Table of contents

1. A Review of General Chemistry5h 5m
2. Molecular Representations1h 14m
3. Acids and Bases2h 46m
4. Alkanes and Cycloalkanes4h 17m
5. Chirality3h 39m
6. Thermodynamics and Kinetics1h 22m
7. Substitution Reactions1h 48m
8. Elimination Reactions2h 30m
9. Alkenes and Alkynes2h 9m
10. Addition Reactions3h 19m
11. Radical Reactions1h 58m
12. Alcohols, Ethers, Epoxides and Thiols2h 42m
13. Alcohols and Carbonyl Compounds2h 17m
14. Synthetic Techniques1h 26m
15. Analytical Techniques:IR, NMR, Mass Spect7h 3m
16. Conjugated Systems6h 13m
17. Ultraviolet Spectroscopy51m
18. Aromaticity2h 34m
19. Reactions of Aromatics: EAS and Beyond5h 1m
20. Phenols55m
21. Aldehydes and Ketones: Nucleophilic Addition4h 56m
22. Carboxylic Acid Derivatives: NAS2h 51m
23. The Chemistry of Thioesters, Phophate Ester and Phosphate Anhydrides1h 10m
24. Enolate Chemistry: Reactions at the Alpha-Carbon1h 53m
25. Condensation Chemistry2h 9m
26. Amines1h 43m
27. Heterocycles2h 0m
28. Carbohydrates5h 53m
29. Amino Acids4h 20m
30. Peptides and Proteins2h 42m
31. Catalysis in Organic Reactions1h 30m
32. Lipids 2h 50m
33. The Organic Chemistry of Metabolic Pathways2h 52m
34. Nucleic Acids1h 32m
35. Transition Metals6h 14m
36. Synthetic Polymers1h 49m

6. Thermodynamics and Kinetics

Gibbs Free Energy

Organic Chemistry

6. Thermodynamics and Kinetics

Gibbs Free Energy

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3:19 minutes

Problem 7b

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.
(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 reactions we have not seen yet, which side, if either, would be favored by increasing the temperature?

(d)

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)

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)

Textbook Question

For each pair of reactions, predict which will happen more quickly.

[For (a) and (b), think about the stability of the bases involved.]

(a)

Textbook Question

For the following acid–base reactions studied in Assessment 5.25, draw a likely transition state. Be sure to indicate in your drawing the degree to which bonds are broken or formed.

(a)

Textbook Question

For the following acid–base reactions studied in Assessment 5.25, draw a likely transition state. Be sure to indicate in your drawing the degree to which bonds are broken or formed.

Textbook Question

For the following acid–base reactions studied in Assessment 5.25, draw a likely transition state. Be sure to indicate in your drawing the degree to which bonds are broken or formed.

(b)

Textbook Question

Calculate ∆G° for the conversion of “axial” methylcyclohexane to “equatorial” methylcyclohexane at 25 °C.

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