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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1:48 minutes

Problem 18b

Textbook Question

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

Verified step by step guidance

Step 1: Understand the problem. The question asks to calculate the Gibbs free energy change (∆G°) for the conversion of axial methylcyclohexane to equatorial methylcyclohexane at 25 °C. This involves using the relationship between ∆G°, equilibrium constant (K), and temperature.

Step 2: Recall the formula for Gibbs free energy change:

∆G° = -RT ln(K)

, where R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and K is the equilibrium constant for the reaction.

Step 3: Convert the temperature from Celsius to Kelvin. Since the temperature is given as 25 °C, use the formula

T(K) = T(°C) + 273.15

to find the temperature in Kelvin.

Step 4: Determine the equilibrium constant (K). The equilibrium constant can be derived from the energy difference between the axial and equatorial conformations. Typically, the equatorial conformation is more stable due to reduced steric hindrance, and the energy difference is often provided or can be looked up in reference materials.

Step 5: Substitute the values of R, T, and K into the formula

∆G° = -RT ln(K)

to calculate the Gibbs free energy change. Ensure the units are consistent (e.g., R in J/mol·K, T in Kelvin, and K as a dimensionless quantity).

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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. It indicates the spontaneity of a reaction; a negative ∆G° suggests that the reaction is spontaneous, while a positive value indicates non-spontaneity. In the context of conformational changes, it helps predict the stability of different molecular conformations.

Conformational Analysis

Conformational analysis is the study of the different spatial arrangements of atoms in a molecule that can be interconverted by rotation around single bonds. In cyclohexane derivatives, such as methylcyclohexane, the axial and equatorial positions significantly influence the molecule's stability due to steric interactions. Understanding these conformations is crucial for predicting the energy changes associated with their interconversion.

Temperature and Reaction Conditions

Temperature plays a vital role in determining the Gibbs Free Energy and the equilibrium between different molecular conformations. At 25 °C, the standard conditions for thermodynamic calculations, the energy difference between axial and equatorial conformations can be quantitatively assessed. This temperature is often used as a reference point for calculating thermodynamic properties, making it essential for accurate predictions in organic chemistry.

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Related Practice

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)

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 the percentage of isopropylcyclohexane molecules that have the isopropyl substituent in an equatorial position at equilibrium. (Its ∆G° value at 25 °C is -2.1 kcal/mol.)

Textbook Question

The relative rate of reaction for the cis alkene (E) is given in Table 22.2. What do you expect the relative rate of reaction for the trans alkene to be?

Textbook Question

Explain why the half-life (the time it takes for one-half of the compound to be metabolized) of Xylocaine is longer than that of Novocaine.

Textbook Question

In a reaction in which reactant A is in equilibrium with product B at 25 °C, what relative amounts of A and B are present at equilibrium if ∆G° at 25 °C is

a. 2.72 kcal/mol?

b. 0.65 kcal/mol?

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