A reaction has an equilibrium constant of 8.5⨉10 3 at 298 K. At 755 K, the equilibrium constant is 0.65. 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.18 - Free Energy and Thermodynamics

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Tro 4th Edition

Ch.18 - Free Energy and Thermodynamics

Problem 82

Chapter 18, Problem 82

A reaction has an equilibrium constant of 8.5⨉10³ at 298 K. At 755 K, the equilibrium constant is 0.65. Find ΔH°_rxnfor the reaction.

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First, we need to understand that the relationship between the equilibrium constant (K), the change in enthalpy of the reaction (ΔH°rxn), and the temperature (T) is given by the Van't Hoff equation: \(\ln\frac{K_2}{K_1} = -\frac{\Delta H°_{rxn}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)\), where R is the gas constant (8.314 J/(mol·K)).

Next, we substitute the given values into the Van't Hoff equation. Here, \(K_1 = 8.5\times10^3\), \(K_2 = 0.65\), \(T_1 = 298 K\), and \(T_2 = 755 K\).

Then, we solve the equation for ΔH°rxn. This involves isolating ΔH°rxn on one side of the equation.

After that, we calculate the value of \(\frac{1}{T_2} - \frac{1}{T_1}\) and \(\ln\frac{K_2}{K_1}\).

Finally, we substitute these calculated values back into the equation to find the value of ΔH°rxn.

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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 high K value indicates that products are favored, while a low K value suggests that reactants are favored. Understanding K is essential for analyzing how temperature changes 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 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 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). This concept is vital for understanding the energy dynamics of chemical reactions.

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Our atmosphere is composed primarily of nitrogen and oxygen, which coexist at 25 °C without reacting to any significant extent. However, the two gases can react to form nitrogen monoxide according to the reaction: N2(g) + O2(g) → 2 NO(g). a. Calculate ΔG° and Kp for this reaction at 298 K. Is the reaction spontaneous? b. Estimate ΔG° at 2000 K. Does the reaction become more spontaneous as temperature increases?

A reaction has an equilibrium constant of 8.5⨉103 at 298 K. At 755 K, the equilibrium constant is 0.65. Find ΔH°rxn for the reaction.

Verified Solution

Key Concepts

Equilibrium Constant (K)

Van 't Hoff Equation

Standard Enthalpy Change (ΔH°rxn)

A reaction has an equilibrium constant of 8.5⨉10³ at 298 K. At 755 K, the equilibrium constant is 0.65. Find ΔH°_rxnfor the reaction.