A reaction has an equilibrium constant of 8.5⨉10³ at 298 K. At 755 K, the equilibrium constant is 55.2. Find ΔH°rxn for the reaction.

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Identify the Van't Hoff equation: \( \ln \left( \frac{K_2}{K_1} \right) = -\frac{\Delta H^\circ_{\text{rxn}}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \).

Assign the given values: \( K_1 = 8.5 \times 10^3 \), \( K_2 = 55.2 \), \( T_1 = 298 \text{ K} \), and \( T_2 = 755 \text{ K} \).

Use the gas constant \( R = 8.314 \text{ J/mol K} \).

Substitute the values into the Van't Hoff equation to solve for \( \Delta H^\circ_{\text{rxn}} \).

Rearrange the equation to isolate \( \Delta H^\circ_{\text{rxn}} \) and solve for it.

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Key Concepts

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

Equilibrium Constant (K)

The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. A higher K value indicates a greater tendency for the reaction to favor products, while a lower K suggests a preference for reactants. Understanding K is essential for analyzing how changes in temperature affect the position of equilibrium.

Van 't Hoff Equation

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

Standard Enthalpy Change (ΔH°rxn)

The standard enthalpy change (ΔH°rxn) is the heat change that occurs when a reaction takes place under standard conditions (1 atm pressure and a specified temperature, usually 298 K). It indicates whether a reaction is exothermic (releases heat, ΔH°rxn < 0) or endothermic (absorbs heat, ΔH°rxn > 0). Knowing ΔH°rxn helps predict how temperature changes will influence the equilibrium position of a reaction.

A reaction has an equilibrium constant of 8.5⨉103 at 298 K. At 755 K, the equilibrium constant is 55.2. Find ΔH°rxn for the reaction.