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?

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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 \( K_2 \).