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The [tex]$\Delta H$[/tex] for a reaction is [tex]$-2 kJ / mol$[/tex], and the [tex]$\Delta S$[/tex] is [tex]$-100 J /(mol * K)$[/tex]. At what temperature will the reaction go forward?
1) Under 20 K
2) Over 20 K
3) Over 200 K
4) Under 200 K
Answer (1)
We are given Δ H = − 2000 J/mol and Δ S = − 100 J/(mol K) .
We want to find the temperature T such that Δ G < 0 , where Δ G = Δ H − T Δ S .
Substituting the given values, we have − 2000 − T ( − 100 ) < 0 .
Solving for T , we get T < 20 K . Therefore, the final answer is Under 20 K .
Explanation
Understanding the Problem We are given the enthalpy change ( Δ H ) and entropy change ( Δ S ) for a reaction and asked to find the temperature at which the reaction will proceed forward. A reaction proceeds forward when the Gibbs free energy change ( Δ G ) is negative. We can use the Gibbs free energy equation to determine the temperature range.
Gibbs Free Energy Equation The Gibbs free energy equation is: Δ G = Δ H − T Δ S where: - Δ G is the Gibbs free energy change, - Δ H is the enthalpy change, - T is the temperature in Kelvin, - Δ S is the entropy change. For the reaction to proceed forward, Δ G < 0 .
Given Values We are given: - Δ H = − 2 kJ/mol = − 2000 J/mol - Δ S = − 100 J/(mol K) We want to find the temperature T such that Δ G < 0 .
Substitution Substitute the given values into the Gibbs free energy equation: − 2000 J/mol − T ( − 100 J/(mol K) ) < 0 Simplify the inequality: − 2000 + 100 T < 0
Solving for Temperature Solve for T : 100 T < 2000 T < 100 2000 T < 20 K Therefore, the reaction will go forward when the temperature is under 20 K.
Final Answer The reaction will proceed forward (i.e., be spontaneous) when the temperature is under 20 K.
Examples
Understanding the spontaneity of chemical reactions is crucial in various real-world applications. For instance, in designing industrial chemical processes, controlling the temperature is essential to ensure reactions proceed efficiently and safely. Similarly, in environmental science, predicting the behavior of pollutants or the degradation of materials often relies on understanding the temperature dependence of chemical reactions. By manipulating temperature, we can optimize reaction yields, minimize unwanted byproducts, and control the rate at which reactions occur, leading to more sustainable and cost-effective solutions.
