Calculate The Equilibrium Constant of The Following Reaction at 25

How to Calculate the Equilibrium Constant

The equilibrium constant (K) of a reaction is a measure of the ratio of product concentrations to reactant concentrations at equilibrium. For reactions where the number of moles of gas changes, the equilibrium constant is temperature-dependent.

To calculate K at 25°C (298.15 K), you'll need:

• The equilibrium constant at a different temperature (K₁)
• The initial temperature (T₁ in Kelvin)
• The change in enthalpy (ΔH) of the reaction
• The universal gas constant (R = 8.314 J·mol⁻¹·K⁻¹)

The Van't Hoff equation relates these quantities to find K at 25°C.

The Van't Hoff Equation

Where:

• K₂ = Equilibrium constant at 25°C (298.15 K)
• K₁ = Equilibrium constant at initial temperature
• ΔH = Change in enthalpy (J/mol)
• R = Universal gas constant (8.314 J·mol⁻¹·K⁻¹)
• T₂ = Final temperature (298.15 K)
• T₁ = Initial temperature (K)

Worked Example

Consider a reaction where K₁ = 0.5 at 50°C (323.15 K) and ΔH = -20,000 J/mol. Calculate K₂ at 25°C (298.15 K).

1. Convert temperatures to Kelvin: T₁ = 323.15 K, T₂ = 298.15 K
2. Plug values into the Van't Hoff equation:
   ln(K₂/0.5) = -(-20,000)/(8.314) × (1/298.15 - 1/323.15)
3. Calculate the right side:
   = 2404.5 × (0.00336 - 0.00309) = 2404.5 × 0.00027 ≈ 0.649
4. Solve for K₂:
   K₂ = 0.5 × e^0.649 ≈ 0.5 × 1.913 ≈ 0.9565

The equilibrium constant at 25°C is approximately 0.9565.

Interpreting the Results

The equilibrium constant tells you:

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

For the example above (K ≈ 0.9565), reactants are slightly favored at 25°C compared to 50°C.