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

Energy Diagram

Organic Chemistry

6. Thermodynamics and Kinetics

Energy Diagram

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5:22 minutes

Problem 57b

Textbook Question

Deuterium (D) is the hydrogen isotope of mass number 2, with a proton and a neutron in its nucleus. The chemistry of deuterium is nearly identical to the chemistry of hydrogen, except that the C―D bond is slightly stronger than the C―H bond by 5.0 kJ/mol (1.2 kcal/mol). Reaction rates tend to be slower when a C―D bond (as opposed to a C―H bond) is broken in a rate-limiting step.
This effect, called a kinetic isotope effect, is clearly seen in the chlorination of methane. Methane undergoes free-radical chlorination 12 times as fast as tetradeuteriomethane (CD₄).

b. Monochlorination of deuterioethane (C₂H₅D) leads to a mixture containing 93% C₂H₄DCl and 7% C₂H₅Cl. Calculate the relative rates of abstraction per hydrogen and deuterium in the chlorination of deuterioethane.

Verified step by step guidance

Step 1: Understand the problem. The goal is to calculate the relative rates of abstraction for hydrogen (H) and deuterium (D) in the chlorination of deuterioethane (C₂H₅D). The problem provides the product distribution: 93% C₂H₄DCl and 7% C₂H₅Cl. This distribution reflects the relative rates of abstraction of H and D by the chlorine radical (Cl⋅).

Step 2: Define the relationship between product distribution and relative rates. The relative rates of abstraction are proportional to the product distribution. Specifically, the rate of H abstraction (k_H) and the rate of D abstraction (k_D) are related to the percentages of C₂H₅Cl and C₂H₄DCl, respectively. Use the formula: \( \frac{k_H}{k_D} = \frac{\text{Percentage of C₂H₅Cl}}{\text{Percentage of C₂H₄DCl}} \).

Step 3: Substitute the given percentages into the formula. From the problem, the percentage of C₂H₅Cl is 7%, and the percentage of C₂H₄DCl is 93%. Substitute these values into the formula: \( \frac{k_H}{k_D} = \frac{7}{93} \).

Step 4: Simplify the ratio. Simplify the fraction \( \frac{7}{93} \) to express the relative rates of abstraction of H and D. This will give you the ratio \( k_H : k_D \).

Step 5: Interpret the result. The calculated ratio \( k_H : k_D \) represents how much faster hydrogen is abstracted compared to deuterium. This difference is due to the kinetic isotope effect, where the C–D bond is stronger and harder to break than the C–H bond.

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Key Concepts

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

Kinetic Isotope Effect

The kinetic isotope effect (KIE) refers to the change in reaction rate that occurs when an atom in a molecule is replaced by one of its isotopes. In organic reactions, bonds involving heavier isotopes, like deuterium, are typically stronger and break more slowly than those involving lighter isotopes, such as hydrogen. This results in observable differences in reaction rates, which can be quantitatively analyzed to provide insights into reaction mechanisms.

Free-Radical Chlorination

Free-radical chlorination is a reaction mechanism where chlorine atoms react with alkanes to form alkyl chlorides through a series of radical intermediates. This process involves three main steps: initiation, propagation, and termination. The rate of chlorination can be influenced by the type of hydrogen being abstracted, as seen in the comparison between methane and deuterated methane, where the presence of deuterium slows the reaction due to the stronger C-D bond.

Relative Rate of Reaction

The relative rate of reaction compares the speed of two or more reactions under similar conditions. It is often expressed as a ratio, indicating how many times faster one reaction occurs compared to another. In the context of chlorination of deuterioethane, calculating the relative rates of abstraction for hydrogen and deuterium allows chemists to understand the influence of isotopic substitution on reaction kinetics and to quantify the effects of the kinetic isotope effect.

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