The change in enthalpy (ΔH°_rxn) for a reaction is -25.8 kJ/mol. The equilibrium constant for the reaction is 1.4⨉10³ at 298 K. What is the equilibrium constant for the reaction at 655 K?

Verified step by step guidance

1. Identify the relationship between the equilibrium constant and temperature using the van 't Hoff equation: \( \ln \left( \frac{K_2}{K_1} \right) = -\frac{\Delta H_{\text{rxn}}^\circ}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \).
2. Substitute the given values into the van 't Hoff equation: \( K_1 = 1.4 \times 10^3 \), \( \Delta H_{\text{rxn}}^\circ = -25.8 \text{ kJ/mol} \) (convert to J/mol), \( T_1 = 298 \text{ K} \), and \( T_2 = 655 \text{ K} \).
3. Convert \( \Delta H_{\text{rxn}}^\circ \) from kJ/mol to J/mol by multiplying by 1000.
4. Use the gas constant \( R = 8.314 \text{ J/mol K} \) in the equation.
5. Solve for \( K_2 \) by calculating \( \ln \left( \frac{K_2}{K_1} \right) \) and then exponentiating to find \( K_2 \).

Key Concepts

Enthalpy Change (ΔH°)

Enthalpy change (ΔH°) is a measure of the heat absorbed or released during a chemical reaction at constant pressure. A negative ΔH° indicates that the reaction is exothermic, meaning it releases heat. This value is crucial for understanding how temperature affects the position of equilibrium in a reaction.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It provides insight into the extent of a reaction and is temperature-dependent, meaning that changes in temperature can alter its value significantly.

Van 't Hoff Equation

The Van 't Hoff equation relates the change in the equilibrium constant (K) with temperature (T) and the enthalpy change (ΔH°) of a reaction. It is expressed as ln(K2/K1) = -ΔH°/R(1/T2 - 1/T1), where R is the gas constant. This equation is essential for calculating the equilibrium constant at different temperatures.