Calculate The Equilibrium Constant at for The Following Reaction

Introduction

Chemical equilibrium is a state where the concentrations of reactants and products remain constant over time. The equilibrium constant (K) quantifies this balance. However, K is temperature-dependent, which is where the van't Hoff equation comes into play.

The van't Hoff equation relates the equilibrium constant at two different temperatures. This allows chemists to predict how changes in temperature will affect the equilibrium position of a reaction.

The van't Hoff Equation

The van't Hoff equation is expressed as:

This equation shows that the natural logarithm of the ratio of equilibrium constants is proportional to the inverse of temperature, with the proportionality constant being ΔH°/R.

Worked Example

Let's calculate the equilibrium constant at 300 K for a reaction where K at 298 K is 1.5, ΔH° is -50 kJ/mol, and R is 8.314 J/mol·K.

1. Convert ΔH° to J/mol: -50 kJ/mol × 1000 = -50,000 J/mol
2. Calculate the temperature terms: 1/298 = 0.003356, 1/300 = 0.003333
3. Plug values into the equation: ln(K₂/1.5) = (-50,000/8.314)(0.003356 - 0.003333)
4. Calculate the difference: 0.003356 - 0.003333 = 0.000023
5. Calculate the proportionality term: -50,000/8.314 ≈ -6012.5
6. Multiply: -6012.5 × 0.000023 ≈ -0.1383
7. Exponentiate to solve for K₂: K₂ = 1.5 × e^(-0.1383) ≈ 1.5 × 0.871 ≈ 1.307

The equilibrium constant at 300 K is approximately 1.307.

Interpreting Results

The equilibrium constant tells you:

• If K > 1: Products are favored at equilibrium
• If K = 1: Equal amounts of reactants and products
• If K < 1: Reactants are favored at equilibrium

For exothermic reactions (ΔH° < 0), increasing temperature shifts equilibrium toward reactants. For endothermic reactions (ΔH° > 0), increasing temperature shifts equilibrium toward products.