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 7b

Chapter 4, Problem 7b

For the following equilibrium processes and the corresponding ∆G° , indicate whether you expect the equilibrium constant to be greater than, equal to, or less than 1. Justify your expectation in words.
(b)

Verified step by step guidance

Step 1: Understand the relationship between Gibbs free energy change (∆G°) and the equilibrium constant (K). The equation that connects these two is ΔG° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin.

Step 2: Analyze the given ∆G° value. In this case, ∆G° = 0.0 kcal/mol. This indicates that there is no free energy difference between the reactants and products.

Step 3: Interpret the equilibrium constant (K) based on ∆G°. When ∆G° = 0, the equation ΔG° = -RT ln(K) simplifies to ln(K) = 0, which means K = 1.

Step 4: Consider the chemical structures provided. The two structures are conformational isomers (chair conformations of cyclohexane with a methyl group in axial and equatorial positions). Since ∆G° = 0, both conformations are equally stable, and the equilibrium constant reflects this balance.

Step 5: Conclude that the equilibrium constant is equal to 1 because the free energy difference is zero, indicating that the forward and reverse reactions occur at the same rate under standard conditions.

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Key Concepts

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

Gibbs Free Energy (∆G)

Gibbs Free Energy (∆G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. A negative ∆G indicates a spontaneous process, while a positive ∆G suggests non-spontaneity. When ∆G is zero, as in this case, the system is at equilibrium, meaning the forward and reverse reactions occur at the same rate.

Equilibrium Constant (K)

The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction. If K > 1, products are favored; if K < 1, reactants are favored. At equilibrium, when ∆G = 0, K is equal to 1, indicating that the concentrations of reactants and products are equal.

Relationship between ∆G and K

The relationship between Gibbs Free Energy (∆G) and the equilibrium constant (K) is described by the equation ∆G° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. This equation shows that if ∆G° is zero, then ln(K) is also zero, leading to K = 1. This indicates that at equilibrium, the concentrations of reactants and products are equal, reflecting a balance in the reaction.

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Related Practice

Textbook Question

For the following equilibrium processes and the corresponding ∆G°, calculate (i) K_eq and (ii) the % composition of the equilibrium mixture (% reactants, % products) at 298 K.

(b)

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Textbook Question

Provide a reasonable arrow-pushing mechanism for the following Lewis acid–Lewis base reactions.

(b)

Textbook Question

For the following equilibrium processes and the corresponding ∆G°, calculate (i) K_eq and (ii) the % composition of the equilibrium mixture (% reactants, % products) at 298 K.

(a)

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Textbook Question

For the following equilibrium processes and the corresponding ∆G°, indicate whether you expect the equilibrium constant to be greater than, equal to, or less than 1. Justify your expectation in words.

(a)

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Textbook Question

Chapter 5 taught us that chemical reactions are random collisions. Experimentally, how can we make molecules collide more often?

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Textbook Question

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

(a) ∆H° = -15 kcal/mol ; ∆S° = +37 cal/mol•K ; T = 273 K

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For the following equilibrium processes and the corresponding ∆G° , indicate whether you expect the equilibrium constant to be greater than, equal to, or less than 1. Justify your expectation in words.(b)

Verified video answer for a similar problem:

Key Concepts

Gibbs Free Energy (∆G)

Equilibrium Constant (K)

Relationship between ∆G and K

For the following equilibrium processes and the corresponding ∆G° , indicate whether you expect the equilibrium constant to be greater than, equal to, or less than 1. Justify your expectation in words.
(b)