The Following Reaction Occurs at 477 K Calculate Kp

What is Kp?

The equilibrium constant (Kp) is a measure of the position of equilibrium in a chemical reaction. It represents the ratio of the partial pressures of the products to the partial pressures of the reactants, each raised to the power of their stoichiometric coefficients.

For a general reaction:

Where P represents the partial pressure of each component.

How to Calculate Kp

To calculate Kp for a reaction at 477 K, you'll need:

• The equilibrium constant at a standard temperature (usually 298 K)
• The change in enthalpy (ΔH) for the reaction
• The universal gas constant (R = 8.314 J/mol·K)

The van't Hoff equation relates Kp to temperature:

Where:

• Kp2 = equilibrium constant at temperature T2
• Kp1 = equilibrium constant at temperature T1
• ΔH = change in enthalpy (J/mol)
• R = gas constant (8.314 J/mol·K)
• T = temperature in Kelvin

Example Calculation

Consider a reaction with Kp = 0.50 at 298 K and ΔH = -50 kJ/mol. Calculate Kp at 477 K.

1. Convert ΔH to J/mol: -50 kJ/mol = -50,000 J/mol
2. Calculate the temperature difference: 1/477 - 1/298 ≈ -0.000626 K^-1
3. Calculate the exponent: -ΔH/R × (1/T2 - 1/T1) = -(-50,000)/(8.314) × (-0.000626) ≈ 3.62
4. Calculate Kp at 477 K: Kp2 = Kp1 × e^3.62 ≈ 0.50 × 37.5 ≈ 18.75

Temperature Dependence

The van't Hoff equation shows that Kp is temperature-dependent:

• For exothermic reactions (ΔH < 0), Kp increases with temperature
• For endothermic reactions (ΔH > 0), Kp decreases with temperature
• The magnitude of change depends on the enthalpy change

This relationship is crucial for understanding reaction behavior under different temperature conditions.