K_c$: Reaction proceeds in forward direction
    • $Q_c = K_c$: System is at equilibrium
    • $Q_c > K_c$: Reaction proceeds in reverse direction
  • Le Chatelier's Principle
    • Concentration: Adding reactant shifts equilibrium forward
    • Temperature:
      • Endothermic: Favoured by increase in $T$
      • Exothermic: Favoured by decrease in $T$
    • Pressure: Increase shifts towards fewer gas moles ($\Delta n_g$)
    • Inert Gas Addition:
      • At Constant Volume: No effect
      • At Constant Pressure: Shifts towards more gas moles
    • Catalyst: Speeds up both rates; no effect on equilibrium composition

• 3. Ionic Equilibrium & Acid-Base Theories

  • Electrolytes
    • Strong Electrolytes: Complete ionization ($\alpha \approx 1$)
    • Weak Electrolytes: Partial ionization ($\alpha \ll 1$)
  • Acid-Base Concepts
    • Arrhenius Theory:
      • Acid: Produces $H^+$ ions in water
      • Base: Produces $OH^-$ ions in water
    • Brønsted-Lowry Theory:
      • Acid: Proton donor
      • Base: Proton acceptor
      • Conjugate Acid-Base Pairs: Differ by a single proton ($H^+$)
    • Lewis Theory:
      • Acid: Electron pair acceptor (e.g., $BF_3$, $AlCl_3$)
      • Base: Electron pair donor (e.g., $NH_3$, $H_2O$)

• 4. Ionization & pH Scale

  • Ionic Product of Water ($K_w$)
    • $K_w = [H^+][OH^-] = 1.0 \times 10^{-14}$ at $298\text{ K}$
  • pH Concept
    • $pH = -\log_{10}[H^+]$
    • $pOH = -\log_{10}[OH^-]$
    • $pH + pOH = 14$
    • Acidic: $pH < 7$ | Neutral: $pH = 7$ | Basic: $pH > 7$
  • Ionization Constants
    • Acid Dissociation Constant ($K_a$)
    • Base Dissociation Constant ($K_b$)
    • Ostwald's Dilution Law: $\alpha = \sqrt{K_a/C}$ for weak electrolytes
  • Common Ion Effect
    • Suppression of dissociation of a weak electrolyte by adding a strong electrolyte containing a common ion

• 5. Salt Hydrolysis & Buffer Solutions

  • Salt Hydrolysis
    • Strong Acid + Strong Base: No hydrolysis ($pH = 7$)
    • Weak Acid + Strong Base: Basic solution ($pH > 7$)
    • Strong Acid + Weak Base: Acidic solution ($pH < 7$)
    • Weak Acid + Weak Base: $pH$ depends on $K_a$ and $K_b$
  • Buffer Solutions
    • Resists change in $pH$ upon adding small amount of acid/base
    • Acidic Buffer: Weak acid + its salt with strong base (e.g., $CH_3COOH + CH_3COONa$)
    • Basic Buffer: Weak base + its salt with strong acid (e.g., $NH_4OH + NH_4Cl$)
    • Henderson-Hasselbalch Equation:
      • $pH = pK_a + \log\frac{[\text{Salt}]}{[\text{Acid}]}$

• 6. Solubility Product ($K_{sp}$)

  • Definition
    • Product of concentrations of ions in a saturated solution of a sparingly soluble salt
  • Condition for Precipitation
    • Ionic Product ($Q_{sp}$) < $K_{sp}$: Un-saturated (No precipitate)
    • Ionic Product ($Q_{sp}$) = $K_{sp}$: Saturated (Equilibrium)
    • Ionic Product ($Q_{sp}$) > $K_{sp}$: Precipitation occurs
  • Applications
    • Qualitative inorganic analysis (Group separation)
    • Purification of common salt ($NaCl$)