Use the reaction [tex]I _2(s) \rightleftharpoons I _2(g), \Delta H=62.4 kJ / mol , \Delta S=0.145[/tex] [tex]kJ /( mol \cdot K )[/tex], for this question.
At what temperature is the reaction at equilibrium?
A. 62 K
B. 0.002 K
C. 157 K
D. 430 K
Answer (2)
At equilibrium, the change in Gibbs free energy is zero: Δ G = 0 .
Use the Gibbs free energy equation: Δ G = Δ H − T Δ S .
Solve for the temperature: T = Δ S Δ H .
Substitute the given values and calculate: T = 0.145 62.4 = 430.34 K . The closest answer is 430 K .
Explanation
Problem Analysis We are given the reaction I 2 ( s ) ⇌ I 2 ( g ) with Δ H = 62.4 m o l k J and Δ S = 0.145 m o l ⋅ K k J . We need to find the temperature at which the reaction is at equilibrium.
Gibbs Free Energy Equation At equilibrium, the change in Gibbs free energy, Δ G , is zero. The Gibbs free energy change is given by the equation: Δ G = Δ H − T Δ S where T is the temperature in Kelvin.
Solving for Temperature To find the temperature at equilibrium, we set Δ G = 0 and solve for T : 0 = Δ H − T Δ S Rearranging the equation to isolate T , we get: T = Δ S Δ H
Calculating the Temperature Now, we substitute the given values of Δ H and Δ S into the equation: T = 0.145 m o l ⋅ K k J 62.4 m o l k J Calculating the temperature T : T = 430.34 K
Final Answer Comparing the calculated temperature with the given options, we find that the closest value is 430 K.
Examples
Understanding equilibrium temperature is crucial in various chemical processes. For instance, in the Haber-Bosch process for ammonia synthesis, controlling the temperature is essential to maximize ammonia production. Similarly, in pharmaceutical manufacturing, maintaining the correct temperature ensures the desired reaction occurs efficiently without unwanted side reactions. The concept of equilibrium temperature helps optimize reaction conditions in many industrial and research applications.
The temperature at which the reaction I 2 ( s ) ⇌ I 2 ( g ) is at equilibrium can be calculated using the Gibbs free energy equation. Substituting the values shows that the equilibrium temperature is approximately 430 K. Thus, the chosen option is 430 K.
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