Chapter 13, Problem 13.49QP

(a)

Interpretation Introduction

Interpretation: The rate law equations and the units of the rate constant for the given reactions are to be stated.

Concept introduction: According to the rate law the rate of reaction depends on the concentration of reactants that are involved in the reaction each raised to the power that may or may not be equal to the stoichiometric coefficient of the reactant in a reaction. The power to which the reactant is raised is called the order of the reactant and the sum of powers of all the reactants that are involved in the reaction gives the order of overall reaction.

To determine: The rate law and the units of the rate constant for the given reaction.

Answer to Problem 13.49QP

Solution

The rate law equation for the given reaction is,

$\text{Rate}=k{\left[{\text{NO}}_{\text{2}}\right]}^1{\left[\text{O}\right]}^1$

The units of rate constant for the above equation is $\underset{\_}{M^{-1}{s}^{-1}}$.

Explanation of Solution

Explanation

As the rate law expression is given in the form of reactants and Oxygen atoms and ${\text{NO}}_2$ are the reactants, therefore the rate law is given as,

$\text{Rate}=k{\left[{\text{NO}}_{\text{2}}\right]}^m{\left[\text{O}\right]}^n$

Where,

• $k$ is the rate constant.
• $m$ and $n$ are the order with respect to the given reactants.

As it is given that the reaction is first order in terms of both the reactants, therefore substitute the value of $m=1$ and $n=1$ in the above equation as,

$\text{Rate}=k{\left[{\text{NO}}_{\text{2}}\right]}^1{\left[\text{O}\right]}^1$

Substitute the units of concentration as $\text{M}$ and the units of rate of reaction as $\text{M}/\text{s}$ in the above equation as,

$\begin{array}{c}\text{Rate}=k{\left[{\text{NO}}_{\text{2}}\right]}^1{\left[\text{O}\right]}^1\\ \frac{\text{M}}{\text{s}}=k{\left[\text{M}\right]}^1{\left[\text{M}\right]}^1\\ k=\underset{\_}{M^{-1}{s}^{-1}}\end{array}$

(b)

Interpretation Introduction

Interpretation: The rate law equations and the units of the rate constant for the given reactions are to be stated.

Concept introduction: According to the rate law the rate of reaction depends on the concentration of reactants that are involved in the reaction each raised to the power that may or may not be equal to the stoichiometric coefficient of the reactant in a reaction. The power to which the reactant is raised is called the order of the reactant and the sum of powers of all the reactants that are involved in the reaction gives the order of overall reaction.

To determine: The rate law and the units of the rate constant for the given reaction.

Answer to Problem 13.49QP

Solution

The rate law equation for the given reaction is,

$\text{Rate}=k{\left[\text{NO}\right]}^2{\left[{\text{Cl}}_{\text{2}}\right]}^1$

The units of rate constant for the above equation is $\underset{\_}{M^{-2}{s}^{-1}}$.

Explanation of Solution

Explanation

As the rate law expression is given in the form of reactants and $\text{NO}$ and ${\text{Cl}}_2$ are the reactants, therefore the rate law is given as,

$\text{Rate}=k{\left[\text{NO}\right]}^m{\left[{\text{Cl}}_{\text{2}}\right]}^n$

Where,

• $k$ is the rate constant.
• $m$ and $n$ are the order with respect to the given reactants.

As it is given that the reaction is second order with respect to $\text{NO}$ and first order with respect to ${\text{Cl}}_2$, therefore substitute the value of $m=2$ and $n=1$ in the above equation as,

$\text{Rate}=k{\left[\text{NO}\right]}^2{\left[{\text{Cl}}_{\text{2}}\right]}^1$

Substitute the units of concentration as $\text{M}$ and the units of rate of reaction as $\text{M}/\text{s}$ in the above equation as,

$\begin{array}{c}\text{Rate}=k{\left[\text{NO}\right]}^2{\left[{\text{Cl}}_{\text{2}}\right]}^1\\ \frac{\text{M}}{\text{s}}=k{\left[\text{M}\right]}^2{\left[\text{M}\right]}^1\\ \frac{\text{M}}{\text{s}}=k{\left[\text{M}\right]}^3\\ k=\underset{\_}{M^{-2}{s}^{-1}}\end{array}$

(c)

Interpretation Introduction

Interpretation: The rate law equations and the units of the rate constant for the given reactions are to be stated.

Concept introduction: According to the rate law the rate of reaction depends on the concentration of reactants that are involved in the reaction each raised to the power that may or may not be equal to the stoichiometric coefficient of the reactant in a reaction. The power to which the reactant is raised is called the order of the reactant and the sum of powers of all the reactants that are involved in the reaction gives the order of overall reaction.

To determine: The rate law and the units of the rate constant for the given reaction.

Answer to Problem 13.49QP

Solution

The rate law equation for the given reaction is,

$\text{Rate}=k{\left[{\text{CHCl}}_3\right]}^1{\left[\text{NO}\right]}^{1/2}$

The units of rate constant for the above equation is $\underset{\_}{M^{-1/2}{s}^{-1}}$.

Explanation of Solution

Explanation

As the rate law expression is given in the form of reactants and $\text{NO}$ and ${\text{CHCl}}_3$ are the reactants, therefore the rate law is given as,

$\text{Rate}=k{\left[{\text{CHCl}}_3\right]}^m{\left[\text{NO}\right]}^n$

Where,

• $k$ is the rate constant.
• $m$ and $n$ are the order with respect to the given reactants.

As it is given that the reaction is first order with respect to ${\text{CHCl}}_3$ and one-half order with respect to $\text{NO}$, therefore substitute the value of $m=1$ and $n=\frac{1}{2}$ in the above equation as,

$\text{Rate}=k{\left[{\text{CHCl}}_3\right]}^1{\left[\text{NO}\right]}^{1/2}$

Substitute the units of concentration as $\text{M}$ and the units of rate of reaction as $\text{M}/\text{s}$ in the above equation as,

$\begin{array}{c}\text{Rate}=k{\left[{\text{CHCl}}_3\right]}^1{\left[\text{NO}\right]}^{1/2}\\ \frac{\text{M}}{\text{s}}=k{\left[\text{M}\right]}^1{\left[\text{M}\right]}^{1/2}\\ \frac{\text{M}}{\text{s}}=k{\left[\text{M}\right]}^{3/2}\\ k=\underset{\_}{M^{-1/2}{s}^{-1}}\end{array}$

(d)

Interpretation Introduction

Interpretation: The rate law equations and the units of the rate constant for the given reactions are to be stated.

Concept introduction: According to the rate law the rate of reaction depends on the concentration of reactants that are involved in the reaction each raised to the power that may or may not be equal to the stoichiometric coefficient of the reactant in a reaction. The power to which the reactant is raised is called the order of the reactant and the sum of powers of all the reactants that are involved in the reaction gives the order of overall reaction.

To determine: The rate law and the units of the rate constant for the given reaction.

Answer to Problem 13.49QP

Solution

The rate law equation for the given reaction is,

$\text{Rate}=k{\left[{\text{O}}_3\right]}^2{\left[\text{O}\right]}^{-1}$

The units of rate constant for the above equation is $\underset{\_}{s^{-1}}$.

Explanation of Solution

Explanation

As the rate law expression is given in the form of reactants and ${\text{O}}_{\text{3}}$ and Oxygen atoms are the reactants, therefore the rate law is given as,

$\text{Rate}=k{\left[{\text{O}}_3\right]}^m{\left[\text{O}\right]}^n$

Where,

• $k$ is the rate constant.
• $m$ and $n$ are the order with respect to the given reactants.

As it is given that the reaction is second order with respect to ${\text{O}}_{\text{3}}$ and $-1$ order with respect to $\text{O}$, therefore substitute the value of $m=1$ and $n=-1$ in the above equation as,

$\text{Rate}=k{\left[{\text{O}}_3\right]}^2{\left[\text{O}\right]}^{-1}$

Substitute the units of concentration as $\text{M}$ and the units of rate of reaction as $\text{M}/\text{s}$ in the above equation as,

$\begin{array}{c}\text{Rate}=k{\left[{\text{O}}_3\right]}^2{\left[\text{O}\right]}^{-1}\\ \frac{\text{M}}{\text{s}}=k{\left[\text{M}\right]}^2{\left[\text{M}\right]}^{-1}\\ \frac{\text{M}}{\text{s}}=k{\left[\text{M}\right]}^1\\ k=\underset{\_}{s^{-1}}\end{array}$

Conclusion

The units of rate constant depend on the order of the reaction.