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 if 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).
(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% C2H4DCl and 7% C2H5Cl
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 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.