A reaction has an equilibrium constant of 8.5⨉10 3 at 298 K. At 755 K, the equilibrium constant is 55.2. Find ΔH°rxn for the reaction.

Hi everyone here we have a question asking what is the change in entropy of the reaction? For reaction with equilibrium constants of 0.98 at Kelvin and 47.9 at 400 Kelvin. So the natural log of our constant plus the change in in therapy for the reaction Over our gas constant Times one over T one equals delta S. For the reaction over our gas constant Equals the natural log of K two plus the change in entropy for our reaction over our gas constant Times one over T two. So the change in entropy for our reaction Equals the natural log of K two over K one over one over T one -1 over T two times are our K one Equals 0.98. R t one Equals Kelvin. R k two equals 0.9. RT two equals 400 Kelvin. So our change in entropy for our reaction equals the natural log of 47. Over 0. over one over 298 Kelvin -1 over 400 Kelvin, which equals 37, 788.49 Jules. And to change that to kill jules, we're going to move the decimal point to the left three places. So 0.788 kg joules. And we're gonna round that to 38 killed jules. And that is our final answer. Thank you for watching. Bye

Ch.19 - Free Energy & Thermodynamics

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Tro 6th Edition

Ch.19 - Free Energy & Thermodynamics

Problem 86

Chapter 19, Problem 86

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.