Chemical Equilibrium: Principles, Calculations, and Applications

Chemical Equilibrium

The Concept of Chemical Equilibrium

Chemical equilibrium is a fundamental concept in chemistry describing a 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. At equilibrium, the system appears static at the macroscopic level, but both reactions continue to occur at the molecular level.

• Dynamic Equilibrium: Both forward and reverse reactions proceed at the same rate.

• Constant Concentrations: The concentrations of all reactants and products remain constant over time at equilibrium.

• Reversibility: Chemical equilibrium can be approached from either direction (starting with reactants or products).

• Example: In a closed container, the reaction N2(g) + 3H2(g) ↔ 2NH3(g) will reach equilibrium regardless of the initial amounts of N2, H2, or NH3.

The Equilibrium Constant

The equilibrium constant (K) quantifies the ratio of product and reactant concentrations at equilibrium for a given reaction at a specific temperature. For a general reaction:

aA + bB ↔ cC + dD

The equilibrium constant expression is:

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

• Kc: Uses concentrations (mol/L).

• Kp: Used for gases, based on partial pressures.

• Unitless: Equilibrium constants are typically reported without units.

• Example: For the Haber process: N2(g) + 3H2(g) ↔ 2NH3(g), $K_c = \frac{[NH_3]^2}{[N_2][H_2]^3}$

Equilibrium Constants in Terms of Pressure (Kp)

For gaseous reactions, the equilibrium constant can be expressed in terms of partial pressures:

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

The relationship between Kp and Kc is given by:

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

where $\Delta n$ is the change in moles of gas (products minus reactants), R is the gas constant, and T is temperature in Kelvin.

Magnitude and Direction of K

• K >> 1: Products are favored at equilibrium.

• K << 1: Reactants are favored at equilibrium.

• Reversing the Reaction: The equilibrium constant for the reverse reaction is the reciprocal of the forward reaction: $K_{reverse} = \frac{1}{K_{forward}}$

• Changing Stoichiometry: If the reaction is multiplied by n, $K_{new} = (K_{original})^n$

• Combining Equilibria: When adding reactions, multiply their equilibrium constants: $K_{overall} = K_1 \times K_2$

Homogeneous vs. Heterogeneous Equilibria

• Homogeneous Equilibrium: All reactants and products are in the same phase (e.g., all gases or all aqueous).

• Heterogeneous Equilibrium: Reactants and products are in different phases (e.g., solids and gases).

• Pure Solids and Liquids: Their concentrations are not included in the equilibrium expression.

• Example: For the decomposition of calcium carbonate: CaCO3(s) ↔ CaO(s) + CO2(g), $K = [CO_2]$

Calculating Equilibrium Constants

To determine the equilibrium constant from experimental data:

1. Tabulate initial and equilibrium concentrations.

2. Calculate the change in concentration for each species.

3. Use stoichiometry to relate changes among all species.

4. Calculate equilibrium concentrations.

5. Substitute values into the equilibrium expression to solve for K.

Reaction Quotient (Q) and Predicting Direction

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

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

• If Q = K: The system is at equilibrium.

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

Calculating Equilibrium Concentrations

Given initial concentrations and K, equilibrium concentrations can be found by:

1. Setting up an ICE (Initial, Change, Equilibrium) table.

2. Expressing changes in terms of a variable (usually x).

3. Substituting equilibrium expressions into the K equation.

4. Solving for x (may require the quadratic formula).

5. Calculating equilibrium concentrations from x.

Le Châtelier’s Principle

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.

• Change in Concentration: Adding a reactant or product shifts equilibrium to consume the added component; removing shifts to replace it.

• Change in Pressure/Volume: For gaseous equilibria, increasing pressure (decreasing volume) shifts equilibrium toward the side with fewer moles of gas; decreasing pressure (increasing volume) shifts toward more moles of gas.

• Change in Temperature: For endothermic reactions, increasing temperature shifts equilibrium toward products (K increases); for exothermic, toward reactants (K decreases).

• Catalysts: Catalysts speed up the attainment of equilibrium but do not affect the equilibrium position or K value.

Summary Table: Effects on Equilibrium

Disturbance	System Response	Effect on K
Add reactant/product	Shifts to consume added component	No change
Remove reactant/product	Shifts to replace removed component	No change
Increase pressure (decrease volume)	Shifts to side with fewer gas moles	No change
Decrease pressure (increase volume)	Shifts to side with more gas moles	No change
Increase temperature (endothermic)	Shifts to products	K increases
Increase temperature (exothermic)	Shifts to reactants	K decreases
Add catalyst	Equilibrium reached faster	No change