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 1 h₂ = 2 h step 2 n + no → n₂o step 2 h + 2 no → n₂o + oh (slow) step 3 oh + h → h₂o step 1 no + no = n₂o₂ step 1 no + no→ no₂ + n (slow) step 2 n₂o₂ + h₂ →n₂o + h₂o (slow) step 2 no₂ + h₂ → no + h₂o step 3 n + no → n₂o

Explanation:

Step1: Determine the rate - law from experimental data

The rate of the reaction $2NO + H_2
ightarrow N_2O + H_2O$ doubles when $[H_2]$ is doubled, so the reaction is first - order with respect to $H_2$. The rate increases by a factor of four when the $NO$ concentration is doubled, so the reaction is second - order with respect to $NO$. The overall rate - law is $r = k[NO]^2[H_2]$.

Step2: Analyze the rate - determining step for each mechanism

Mechanism 1:

The rate - determining step is step 1: $NO + H_2
ightarrow N + H_2O$ (slow). The rate law for this step is $r = k_1[NO][H_2]$, which does not match the experimental rate law.

Mechanism 2:

The rate - determining step is step 2: $H + 2NO
ightarrow N_2O+OH$ (slow). The rate law for this step is $r = k_2[H][NO]^2$. Since $[H]$ is related to $[H_2]$ by the equilibrium $H_2
ightleftharpoons2H$ (step 1), and assuming the equilibrium is fast, $[H]=K_{eq}^{\frac{1}{2}}[H_2]^{\frac{1}{2}}$. The overall rate law is not $r = k[NO]^2[H_2]$, so this mechanism is not consistent.

Mechanism 3:

The rate - determining step is step 1: $NO + NO
ightleftharpoons N_2O_2$ (slow). The rate law for this step is $r = k_3[NO]^2$. The second step $N_2O_2 + H_2
ightarrow N_2O + H_2O$ (slow) makes the overall rate law not consistent with the experimental one.

Mechanism 4:

The rate - determining step is step 1: $NO + NO
ightarrow NO_2+N$ (slow). The rate law for this step is $r = k_4[NO]^2$. The subsequent steps do not change the fact that the rate - determining step does not involve $H_2$ in the correct way, so this mechanism is not consistent.

Since none of the given mechanisms have a rate - law that matches the experimental rate - law $r = k[NO]^2[H_2]$, the answer is none of the above mechanisms are consistent.

Answer:

None of the above mechanisms are consistent.