Chemical Equilibrium: Equilibrium Constants, ICE Tables, and Le Chatelier’s Principle

Chemical Equilibrium

Introduction to Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products over time. The system is dynamic, with reactions continuing to occur at the molecular level.

• Dynamic equilibrium: Both forward and reverse reactions continue, but there is no net change in concentrations.

• Equilibrium position: The relative concentrations of reactants and products at equilibrium.

The Law of Mass Action and Equilibrium Constant Expressions

Law of Mass Action

The law of mass action relates the concentrations of reactants and products at equilibrium to a constant, K, known as the equilibrium constant.

• For a general reaction: aA + bB → cC + dD

The equilibrium constant expression is:

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

• Products are always in the numerator; reactants in the denominator.

• Concentrations are raised to the power of their coefficients in the balanced equation.

Equilibrium Constant for Gaseous Systems (Kp)

For reactions involving gases, the equilibrium constant can also be expressed in terms of partial pressures:

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

• P represents the partial pressure of each gas.

Relationship Between Kc and Kp

The relationship between the equilibrium constant in terms of concentration (Kc) and pressure (Kp) is given by:

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

• R = 0.0821 L·atm/(mol·K) (gas constant)

• T = temperature in Kelvin

• Δn = (moles of gaseous products) − (moles of gaseous reactants)

Manipulating Equilibrium Constants

Change in Reaction	Effect on K
Reaction is reversed	Invert the expression ($K' = 1/K$)
Reaction coefficients are multiplied by n	Raise K to the nth power ($K' = K^n$)
Two reactions are added	Multiply the two K values ($K_{overall} = K_1 \times K_2$)

Heterogeneous Equilibria

For reactions involving solids or pure liquids, their concentrations are not included in the equilibrium expression because their concentrations do not change during the reaction.

• Example: $CO_2(g) + H_2O(l) \rightleftharpoons H_2CO_3(aq)$

• Equilibrium expression: $K = [H_2CO_3]/[CO_2]$

Calculating Equilibrium Concentrations and Partial Pressures

ICE Tables

ICE tables (Initial, Change, Equilibrium) are used to organize and solve equilibrium problems.

• I: Initial concentrations or pressures

• C: Change in concentrations or pressures (usually represented by x)

• E: Equilibrium concentrations or pressures

Example for $2NO_2 \rightleftharpoons N_2O_4$:

	NO2	N2O4
I	1.66	0
C	−2x	+x
E	1.66−2x	x

Substitute equilibrium values into the equilibrium expression and solve for x, often using the quadratic formula if necessary.

$K = \frac{x}{(1.66-2x)^2}$

Reaction Quotient (Q) and Predicting Direction of Reaction

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

• If Q < K: Reaction proceeds forward (toward products).

• If Q > K: Reaction proceeds in reverse (toward reactants).

• If Q = K: System is at equilibrium.

Le Chatelier’s Principle

Effect of Concentration Changes

• Adding reactant shifts equilibrium toward products.

• Removing reactant shifts equilibrium toward reactants.

Effect of Volume/Pressure Changes

• Decreasing volume (increasing pressure) shifts equilibrium toward the side with fewer moles of gas.

• Increasing volume (decreasing pressure) shifts equilibrium toward the side with more moles of gas.

Effect of Temperature Changes

• For exothermic reactions (heat as product): Increasing temperature shifts equilibrium left (toward reactants); K decreases.

• For endothermic reactions (heat as reactant): Increasing temperature shifts equilibrium right (toward products); K increases.

Summary Table: Effects on Equilibrium

Change	Direction of Shift
Add reactant	Toward products
Remove reactant	Toward reactants
Decrease volume	Toward fewer moles of gas
Increase temperature (exothermic)	Toward reactants
Increase temperature (endothermic)	Toward products

Worked Example: Solving for Equilibrium Partial Pressures

Given: $2NO_2 \rightleftharpoons N_2O_4$, initial $P_{NO_2} = 1.66$ atm, $K = 0.125$

• Set up ICE table and equilibrium expression.

• Solve for x using the quadratic formula.

• Choose the physically reasonable value for x.

• Calculate equilibrium partial pressures.

Finding Equilibrium Constants from Experimental Data

Given initial and equilibrium concentrations, substitute values into the equilibrium expression to solve for K.

$K = \frac{[\text{products}]^{\text{coefficients}}}{[\text{reactants}]^{\text{coefficients}}}$

Key Terms

• Equilibrium constant (K): A value that expresses the ratio of product to reactant concentrations at equilibrium.

• Reaction quotient (Q): Calculated like K, but with initial concentrations/pressures.

• ICE table: A tool for organizing equilibrium calculations (Initial, Change, Equilibrium).

• Le Chatelier’s Principle: Predicts how a system at equilibrium responds to disturbances.