Introduction to Chemical Equilibrium

Chemical equilibrium represents a fascinating state where forward and reverse reactions occur at equal rates. This dynamic balance creates stable concentrations of reactants and products, making it crucial for understanding countless chemical processes in nature and industry.

What Makes Chemical Equilibrium Special?

Chemical equilibrium occurs when the rate of forward reaction equals the rate of reverse reaction. At this point, concentrations remain constant, though molecules continue reacting dynamically.

Key Characteristics of Chemical Equilibrium:

  • Dynamic process with continuous molecular motion
  • Constant concentrations of all species
  • Equal forward and reverse reaction rates
  • Achievable from either reaction direction
  • Temperature-dependent equilibrium position

General Equilibrium Expressions and Constants

Understanding equilibrium expressions forms the foundation for quantitative analysis of chemical equilibrium. These mathematical relationships help predict reaction behavior and calculate equilibrium concentrations.

The Equilibrium Constant Expression

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

Kc = [C]c[D]d / [A]a[B]b

Example: Haber Process

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Equilibrium expression:

Kc = [NH₃]² / [N₂][H₂]³

Types of Equilibrium Constants

  • Kc: Concentration-based equilibrium constant
  • Kp: Pressure-based equilibrium constant for gases
  • Ka: Acid dissociation constant
  • Kb: Base dissociation constant
  • Ksp: Solubility product constant

Reaction Quotient: Predicting Equilibrium Direction

The reaction quotient (Q) uses the same mathematical form as the equilibrium constant but applies to any moment during the reaction. Comparing Q with K reveals which direction the reaction will proceed.

Qc = [C]c[D]d / [A]a[B]b

Predicting Reaction Direction:

  • Q < K: Reaction proceeds forward (→)
  • Q = K: System at equilibrium
  • Q > K: Reaction proceeds reverse (←)

Real-World Examples of Chemical Equilibrium

1. Hemoglobin-Oxygen Equilibrium

Hb + 4O₂ ⇌ Hb(O₂)₄

This equilibrium enables oxygen transport in blood. High oxygen concentrations in lungs favor forward reaction, while low concentrations in tissues favor reverse reaction.

2. Carbonic Acid Equilibrium

CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻

This equilibrium system maintains blood pH and enables CO₂ transport from tissues to lungs.

3. Industrial Ammonia Production

N₂(g) + 3H₂(g) ⇌ 2NH₃(g) + heat

The Haber process demonstrates how temperature and pressure manipulation optimizes ammonia production for fertilizers.

Le Chatelier’s Principle: Predicting Equilibrium Shifts

Le Chatelier’s principle states that when stress is applied to a system at equilibrium, the system responds by shifting to counteract that stress and restore equilibrium.

Types of Stress and System Response:

  • Concentration changes: System shifts away from added species
  • Temperature changes: System shifts to absorb or release heat
  • Pressure changes: System shifts toward fewer gas molecules
  • Volume changes: System shifts to counteract pressure effects

Effect of Temperature on Chemical Equilibrium

Temperature changes affect equilibrium position based on reaction enthalpy:

  • Exothermic reactions: Higher temperature shifts equilibrium left
  • Endothermic reactions: Higher temperature shifts equilibrium right

Example: Effect of Temperature on N₂O₄ ⇌ 2NO₂

N₂O₄(g) ⇌ 2NO₂(g) ΔH = +58 kJ/mol

This endothermic reaction shifts right when heated (more brown NO₂ forms) and left when cooled (more colorless N₂O₄ forms).

Numerical Problems: Mastering Chemical Equilibrium Calculations

Problem 1: Calculating Equilibrium Constant

Question: For the reaction H₂(g) + I₂(g) ⇌ 2HI(g), equilibrium concentrations are: [H₂] = 0.20 M, [I₂] = 0.15 M, [HI] = 1.2 M. Calculate Kc.

Solution:

  1. Write the equilibrium expression: Kc = [HI]² / [H₂][I₂]
  2. Substitute values: Kc = (1.2)² / (0.20)(0.15)
  3. Calculate: Kc = 1.44 / 0.030 = 48

Answer: Kc = 48

Problem 2: ICE Table Calculation

Question: For PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), Kc = 0.042 at 500K. If initial [PCl₅] = 2.0 M, find equilibrium concentrations.

Solution using ICE Table:

PCl₅PCl₃Cl₂
I2.000
C-x+x+x
E2.0-xxx
  1. Kc = [PCl₃][Cl₂] / [PCl₅] = x² / (2.0-x) = 0.042
  2. x² = 0.042(2.0-x) = 0.084 – 0.042x
  3. x² + 0.042x – 0.084 = 0
  4. Using quadratic formula: x = 0.27 M

Answer: [PCl₅] = 1.73 M, [PCl₃] = [Cl₂] = 0.27 M

Problem 3: Le Chatelier’s Principle Application

Question: For the exothermic reaction 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), predict the effect of: (a) increasing temperature, (b) adding SO₂, (c) decreasing pressure.

Solution:

  1. (a) Increasing temperature: Equilibrium shifts left (endothermic direction) to absorb excess heat. Less SO₃ forms.
  2. (b) Adding SO₂: Equilibrium shifts right to consume excess SO₂. More SO₃ forms.
  3. (c) Decreasing pressure: Equilibrium shifts left toward more gas molecules (3 moles vs 2 moles). Less SO₃ forms.

Advanced Chemical Equilibrium Concepts

Relationship Between Kc and Kp

Kp = Kc(RT)Δn

Where Δn = (moles of gaseous products) – (moles of gaseous reactants)

Temperature Dependence of Equilibrium Constants

ln(K₂/K₁) = -ΔH°/R × (1/T₂ – 1/T₁)

This Van’t Hoff equation relates equilibrium constants at different temperatures to reaction enthalpy.

Important References: