Chapter 19, Problem 19.80QP

(a)

Interpretation Introduction

Interpretation:

The following has to be determined from the given information.

1. (a) The order of the given reaction

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.

Half-life: The time required for half of a reactant to be consumed in a reaction is said to be half-life.

• Half-life of a reaction is represented by the symbol as $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
• Half-life is discovered by Ernest Rutherford's in 1907 from the original term half-life period.
• The half-life period is then shortened as half-life in early 1950s.

Answer to Problem 19.80QP

(a)

The order of the given reaction is 3

Explanation of Solution

To determine the order of the given reaction

From the given information,

Compare the experiment 1 and 2, we can come over that the concentration of NO is constant and the concentration of ${\text{H}}_{\text{2}}$ has to be decreased by one-half and the initial rate of the reaction is also decreased by one-half.  Hence, the initial rate is directly proportional to the concentration of ${\text{H}}_{\text{2}}$; so $\text{x = 1}$

 Compare the experiment 1 and 3, we can come over that the concentration of ${\text{H}}_{\text{2}}$ is constant and the concentration of NO is decreases by one-half.  Therefore, the initial rate of the reaction is directly proportional to the concentration square of NO; y=2

The rate law for the overall reaction is ${\text{rate = k[H}}_{\text{2}}{\text{][NO]}}^{\text{2}}$

The order for this reaction is $1+2=3$

Therefore, the order of the reaction is 3

(b)

Interpretation Introduction

Interpretation:

The following has to be determined from the given information.

1. (b) Rate constant of the given reaction

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.

Half-life: The time required for half of a reactant to be consumed in a reaction is said to be half-life.

• Half-life of a reaction is represented by the symbol as $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
• Half-life is discovered by Ernest Rutherford's in 1907 from the original term half-life period.
• The half-life period is then shortened as half-life in early 1950s.

Answer to Problem 19.80QP

The following are determined from the given information.

(b)

Rate constant of the given reaction is $\text{k}=0.38/M^2.s$

Explanation of Solution

To determine the rate constant of the given reaction

From the given data of experiment 1,

We can calculate the rate constant as follows,

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

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

Now substitute the values in the above said formula to get rate constant.

$\text{k}=\frac{2.4\times {10}^{-6}M/s}{\left(0.010M\right){\left(0.025M\right)}^2}=0.38/M^2.s$

$\text{k}=0.38/M^2.s$

(c)

Interpretation Introduction

Interpretation:

The following has to be determined from the given information.

1. (c) A plausible mechanism that is consistent with the rate law

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.

Half-life: The time required for half of a reactant to be consumed in a reaction is said to be half-life.

• Half-life of a reaction is represented by the symbol as $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
• Half-life is discovered by Ernest Rutherford's in 1907 from the original term half-life period.
• The half-life period is then shortened as half-life in early 1950s.

Answer to Problem 19.80QP

(c)

A plausible mechanism that is consistent with the rate law is suggested

Explanation of Solution

To suggest a plausible mechanism that is consistent with the rate law

From the rate law, the slow step is the rate determining step.  Hence, the slow reaction must be happen between hydrogen and nitric oxide to produce intermediate oxygen and which is the rate determining step.  Then formed oxygen intermediate reacts with hydrogen to produce water molecule is the fast step and is not part of the rate determining step.  Therefore, the reaction mechanism has to be represented as follows.

$\begin{array}{l}\underset{\_}{\begin{array}{l}{\text{H}}_{\text{2}}\text{ + 2NO }\to {\text{N}}_{\text{2}}{\text{ + H}}_{\text{2}}\text{O + O }\left(\text{slow step}\right)\\ \\ \text{O + H2 }\to \text{H2O }\left(\text{ fast step}\right)\\ \end{array}}\\ {\text{2H}}_{\text{2}}\text{ + 2NO }\to {\text{ N}}_{\text{2}}{\text{ + 2H}}_{\text{2}}\text{O}\end{array}$