Question

For each rate equation, what effect does the indicated concentration change have on the overall rate of the reaction?

[1] $\mathbf{rate}\mathbf{}\mathbf{=}\mathbf{k}\left[{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}\right]\left[{}^{-}\mathrm{OH}\right]$

1. tripling the concentration of ${\mathbf{CH}}_{\mathbf{3}}{\mathbf{CH}}_{\mathbf{2}}\mathbf{Br}$only
2. tripling the concentration of – OH only
3. tripling the concentration of both ${\mathbf{CH}}_{\mathbf{3}}{\mathbf{CH}}_{\mathbf{2}}\mathbf{Br}$ and – OH

[2]role="math" localid="1648280223497" $\mathbf{rate}\mathbf{=}\mathbf{k}\mathbf{\left[}{\left({\mathrm{CH}}_3\right)}_{\mathbf{3}}\mathbf{COH}\mathbf{\right]}$

1. doubling the concentration of ${\left({\mathrm{CH}}_3\right)}_{\mathbf{3}}\mathbf{COH}$
2. increasing the concentration of ${\mathbf{\left(}{\mathbf{CH}}_{\mathbf{3}}\mathbf{\right)}}_{\mathbf{3}}\mathbf{COH}$ by a factor of 10

Short answer

Answer

[1]

1. The reaction rate increases three times the initial rate.
2. The rate of the reaction increases by a factor of three.
3. The reaction rate increases by a factor of nine.

[2]

1. The rate of the reaction increases by a factor of two.
2. The reaction rate increases by a factor of ten.

Step-by-step solution

Step-by-Step SolutionStep 1: Rate of a reaction

The rate of a reaction is directly proportional/related to the concentration of the species involved in its rate-determining step.

An increase in the concentration of these species leads to an increase in the rate of the reaction.

Effect on the rate of a reaction in case [1]

${\mathrm{rate}}_1=\left[{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}\right]\left[{}^{-}\mathrm{OH}\right]$

Here, the rate of the reaction depends on the concentration of ${\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}$and.

a. On tripling the concentration of ${\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}$. $$\begin{gathered} {\mathrm{rate}}_2=\left[3{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}\right]\left[{}^{-}\mathrm{OH}\right] \\ =3\times \left[{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}\right]\left[{}^{-}\mathrm{OH}\right] \\ =3{\mathrm{rate}}_1 \end{gathered}$$

On tripling the concentration of ${\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}$, the rate of the reaction increases by three times the initial rate.

b. On tripling the concentration of -OH

$$\begin{gathered} {\mathrm{rate}}_2=\left[{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}\right]\left[3{\times }^{-}\mathrm{OH}\right] \\ =3\times \left[{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}\right]\left[{}^{-}\mathrm{OH}\right] \\ =3{\mathrm{rate}}_1 \end{gathered}$$

On tripling the concentration of -OH, the rate of the reaction increases three times the initial rate.

c. On tripling the concentration of both ${\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}$and – OH$$\begin{gathered} {\mathrm{rate}}_2=\left[3{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}\right]\left[3{\times }^{-}\mathrm{OH}\right] \\ =9\times \left[{\mathrm{CH}}_3{\mathrm{CH}}_2\mathrm{Br}\right]\left[{}^{-}\mathrm{OH}\right] \\ =9{\mathrm{rate}}_1 \end{gathered}$$

On tripling the concentration of both the species, the reaction rate increases by a factor of 9.

Effect on the rate of a reaction in case [2]

${\mathrm{rate}}_1=\left[{\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}\right]$

a. doubling the concentration of${\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}$

$\begin{array}{rcl}{\mathrm{rate}}_1& =& \left[2\times {\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}\right]\\ & =& 2\times \left[{\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}\right]\\ & =& 2{\mathrm{rate}}_1\end{array}$

On doubling the concentration of ${\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}$,the rate of the reaction becomes twice the initial rate

b. Increasing the concentration of${\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}$by a factor of 10

$\begin{array}{rcl}{\mathrm{rate}}_1& =& \left[10\times {\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}\right]\\ & =& 10\times \left[{\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}\right]\\ & =& 10{\mathrm{rate}}_1\end{array}$

On increasing the concentration of by a factor of 10${\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}$,the reaction rate also increases by a factor of 10.