Chapter 9, Problem 9.6P

Interpretation Introduction

(a)

Interpretation:

The overall kinetic order, order in each reactant and dimensions of the rate constant of an addition reaction of bromine to an alkene with the given rate law are to be stated.

Concept introduction:

The kinetic order of a reaction is given by the sum of the powers of all concentrations in the rate law.

The kinetic order in each reactant is the power to which its concentration is raised in the rate law.

Answer to Problem 9.6P

Overall kinetic order of the addition reaction of bromine to an alkene with $\text{rate}=k\left[\text{alkene}\right]{\left[{\text{Br}}_{\text{2}}\right]}^{\text{2}}$ is $3$.

The reaction is first order in alkene and second order in bromine.

The dimensions of the rate constant $\left(k\right)$ is ${\text{mol}}^{-2}{\text{L}}^2{\sec }^{-1}$.

Explanation of Solution

The rate law for the addition reaction of bromine to an alkene is shown below.

$\text{rate}=k\left[\text{alkene}\right]{\left[{\text{Br}}_{\text{2}}\right]}^{\text{2}}$

The overall kinetic order of the reaction is the sum of power of concentration of alkene $\left(1\right)$ and power of concentration of bromine $\left(2\right)$. Therefore the overall kinetic order of the addition reaction of bromine to an alkene is $1+2=3$.

The rate law for the addition reaction of bromine to an alkene is shown below.

$\text{rate}=k\left[\text{alkene}\right]{\left[{\text{Br}}_{\text{2}}\right]}^{\text{2}}$

The power of concentration of alkene is one and power of concentration of bromine is two. Therefore, reaction is first order in alkene and second order in bromine.

The rate law is shown below.

$\text{rate}=k\left[\text{alkene}\right]{\left[{\text{Br}}_{\text{2}}\right]}^{\text{2}}$…(1)

Rearrange equation $\left(1\right)$ to find out the dimension of rate constant $\left(k\right)$ as shown below.

$\begin{array}{rll}k& =& \frac{\text{rate}}{\left[\text{alkene}\right]{\left[{\text{Br}}_{\text{2}}\right]}^{\text{2}}}\\ \text{Dimension}\text{of}k& =& \frac{\text{Dimension}\text{of}\text{rate}}{\left[\text{alkene}\right]{\left[{\text{Br}}_{\text{2}}\right]}^{\text{2}}}\\ & =& \frac{\text{mol}{\text{L}}^{-1}{\text{sec}}^{-1}}{\text{mol}{\text{L}}^{-1}{\left(\text{mol}{\text{L}}^{-1}\right)}^2}\\ & =& \frac{{\text{sec}}^{-1}}{{\text{mol}}^2{\text{L}}^{-2}}\end{array}$

$\text{Dimension}\text{of}k={\text{mol}}^{-2}{\text{L}}^2{\sec }^{-1}$

Therefore, the dimensions of the rate constant $\left(k\right)$ is ${\text{mol}}^{-2}{\text{L}}^2{\sec }^{-1}$.

Conclusion

Overall kinetic order of the addition reaction of bromine to an alkene with $\text{rate}=k\left[\text{alkene}\right]{\left[{\text{Br}}_{\text{2}}\right]}^{\text{2}}$ is $3$.

The reaction is first order in alkene and second order in bromine.

The dimensions of the rate constant $\left(k\right)$ is ${\text{mol}}^{-2}{\text{L}}^2{\sec }^{-1}$.

Interpretation Introduction

(b)

Interpretation:

The overall kinetic order, order in each reactant and dimensions of the rate constant of substitution reaction of an alkyl halide with the given rate law are to be stated.

Concept introduction:

The kinetic order of a reaction is given by the sum of the powers of all concentrations in the rate law.

The kinetic order in each reactant is the power to which its concentration is raised in the rate law.

Answer to Problem 9.6P

Overall kinetic order of the substitution reaction of an alkyl halide with the rate law $\text{rate}=k\left[\text{alkylhalide}\right]$ is $1$.

The reaction is first order in alkyl halide.

The dimensions of the rate constant $\left(k\right)$ is ${\sec }^{-1}$.

Explanation of Solution

The rate law for the substitution reaction of an alkyl halide is shown below.

$\text{rate}=k\left[\text{alkylhalide}\right]$

The overall kinetic order of the reaction is the power of concentration of an alkyl halide. Therefore, the overall kinetic order of the substitution reaction of an alkyl halide is $1$.

The rate law for the substitution reaction of an alkyl halide is shown below.

$\text{rate}=k\left[\text{alkylhalide}\right]$

The power of concentration of an alkyl halide is one. Therefore, reaction is first order in alkyl halide.

The rate law is shown below.

$\text{rate}=k\left[\text{alkylhalide}\right]$…(1)

Rearrange equation $\left(1\right)$ to find out the dimension of rate constant $\left(k\right)$ as shown below.

$\begin{array}{rll}\text{Dimension}\text{of}k& =& \frac{\text{Dimension}\text{of}\text{rate}}{\left[\text{alkylhalide}\right]}\\ & =& \frac{\text{mol}{\text{L}}^{-1}{\text{sec}}^{-1}}{\text{mol}{\text{L}}^{-1}}\\ & =& {\text{sec}}^{-1}\end{array}$

Therefore, the dimensions of the rate constant $\left(k\right)$ is ${\sec }^{-1}$.

Conclusion

Overall kinetic order of the substitution reaction of an alkyl halide with the rate law $\text{rate}=k\left[\text{alkylhalide}\right]$ is $1$.

The reaction is first order in alkyl halide.

The dimensions of the rate constant $\left(k\right)$ is ${\sec }^{-1}$.