Equilibrium

Divided into Chemical Equilibrium (Reactions) and Ionic Equilibrium (Acids/Bases). This chapter bridges Thermodynamics and Kinetics. Success here depends on knowing when to make mathematical approximations.

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⚠️ Prerequisites

Thermodynamics: $\Delta G = -RT \ln K$ relationship.
Logarithms: Calculating pH requires fluent log manipulation.
Quadratic Equations: Needed for solving equilibrium concentrations (ICE tables).

🧠 Study Approach

The Art of Approximation: In Ionic Equilibrium, $1 - \alpha \approx 1$ is your best friend. Always check if $K_a < 10^{-3}$; if so, neglect $x$ in the denominator to avoid complex quadratics.

Study Sequence

1. Chemical Equilibrium Basics

Law of Mass Action. Equilibrium Constant ($K_c$ vs $K_p$). Relation: $K_p = K_c(RT)^{\Delta n_g}$. Units of K.

2. Le Chatelier's Principle (CRITICAL)

Effect of concentration, pressure, temperature, and inert gas addition on equilibrium position.
Rule: Equilibrium shifts to undo the change you imposed.

3. Theories of Acids & Bases

Arrhenius vs Bronsted-Lowry (Conjugate Pairs) vs Lewis concept.
Ionic Product of Water ($K_w$): Effect of temperature on pH of neutral water (pH < 7 at high temp).

4. pH Scale & Weak Acids/Bases

Calculating pH for Strong Acids. Ostwald's Dilution Law for Weak Acids ($K_a = C\alpha^2$).
Common Ion Effect: Suppression of dissociation.

5. Salt Hydrolysis

Determining if a salt solution is acidic, basic, or neutral. Formulas for pH of: SA-SB (7), WA-SB (>7), SA-WB (<7), WA-WB (depends on $K_a/K_b$).

6. Buffer Solutions

Acidic vs Basic Buffers. Mechanism of action.
Henderson-Hasselbalch Equation: The most frequent question type in exams.

7. Solubility Product ($K_{sp}$)

Relation between Solubility ($S$) and $K_{sp}$ for various salts (AB, $AB_2$, $A_2B_3$). Condition for precipitation ($Q_{ip} > K_{sp}$). Application of Common Ion Effect on solubility.

🎯 How to Practice

ICE Tables: For Chemical Equilibrium, practice setting up ICE (Initial, Change, Equilibrium) tables. Master writing expressions like $x$, $2x$, or $3x$ based on stoichiometry.

Identify the Solution: Before calculating pH, categorize the mix: Is it Strong Acid? Weak Acid? Buffer? Or Hydrolysis? This categorization is 80% of the solution.

Mental Le Chatelier: Predict shifts instantly without writing. "Add $N_2$ $\to$ System consumes $N_2$ $\to$ Shift Forward".

📝 Quick Revision Formulas

Chemical Equilibrium $$K_p = K_c(RT)^{\Delta n_g}$$ $$\Delta G^\circ = -2.303 RT \log K$$

Weak Acid / Ostwald $$[H^+] = C\alpha = \sqrt{K_a \cdot C}$$ $$pH = \frac{1}{2}(pK_a - \log C)$$

Henderson Equation (Acidic Buffer) $$pH = pK_a + \log \frac{[\text{Salt}]}{[\text{Acid}]}$$

Hydrolysis (WA-SB Salt) $$pH = 7 + \frac{1}{2}(pK_a + \log C)$$

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Lesson Plan: Equilibrium