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 13a

Chapter 4, Problem 13a

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?

Verified step by step guidance

Identify the condition for a process to be neither favored nor disfavored. This occurs when the Gibbs free energy change (∆G°) is equal to zero. The equation for Gibbs free energy is:

∆G° = ∆H° - T∆S°

Set ∆G° to zero in the equation:

0 = ∆H° - T∆S°

. Rearrange the equation to solve for temperature (T):

T = ∆H° / ∆S°

Convert the units of ∆H° and ∆S° to ensure consistency. ∆H° is given in kcal/mol, so convert it to cal/mol:

∆H° = 11.7 \, \(\text{kcal/mol}\) \, × \, 1000 \, \(\text{cal/kcal}\) = 11700 \, \(\text{cal/mol}\)

. ∆S° is already in cal/mol·K, so no conversion is needed.

Substitute the values of ∆H° and ∆S° into the equation for T:

T = 11700 \, \(\text{cal/mol}\) / 33 \, \(\text{cal/mol·K}\)

Perform the division to calculate the temperature (T) in Kelvin. This will give the temperature at which the process is neither favored nor disfavored.

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Key Concepts

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

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the favorability of a reaction at constant temperature and pressure. It is defined by the equation G = ∆H - T∆S, where ∆H is the change in enthalpy, T is the temperature in Kelvin, and ∆S is the change in entropy. A reaction is spontaneous when G is negative, indicating that the process can occur without external energy input.

Enthalpy (∆H)

Enthalpy (∆H) is a measure of the total heat content of a system. In the context of a chemical reaction, a positive ∆H indicates that the reaction absorbs heat from the surroundings, making it endothermic. This can lead to an unfavorable reaction under certain conditions, as it requires energy input to proceed.

Entropy (∆S)

Entropy (∆S) is a measure of the disorder or randomness in a system. A positive change in entropy suggests that the products of a reaction are more disordered than the reactants, which is generally favorable for spontaneity. In the Gibbs Free Energy equation, a favorable entropy can offset an unfavorable enthalpy, influencing the overall spontaneity of the reaction at different temperatures.

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Related Practice

Textbook Question

Calculate ∆H° for the following equilibrium processes.

(a)

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Textbook Question

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

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Textbook Question

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

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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

Calculate ∆H° for the following equilibrium processes.

(b)

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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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