Chemical and Ionic Equilibrium

Equilibrium is a dynamic state where forward and reverse reactions occur at equal rates. Understanding equilibrium is crucial for predicting reaction behavior.

Overview

graph TD
    A[Equilibrium] --> B[Chemical Equilibrium]
    A --> C[Ionic Equilibrium]
    B --> B1[Law of Mass Action]
    B --> B2[Le Chatelier's Principle]
    C --> C1[Acids and Bases]
    C --> C2[pH and pOH]
    C --> C3[Buffer Solutions]
    C --> C4[Solubility Product]

Chemical Equilibrium

Dynamic Equilibrium

At equilibrium:

• Rate of forward reaction = Rate of reverse reaction
• Concentrations remain constant
• Process continues at molecular level

Law of Mass Action

For reaction: $aA + bB \rightleftharpoons cC + dD$

$$\boxed{K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}}$$

Equilibrium Constants

In terms of concentration ($K_c$):

$$K_c = \frac{\prod [products]^{coefficients}}{\prod [reactants]^{coefficients}}$$

In terms of partial pressure ($K_p$):

$$K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$$

Relation between $K_p$ and $K_c$:

$$\boxed{K_p = K_c(RT)^{\Delta n_g}}$$

where $\Delta n_g$ = (moles of gaseous products) - (moles of gaseous reactants)

Characteristics of K

Property	Effect on K
Temperature	Changes K
Concentration	No effect
Pressure	No effect
Catalyst	No effect

Reaction Quotient (Q)

$Q$ has same form as $K$ but for non-equilibrium conditions.

• $Q < K$: Reaction proceeds forward
• $Q > K$: Reaction proceeds backward
• $Q = K$: System at equilibrium

Degree of Dissociation (α)

$$\alpha = \frac{\text{amount dissociated}}{\text{initial amount}}$$

For $A \rightleftharpoons B + C$ with initial concentration $C_0$:

$$K_c = \frac{\alpha^2 C_0}{1-\alpha}$$

If $\alpha << 1$:

$$\alpha = \sqrt{\frac{K_c}{C_0}}$$

Le Chatelier’s Principle

When a system at equilibrium is disturbed, it shifts to minimize the disturbance.

Effect of Concentration

• Add reactant → Shifts forward
• Add product → Shifts backward
• Remove reactant → Shifts backward
• Remove product → Shifts forward

Effect of Pressure

• Increase pressure → Shifts towards fewer moles of gas
• Decrease pressure → Shifts towards more moles of gas

Effect of Temperature

• Increase temperature → Shifts in endothermic direction
• Decrease temperature → Shifts in exothermic direction

Effect of Catalyst

• No effect on equilibrium position
• Equilibrium reached faster

graph TD
    A[Le Chatelier's Principle] --> B[Change Concentration]
    A --> C[Change Pressure]
    A --> D[Change Temperature]
    B --> B1[Shifts away from added species]
    C --> C1[Shifts towards fewer gas moles]
    D --> D1[Shifts in endothermic direction on heating]

Ionic Equilibrium

Arrhenius Theory

• Acid: Produces $H^+$ in water
• Base: Produces $OH^-$ in water

Brønsted-Lowry Theory

• Acid: Proton donor
• Base: Proton acceptor

Lewis Theory

• Acid: Electron pair acceptor
• Base: Electron pair donor

Conjugate Acid-Base Pairs

$$HA + B \rightleftharpoons A^- + BH^+$$

• $HA$ and $A^-$ are conjugate acid-base pair
• $B$ and $BH^+$ are conjugate acid-base pair

Ionization of Water

$$H_2O \rightleftharpoons H^+ + OH^-$$

Ionic product of water:

$$\boxed{K_w = [H^+][OH^-] = 10^{-14} \text{ at 25°C}}$$

pH Scale

$$\boxed{pH = -\log[H^+]}$$ $$\boxed{pOH = -\log[OH^-]}$$ $$\boxed{pH + pOH = 14 \text{ (at 25°C)}}$$

Solution	pH	[H⁺]
Acidic	< 7	> 10⁻⁷
Neutral	7	10⁻⁷
Basic	> 7	< 10⁻⁷

Ionization of Weak Acids and Bases

Weak Acid (HA)

$$HA \rightleftharpoons H^+ + A^-$$ $$K_a = \frac{[H^+][A^-]}{[HA]}$$

For initial concentration $C$:

$$[H^+] = \sqrt{K_a \cdot C}$$

(if $\alpha << 1$)

$$\boxed{pH = \frac{1}{2}(pK_a - \log C)}$$

Weak Base (BOH)

$$BOH \rightleftharpoons B^+ + OH^-$$ $$K_b = \frac{[B^+][OH^-]}{[BOH]}$$ $$[OH^-] = \sqrt{K_b \cdot C}$$ $$\boxed{pOH = \frac{1}{2}(pK_b - \log C)}$$

Relation between $K_a$ and $K_b$

$$\boxed{K_a \times K_b = K_w}$$ $$pK_a + pK_b = pK_w = 14$$

Buffer Solutions

Solutions that resist change in pH on addition of small amounts of acid or base.

Acidic Buffer

Weak acid + Salt of weak acid with strong base (e.g., CH₃COOH + CH₃COONa)

$$\boxed{pH = pK_a + \log\frac{[salt]}{[acid]}}$$

(Henderson equation)

Basic Buffer

Weak base + Salt of weak base with strong acid (e.g., NH₄OH + NH₄Cl)

$$\boxed{pOH = pK_b + \log\frac{[salt]}{[base]}}$$

Buffer Capacity

Maximum when $[acid] = [salt]$, i.e., $pH = pK_a$

Hydrolysis of Salts

Salt Type	pH	Example
Strong acid + Strong base	7	NaCl
Strong acid + Weak base	< 7	NH₄Cl
Weak acid + Strong base	> 7	CH₃COONa
Weak acid + Weak base	Depends on $K_a$ and $K_b$	CH₃COONH₄

Solubility Product ($K_{sp}$)

For sparingly soluble salt $A_xB_y$:

$$A_xB_y \rightleftharpoons xA^{y+} + yB^{x-}$$ $$\boxed{K_{sp} = [A^{y+}]^x[B^{x-}]^y}$$

Relationship with Solubility (S)

For $AB$ type: $K_{sp} = S^2$ For $AB_2$ type: $K_{sp} = 4S^3$ For $A_2B_3$ type: $K_{sp} = 108S^5$

Common Ion Effect

Addition of a common ion decreases solubility.

Practice Problems

1. Calculate $K_p$ for $N_2 + 3H_2 \rightleftharpoons 2NH_3$ at 400°C if $K_c = 0.5$ mol⁻² L².

2. Find pH of 0.1 M CH₃COOH solution. ($K_a = 1.8 \times 10^{-5}$)

3. Calculate the pH of a buffer containing 0.1 M acetic acid and 0.15 M sodium acetate. ($pK_a = 4.74$)

4. The $K_{sp}$ of AgCl is $1.8 \times 10^{-10}$. Calculate its solubility in 0.1 M NaCl.

Further Reading

• Chemical Kinetics
• Redox Reactions and Electrochemistry