Chemical Equilibrium and Le Châtelier’s Principle

Chemical Equilibrium

Introduction to Equilibrium

Chemical equilibrium is a fundamental concept in chemistry describing the state in which the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products. This dynamic process is central to understanding how chemical systems respond to changes in conditions.

• Dynamic Equilibrium: Both forward and reverse reactions continue to occur, but at equal rates, so concentrations remain constant.

• Example: The decomposition and formation of dinitrogen tetroxide and nitrogen dioxide: $\mathrm{N_2O_4 (g) \rightleftharpoons 2NO_2 (g)}$

Reversible Reactions

Many chemical reactions are reversible, meaning they can proceed in both the forward and reverse directions. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction.

• Representation: $\mathrm{A \rightleftharpoons B}$

• Dynamic Nature: Molecules are constantly reacting, but the overall concentrations do not change.

Equilibrium Constants

Equilibrium Constant Expressions

The equilibrium constant ($K$) quantifies the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their stoichiometric coefficients.

• General Form: For a reaction $aA + bB \rightleftharpoons cC + dD$:

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

• Writing Expressions: Only include species in the gas or aqueous phase; pure solids and liquids are omitted.

Equilibrium Constant for Gases ($K_p$)

For reactions involving gases, the equilibrium constant can be expressed in terms of partial pressures ($K_p$):

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

• Relationship between $K_p$ and $K_c$: $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the change in moles of gas.

Reaction Quotient ($Q$)

The reaction quotient ($Q$) is calculated using the same expression as $K$, but with initial (not necessarily equilibrium) concentrations or pressures.

• Comparison: If $Q < K$, the reaction proceeds forward; if $Q > K$, it proceeds in reverse; if $Q = K$, the system is at equilibrium.

Le Châtelier’s Principle

Definition and Application

Le Châtelier’s Principle states that if a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, the system will shift its equilibrium position to counteract the disturbance.

• Concentration: Adding reactants shifts equilibrium toward products; removing reactants shifts toward reactants.

• Pressure: Increasing pressure (by decreasing volume) shifts equilibrium toward the side with fewer moles of gas.

• Temperature: Increasing temperature favors the endothermic direction; decreasing temperature favors the exothermic direction.

Examples and Applications

• Haber Process: The synthesis of ammonia ($\mathrm{N_2 + 3H_2 \rightleftharpoons 2NH_3}$) is optimized by manipulating pressure and temperature according to Le Châtelier’s Principle.

Equilibrium Calculations

Solving for Equilibrium Concentrations

To determine equilibrium concentrations, set up an ICE (Initial, Change, Equilibrium) table and solve for unknowns using the equilibrium constant expression.

• Steps:

  1. Write the balanced equation and $K$ expression.

  2. Set up the ICE table.

  3. Substitute values and solve for $x$ (the change in concentration).

  4. Check assumptions (e.g., if $K$ is very small, the change may be negligible).

Assumptions in Calculations

• If $K$ is very small and the initial concentration is much larger than the change, the change can be neglected for simplification.

• Check that the assumption is valid by ensuring the change is less than 5% of the initial concentration.

Summary Table: Effects of Changes on Equilibrium

Change	System Response
Increase [Reactant]	Shifts toward products
Increase [Product]	Shifts toward reactants
Increase Pressure (decrease volume)	Shifts toward side with fewer moles of gas
Increase Temperature (endothermic)	Shifts toward products
Increase Temperature (exothermic)	Shifts toward reactants

Key Terms

• Equilibrium Constant ($K$): A numerical value expressing the ratio of product to reactant concentrations at equilibrium.

• Le Châtelier’s Principle: The rule predicting how a system at equilibrium responds to disturbances.

• Reaction Quotient ($Q$): The ratio of concentrations or pressures at any point, used to predict the direction of shift to reach equilibrium.

• ICE Table: A tool for organizing initial, change, and equilibrium concentrations in equilibrium calculations.

Additional info: These notes are based on lecture slides and include expanded explanations, definitions, and examples for clarity and completeness.