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Ch.18 - Free Energy and Thermodynamics
Chapter 18, Problem 81

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: \( \ln \left( \frac{K_2}{K_1} \right) = -\frac{\Delta H_{\text{rxn}}^\circ}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \).
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 \( T_2 = 655 \text{ K} \).
Convert \( \Delta H_{\text{rxn}}^\circ \) from kJ/mol to J/mol by multiplying by 1000.
Use the gas constant \( R = 8.314 \text{ J/mol K} \) in the equation.
Solve for \( K_2 \) by calculating \( \ln \left( \frac{K_2}{K_1} \right) \) and then exponentiating to find \( K_2 \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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Equilibrium Constant K

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.
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Van der Waals Equation