Ch. 5 - Chemical Reaction Analysis: Thermodynamics and Kinetics

Mullins - Organic Chemistry: A Learner Centered Approach 1st Edition

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Mullins 1st Edition

Ch. 5 - Chemical Reaction Analysis: Thermodynamics and Kinetics

Problem 12a

Chapter 4, Problem 12a

At what temperature does the entropy change of a process not contribute to the favorability of a process?

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Understand the relationship between Gibbs free energy (ΔG), enthalpy change (ΔH), entropy change (ΔS), and temperature (T) using the equation ΔG = ΔH - TΔS.

Recognize that the entropy change (ΔS) does not contribute to the favorability of a process when the term TΔS becomes zero. This happens when T = 0 Kelvin.

Recall that at absolute zero (0 Kelvin), molecular motion ceases, and entropy is at its minimum value, meaning entropy change does not influence the process.

Consider the practical implications: While this is a theoretical concept, real-world processes do not occur at 0 Kelvin due to the third law of thermodynamics, which states that absolute zero is unattainable.

Conclude that the temperature at which entropy change does not contribute to favorability is 0 Kelvin, but this is a theoretical limit rather than a practical condition.

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Key Concepts

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

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of ways a system can be arranged, with higher entropy indicating greater disorder. Entropy changes during a process can influence its spontaneity, as systems tend to evolve towards states of higher entropy.

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the favorability of a process at constant temperature and pressure. The change in Gibbs Free Energy (ΔG) is calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A process is spontaneous when ΔG is negative.

Temperature's Role in Entropy and Favorability

Temperature plays a crucial role in determining the impact of entropy on the favorability of a process. At absolute zero (0 K), the entropy change becomes negligible, and thus, the contribution of entropy to the Gibbs Free Energy equation is minimal. As temperature increases, the influence of entropy on spontaneity becomes more significant, particularly when ΔS is positive.

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Related Practice

Textbook Question

For the following values of ∆H° , ∆S°, and T, tell whether the process would be favored.

(b) ∆H° = +7.34 kcal/mol ; ∆S° = +43 cal/mol•K ; T = 325 K

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Textbook Question

Which of the following carbocations would you expect to undergo rearrangement?

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Textbook Question

For the following values of ∆H° , ∆S°, and T, tell whether the process would be favored.

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Textbook Question

A certain process has ∆H° = 11.7 kcal/mol and AS° = +33cal/mol•K . That is, this reaction has an unfavorable enthalpy but a favorable entropy term. At what temperature will the process be neither favored nor disfavored?

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Textbook Question

For the following values of ∆H° , ∆S°, and T, tell whether the process would be favored.

(d) ∆H° = -8.3 kcal/mol ; ∆S° = -12 cal/mol•K ; T = 298 K

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Textbook Question

Considering the process described in Assessment 5.13, will it be favored or disfavored at a temperature higher than the one you calculated? How about at a temperature below what you calculated?

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