Chemical Equilibrium

A state in which the rate of the forward reaction equals the rate of the reverse reaction, resulting in constant concentrations of reactants and products over time.

Definition

Dynamic equilibrium occurs in reversible reactions when:

  • Forward reaction rate = Reverse reaction rate
  • Concentrations of reactants and products remain constant (but not necessarily equal)
  • The system is closed (no exchange with surroundings)
  • Macroscopic properties are constant

Key Concepts

Equilibrium Constant (Kc)

For a general reaction: aA + bB ⇌ cC + dD

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

  • Square brackets denote molar concentrations
  • Pure solids and liquids are omitted (activity = 1)
  • Kc is temperature-dependent only

Equilibrium Constant (Kp)

For gaseous reactions:

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

Relationship between Kc and Kp

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

Where:

  • R = gas constant (0.0821 L·atm/mol·K)
  • T = temperature in Kelvin
  • Δn = moles of gaseous products - moles of gaseous reactants

Reaction Quotient (Q)

Used to predict direction of reaction:

  • Q < K: Reaction proceeds forward (to the right)
  • Q > K: Reaction proceeds backward (to the left)
  • Q = K: System at equilibrium

Le Chatelier's Principle

If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the disturbance.

Factors Affecting Equilibrium

Factor Change Effect on Equilibrium
Concentration Increase reactant Shifts toward products
Pressure Increase (decrease volume) Shifts toward fewer moles of gas
Temperature Increase (exothermic) Shifts toward reactants
Temperature Increase (endothermic) Shifts toward products
Catalyst Add No shift; speeds both directions equally

Magnitude of K

K Value Interpretation
K >> 1 Products favored at equilibrium
K ≈ 1 Significant amounts of both reactants and products
K << 1 Reactants favored at equilibrium

Ionic Equilibria (Acid-Base Equilibrium)

Ionic equilibria describe the reversible dissociation of weak acids and bases in aqueous solution, governed by the same equilibrium principles as $K_c$ and $K_p$.

Auto-Ionisation of Water

Water undergoes auto-ionisation: $$H_2O(l) + H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)$$

The ionic product of water: $$K_w = [H_3O^+][OH^-] = [H^+][OH^-]$$

At 298 K (25 °C): $$K_w = 1.0 \times 10^{-14} \text{ mol}^2 \text{ dm}^{-6}$$

Taking negative logarithms: $$pH + pOH = 14 \quad \text{where} \quad pH = -\log[H^+], \quad pOH = -\log[OH^-]$$

[!note] Temperature Dependence Water ionisation is endothermic, so $K_w$ increases with temperature.

Temperature (°C) $K_w$ (mol² dm⁻⁶)
0 $1.1 \times 10^{-15}$
20 $6.8 \times 10^{-15}$
50 $5.5 \times 10^{-14}$
100 $5.1 \times 10^{-13}$ 
O

[OH3+]

[OH-]

Degree of Dissociation ($\alpha$)

For weak acids and weak bases that only partially dissociate:

Weak acid: $$\alpha = \frac{[H_3O^+]_{\text{eq}}}{[HA]0} \quad \text{or} \quad %\alpha = \frac{[H_3O^+]{\text{eq}}}{[HA]_0} \times 100%$$

Weak base: $$\alpha = \frac{[OH^-]_{\text{eq}}}{[B]0} \quad \text{or} \quad %\alpha = \frac{[OH^-]{\text{eq}}}{[B]_0} \times 100%$$

[!important] Key Properties

  • For weak acids/bases: $\alpha < 1$ (or $%\alpha < 100%$)
  • For strong acids/bases: $\alpha = 1$ (or $%\alpha = 100%$)
  • $\alpha$ is affected by concentration (dilution increases $\alpha$)
  • $K_a$ and $K_b$ are not affected by concentration

Acid and Base Dissociation Constants

Weak acid ($K_a$): $$HA(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + A^-(aq)$$

$$K_a = \frac{[H_3O^+][A^-]}{[HA]} \qquad pK_a = -\log K_a$$

Weak base ($K_b$): $$B(aq) + H_2O(l) \rightleftharpoons BH^+(aq) + OH^-(aq)$$

$$K_b = \frac{[BH^+][OH^-]}{[B]} \qquad pK_b = -\log K_b$$

Relationship between $K_a$ and $K_b$

For a conjugate acid-base pair: $$K_a \times K_b = K_w = 1.0 \times 10^{-14} \text{ (at 25 °C)}$$

$$pK_a + pK_b = 14$$

Relationship between $\alpha$, $K_a$, and $K_b$

When $%\alpha < 10%$ (small dissociation):

Weak acids: $$\alpha = \sqrt{\frac{K_a}{c}}$$

Weak bases: $$\alpha = \sqrt{\frac{K_b}{c}}$$

The degree of dissociation is inversely proportional to the square root of concentration.

[!important] Validity These formulae are only valid when $%\alpha < 10%$.

ICE Table Method and the Assumption

For weak acid/base equilibrium calculations, use an ICE (Initial, Change, Equilibrium) table:

Acid/Base Conjugate $H_3O^+$ / $OH^-$
Initial $C_0$ 0 0
Change $-x$ $+x$ $+x$
Equilibrium $C_0 - x$ $x$ $x$

[!tip] The "x is small" Assumption When $K_a$ or $K_b$ is very small, assume $x \ll C_0$, so: $$C_0 - x \approx C_0$$ This avoids solving a quadratic equation. Always verify by checking if $%\alpha < 10%$.

Example Species

CC(=O)O

CC(=O)[O-]

N

[NH4+]

F

[F-]

O=CO

Oc1ccccc1

Nc1ccccc1

CNC

CN

c1ccncc1

Related Topics

Sources