Chapter 19, Problem 19.63QP

Interpretation Introduction

Interpretation:

Which of the given mechanisms can be ruled out of the basis of the observed rate expression have to be determined.

Concept introduction:

Order of a reaction:  The sum of exponents of the concentrations in the rate law for the reaction is said to be order of a reaction.

Rate law: It is an equation that related to the rate of reaction to the concentrations or pressures of substrates (reactants).  It is also said to be as rate equation.

Explanation of Solution

To ruled out the mechanism I

The given mechanism I is

$\begin{array}{l}{H}_2+NO\to H_{2}O+N(Slow)\\ N+NO\to N_2+O(fast)\\ O+H_2\to H_{2}O(fast)\end{array}$

From the above given information, experimentally determined rate law for the reaction of hydrogen and nitrous oxide is first order.  In this mechanism, the bimolecular step is slow and the rate law can be written as follows.

${\text{rate = k[H}}_{\text{2}}\text{][NO]}$

So, mechanism I should be discarded.

The given mechanism II is

$\begin{array}{l}{H}_2+2NO\to N_{2}O+H_{2}O(Slow)\\ N_{2}O+H_2\to N_2+H_{2}O(fast)\end{array}$

From the above information, the collision between two nitrous oxide molecules with one hydrogen molecule is the rate determining step why because which is slow step the rate law can be written as follows

${\text{rate = k[H}}_{\text{2}}{\text{][NO]}}_{\text{2}}$

So, mechanism II is a possibility.

The given mechanism III is

$\begin{array}{l}2NO\rightleftarrows N_2{O}_2(Slow)\\ N_2{O}_2+H_2\to N_{2}O+H_{2}O(fast)\\ N_{2}O+H_2\to N_2+H_{2}O(fast)\end{array}$

From the above information, the forward and reverse reactions in the first fast steps were in dynamic equilibrium, so the rate for this are equal.

${\text{k}}_{\text{f}}{\text{[NO]}}^{\text{2 }}{\text{= k}}_{\text{r}}{\text{[N}}_{\text{2}}{\text{O}}_{\text{2}}\text{]}$

The collision between hydrogen and ${\text{N}}_{\text{2}}{\text{O}}_{\text{2}}$ molecules is the slow step and is rate determining step and rate law for this step is

${\text{rate = k}}_{\text{2}}{\text{[H}}_{\text{2}}{\text{][N}}_{\text{2}}{\text{O}}_{\text{2}}\text{]}$

By solving the dynamic equilibrium equation,

$\text{rate =}\frac{k_2{k}_f}{k_r}{\text{[H}}_{\text{2}}{\text{][NO]}}^{\text{2}}={\text{ k}}_{\text{2}}{\text{[H}}_{\text{2}}{\text{][NO]}}^{\text{2}}$

So, mechanism III is a possibility.

Conclusion

Which of the given mechanisms can be ruled out o the basis of the observed rate expression was determined.