Equilibrium Expressions: Calculations and Units

Introduction

This section covers calculations involving equilibrium expressions (including units) for a closed homogeneous equilibrium system. It also discusses the dependence of the equilibrium constant (K) value on the system temperature and the equation used to represent the reaction.

Key Definitions

• Equilibrium: A state where the rate of the forward reaction equals the rate of the reverse reaction.
• Closed System: A system where no matter can enter or leave, but energy can.
• Homogeneous Equilibrium: An equilibrium where all reactants and products are in the same phase (e.g., all gases or all aqueous solutions).
• Equilibrium Constant (K): A value that expresses the ratio of products to reactants at equilibrium. It indicates the extent to which a reaction will proceed to completion.
• Reaction Quotient (Q): A measure of the relative amounts of products and reactants present in a reaction at any given time. It predicts the direction the reaction will shift to reach equilibrium.

Equilibrium Expression

For a general reversible reaction:

$$aA + bB
ightleftharpoons cC + dD$$

The equilibrium expression is:

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

Where:
* [A], [B], [C], and [D] are the equilibrium concentrations of reactants and products, usually expressed in mol L⁻¹ (M).
* a, b, c, and d are the stoichiometric coefficients from the balanced chemical equation.

Calculating K

1. Write the balanced chemical equation.
2. Write the equilibrium expression.
3. Determine the equilibrium concentrations of all reactants and products. This may be given directly, or you may need to calculate it using an ICE table (Initial, Change, Equilibrium).
4. Substitute the equilibrium concentrations into the equilibrium expression and solve for K.

Units of K

The units of K depend on the specific equilibrium expression. To determine the units:

1. Write the equilibrium expression.
2. Substitute the concentration unit (M or mol L⁻¹) for each concentration term.
3. Simplify the expression.

Example:
For the reaction: $N_2(g) + 3H_2(g)
ightleftharpoons 2NH_3(g)$

$$K = \frac{[NH_3]^2}{[N_2][H_2]^3}$$

Substituting units:

$$K = \frac{(mol L^{-1})^2}{(mol L^{-1})(mol L^{-1})^3} = \frac{(mol L^{-1})^2}{(mol L^{-1})^4} = (mol L^{-1})^{-2} = L^2 mol^{-2}$$

Therefore, the units of K for this reaction are L² mol⁻².

Dependence of K on Temperature

The value of K is temperature-dependent.
* For exothermic reactions (ΔH < 0), K decreases as temperature increases.
* For endothermic reactions (ΔH > 0), K increases as temperature increases.

This relationship is governed by Le Chatelier’s principle: increasing the temperature favors the reaction that absorbs heat (endothermic), shifting the equilibrium and changing the ratio of products to reactants.

Dependence of K on the Equation

The value of K depends on how the balanced chemical equation is written.

• Reversing the equation: If you reverse the direction of the reaction, the new equilibrium constant (K’) is the reciprocal of the original K: $K’ = \frac{1}{K}$
• Multiplying the equation by a factor: If you multiply the entire equation by a factor ‘n’, the new equilibrium constant (K’) is the original K raised to the power of ‘n’: $K’ = K^n$

Reaction Quotient (Q)

• Q is calculated using the same expression as K, but with initial or non-equilibrium concentrations.

• Q is used to predict the direction a reaction will shift to reach equilibrium.

  • If Q < K: The ratio of products to reactants is too small. The reaction will shift to the right (towards products) to reach equilibrium.
  • If Q > K: The ratio of products to reactants is too large. The reaction will shift to the left (towards reactants) to reach equilibrium.
  • If Q = K: The system is at equilibrium.

Summary

Understanding equilibrium expressions, including how to calculate K, determine its units, and interpret its dependence on temperature and the reaction equation, is crucial for predicting and controlling the extent of chemical reactions. The reaction quotient, Q, provides a valuable tool for assessing the direction a reaction will proceed to reach equilibrium.