Which of the folliwng is the correct order of the order of the rate of reaction of `C_(6)H_(6), C_(6)D_(6)` and `C_(6) T_(6)` towards nitration?

Options

A. `C_(6) H_(6) gt C_(6) D_(6) gt C_(6) T_(6)`
B. `C_(6) H_(6) = C_(6) D_(6) = C_(6) T_(6)`
C. `C_(6) H_(6) gt C_(6) D_(6) = C_(6) T_(6)`
D. `C_(6)T_(6) gt C_(6) D_(6) gt C_(6) H_(6)`

Explanation

To determine the correct order of the rate of reaction of \( C_6H_6 \) (benzene), \( C_6D_6 \) (benzene-d6), and \( C_6T_6 \) (benzene-t6) towards nitration, we can follow these steps:

### Step 1: Understand the Reaction
Nitration of benzene involves the electrophilic substitution of a hydrogen atom with a nitro group (\( NO_2^+ \)). The reaction is typically carried out using a mixture of concentrated sulfuric acid and concentrated nitric acid.

### Step 2: Identify the Electrophile
In this reaction, the electrophile is the nitronium ion (\( NO_2^+ \)). The rate of the reaction is determined by how quickly this electrophile can attack the benzene ring.

### Step 3: Consider the Isotopes
The compounds \( C_6H_6 \), \( C_6D_6 \), and \( C_6T_6 \) contain different isotopes of hydrogen:
- \( C_6H_6 \): Benzene with regular hydrogen
- \( C_6D_6 \): Benzene with deuterium (heavy hydrogen)
- \( C_6T_6 \): Benzene with tritium (heavier hydrogen)

### Step 4: Analyze the Rate-Determining Step
The rate-determining step in the nitration reaction is the attack of the nitronium ion on the benzene ring. This step does not involve the breaking of the carbon-hydrogen bond directly, as the bond breaking occurs after the electrophile has already attacked the ring.

### Step 5: Determine the Kinetic Isotope Effect
Since the rate-determining step does not involve the breaking of the C-H, C-D, or C-T bonds, there is no kinetic isotope effect in this reaction. This means that the presence of different isotopes does not significantly affect the rate of the reaction.

### Step 6: Conclusion
As a result, the rates of reaction for all three compounds towards nitration are the same. Therefore, the correct order of the rate of reaction is:
\[ \text{Rate: } C_6H_6 = C_6D_6 = C_6T_6 \]

### Final Answer
The correct answer is that all three compounds react at the same rate towards nitration.

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