Question

1. the rate of the reaction shown below was studied 2 no + h₂ → n₂o + h₂o. it was found that the rate doubled when the h₂ was doubled. it was also found that the rate increased by a factor of four when the no concentration was doubled. which of the following mechanisms is/are consistent with these data? step 1 no + h₂ → n + h₂o (slow) step 2 n + no → n₂o; step 1 h₂ ⇌ 2 h (slow) step 2 h + 2 no → n₂o + oh (slow) step 3 oh + h → h₂o; step 1 no + no ⇌ n₂o₂ (slow) step 2 n₂o₂ + h₂ →n₂o + h₂o (slow); step 1 no + no→ no₂ + n (slow) step 2 no₂ + h₂ → no + h₂o step 3 n + no → n₂o

Explanation:

Step1: Determine rate - law from experimental data

The rate of the reaction $2NO + H_2
ightarrow N_2O + H_2O$ doubles when $[H_2]$ is doubled and increases by a factor of four when $[NO]$ is doubled. So the rate - law is $rate = k[NO]^2[H_2]$. The overall order of the reaction is 3 and the order with respect to $NO$ is 2 and with respect to $H_2$ is 1.

Step2: Analyze each mechanism

Mechanism 1:

For the mechanism:
Step 1: $NO + H_2
ightarrow N + H_2O$ (slow)
Step 2: $N+NO
ightarrow N_2O$
The rate - determining step is the slow step. The rate law for this mechanism is $rate = k[NO][H_2]$, which is not consistent with the experimental rate - law.

Mechanism 2:

Step 1: $H_2
ightleftharpoons2H$ (slow)
Step 2: $H + 2NO
ightarrow N_2O+OH$ (slow)
Step 3: $OH + H
ightarrow H_2O$
The rate - determining step is the slowest step. If we assume the first step is the rate - determining step, the rate law is $rate = k[H_2]$, which is not consistent with the experimental rate - law.

Mechanism 3:

Step 1: $NO + NO
ightleftharpoons N_2O_2$ (slow)
Step 2: $N_2O_2+H_2
ightarrow N_2O + H_2O$
The rate - determining step is the first step. The rate law for this mechanism is $rate = k[NO]^2$, which is not consistent with the experimental rate - law.

Mechanism 4:

Step 1: $NO + NO
ightarrow NO_2+N$ (slow)
Step 2: $NO_2 + H_2
ightarrow NO + H_2O$
Step 3: $N+NO
ightarrow N_2O$
The rate - determining step is the first step. The rate law for this mechanism is $rate = k[NO]^2$, which is not consistent with the experimental rate - law.

Since none of the given mechanisms match the experimental rate - law, the answer is none of the above.

Answer:

None of the above mechanisms are consistent with the data.