Dynamic Equilibria in Homogeneous Systems

Introduction to Dynamic Equilibrium

• Dynamic Equilibrium: A state where the rate of the forward reaction equals the rate of the reverse reaction. The concentrations of reactants and products remain constant, but the reactions are still occurring.
• Homogeneous Equilibrium: All reactants and products are in the same phase (e.g., all gases or all aqueous solutions).
• Closed System: A system where no reactants or products can enter or leave, essential for establishing equilibrium.

Representation of Equilibrium

• Balanced Chemical Equation: Represents the equilibrium reaction, including states (g, l, s, aq).
  • Example: N2(g) + 3H2(g) <=> 2NH3(g)
• Thermochemical Equation: Includes the enthalpy change (ΔH) of the reaction.
  • Example: N2(g) + 3H2(g) <=> 2NH3(g) ΔH = -92 kJ/mol (exothermic)
• Concentration-Time Graphs: Shows the change in concentration of reactants and products over time, eventually reaching a constant level at equilibrium.

Characteristics of Dynamic Equilibrium

• Reversible Reaction: Reactions that can proceed in both the forward and reverse directions.
• Constant Macroscopic Properties: Observable properties such as color, pressure, and concentration remain constant at equilibrium.
• Dynamic at the Microscopic Level: The forward and reverse reactions continue to occur, maintaining the equilibrium.

Factors Affecting Equilibrium Position

Le Chatelier’s Principle

If a change of condition is applied to a system in equilibrium, the system will shift in a direction that relieves the stress.

• Changes in Temperature:
  • Increasing Temperature: Shifts the equilibrium in the endothermic direction (ΔH > 0).
  • Decreasing Temperature: Shifts the equilibrium in the exothermic direction (ΔH < 0).
• Changes in Concentration:
  • Adding Reactants: Shifts the equilibrium towards the products.
  • Adding Products: Shifts the equilibrium towards the reactants.
  • Removing Reactants: Shifts the equilibrium towards the reactants.
  • Removing Products: Shifts the equilibrium towards the products.
• Changes in Volume (for gaseous systems):
  • Decreasing Volume (Increasing Pressure): Shifts the equilibrium towards the side with fewer moles of gas.
  • Increasing Volume (Decreasing Pressure): Shifts the equilibrium towards the side with more moles of gas.

Concentration-Time Graphs and Equilibrium Shifts

• Show how concentrations change when the equilibrium is disturbed.
• The system will eventually re-establish equilibrium, but the new equilibrium concentrations may differ from the original.

Equilibrium Constant (K)

Equilibrium Expression

• A mathematical expression that relates the concentrations of reactants and products at equilibrium.
• For the general reaction: aA + bB <=> cC + dD
• The equilibrium constant is: \(K = \frac{[C]^c[D]^d}{[A]^a[B]^b}\)
• [A], [B], [C], [D] are the equilibrium concentrations of reactants and products.
• a, b, c, d are the stoichiometric coefficients from the balanced equation.

Magnitude of K

• Large K: Indicates that the equilibrium favors the products; the reaction proceeds nearly to completion.
• Small K: Indicates that the equilibrium favors the reactants; very little product is formed.
• K ≈ 1: Indicates that significant amounts of both reactants and products are present at equilibrium.

Temperature Dependence of K

• The value of K is temperature-dependent. Changing the temperature will change the value of K.
• For exothermic reactions, K decreases with increasing temperature.
• For endothermic reactions, K increases with increasing temperature.

Units of K

• The units of K depend on the specific equilibrium expression.
• Calculate by substituting the units of concentration (e.g., M) into the equilibrium expression and simplifying.

Reaction Quotient (Q)

Definition

• A measure of the relative amounts of products and reactants present in a reaction at any given time.
• Calculated using the same expression as K, but with non-equilibrium concentrations.
• \(Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}\) (using current concentrations)

Comparing Q and K

• Q < K: The ratio of products to reactants is less than at equilibrium. The reaction will proceed in the forward direction to reach equilibrium.
• Q > K: The ratio of products to reactants is greater than at equilibrium. The reaction will proceed in the reverse direction to reach equilibrium.
• Q = K: The system is at equilibrium.

Calculations Involving Equilibrium

ICE Tables

• A systematic way to calculate equilibrium concentrations.
• Initial concentrations
• Change in concentrations
• Equilibrium concentrations

Steps for Equilibrium Calculations

1. Write the balanced chemical equation.
2. Write the equilibrium expression.
3. Set up an ICE table.
4. Calculate the change in concentrations using stoichiometry.
5. Calculate the equilibrium concentrations.
6. Substitute the equilibrium concentrations into the equilibrium expression to calculate K or Q.

Application of Le Chatelier’s Principle to Optimise Yield

• Optimising Yield: Adjusting conditions to favor the formation of products.
• Industrial Processes: Le Chatelier’s principle is used to optimise conditions in industrial processes to maximise product yield and minimise costs.
• Example: Haber-Bosch process for ammonia synthesis (N2 + 3H2 <=> 2NH3) uses high pressure and moderate temperature to favor ammonia formation.

Key Terms

• Dynamic Equilibrium
• Homogeneous Equilibrium
• Le Chatelier’s Principle
• Equilibrium Constant (K)
• Reaction Quotient (Q)
• Equilibrium Expression
• Concentration-Time Graph

Summary

Understanding dynamic equilibria is crucial for optimising chemical reactions. By applying Le Chatelier’s principle and using equilibrium expressions, we can predict and control the yield of chemical reactions in various systems.