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Deuterium (D) is the hydrogen isotope of mass number 2,

Organic Chemistry | 8th Edition | ISBN: 9780321768414 | Authors: L.G. Wade Jr ISBN: 9780321768414 33

Solution for problem 56SP Chapter 4

Organic Chemistry | 8th Edition

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Organic Chemistry | 8th Edition | ISBN: 9780321768414 | Authors: L.G. Wade Jr

Organic Chemistry | 8th Edition

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Problem 56SP

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 bond is slightly stronger than the bond by 5.0 kJ/mol (1.2 kcal/mol). Reaction rates tend to be slower if a bond (as opposed to a 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).

Faster: CH4 + ClCH3Cl + HCl         relative rate = 12

Slower: CD4 + ClCD3Cl + DCl         relative rate = 1

(a) Draw the transition state for the rate-limiting step of each of these reactions, showing how a bond to hydrogen or deuterium is being broken in this step.

(b) Monochlorination of deuterioethane (C2H5D) leads to a mixture containing 93% C1H4DCI and 7% C2H5CI. Calculate the relative rates of abstraction per hydrogen and deuterium in the chlorination of deuterioethane.

(c) Consider the thermodynamics of the chlorination of methane and the chlorination of ethane, and use the Hammond postulate to explain why one of these reactions has a much larger isotope effect than the other.

Step-by-Step Solution:

Solution 56SP:

Step 1: (a) Here, we are going to compare the rate  rate-limiting step of each of these reactions, showing how a bond to hydrogen or deuterium is being broken in this step.

Transition states have high energies because bonds must begin to break before other

bonds can form.

 Transition state formation for the 1st reaction is as follows:

CH4 + Cl. →  CH3Cl +HCl

Here, Carbon to Hydrogen bond starts to break and Hydrogen to Chlorine starts forming.

CD4 + Cl. →  CD3Cl +DCl

Here, Carbon to Deuterium  bond starts to break and Deuterium to Chlorine starts forming.

Step 1: (b)

Here, we are going to Calculate the relative rates of abstraction per hydrogen and deuterium in the chlorination of deuterio ethane.

Monochlorination of deuterio ethane (C2H5D) is as follows:

Here, D-replacement is : (7% / 1D) = 7 (reactivity factor)

H-replacement is : (93% / 5D) = 18.6 (reactivity factor)

Thus, the relative reactivity H : D abstraction is = 18.6/7 = 2.7

Therefore, it is found that each H atom is abstracted 2.7 times faster than D.

Step 3: (c)

The 1st propagation step of chlorination of methane is

The enthalpy change for the reaction is +4.0 kJ/mol which is an endothermic reaction.

The enthalpy change for the reaction is -21.0 kJ/mol which is an exothermic reaction.

According to Hammond postulate, activation energy is dominated in case endothermic reaction where transition state is more closer to the energy of the product. Therefore, there is a greater change in the transition state in methane molecule whereas the same change occur in ethane molecule in its transition state energy.

Thus, the abstraction rate of deuterium will be slow in both the molecules, whereas the abstraction rate  will be more effective in methane than ethane.

Step 2 of 3

Chapter 4, Problem 56SP is Solved
Step 3 of 3

Textbook: Organic Chemistry
Edition: 8
Author: L.G. Wade Jr
ISBN: 9780321768414

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Deuterium (D) is the hydrogen isotope of mass number 2,