Chapter 13, Problem 13.65QP

(a)

Interpretation Introduction

Interpretation: The average rate of consumption of $\text{HCN}$ from $\text{11}\text{.12}\text{min}$ to $\text{40}\text{.35}\text{min}$ and the average rate of consumption of propionaldehyde over the same period is to be calculated.

Concept introduction: Rate law of a chemical reaction describes the relationship between concentrations of reactants and the rate of that particular reaction.

To determine: The average rate of consumption of $\text{HCN}$ from $\text{11}\text{.12}\text{min}$ to $\text{40}\text{.35}\text{min}$.

Answer to Problem 13.65QP

Solution

The average rate of consumption of $\text{HCN}$ from $\text{11}\text{.12}\text{min}$ to $\text{40}\text{.35}\text{min}$ is $\underset{\_}{-3.55\times 10^{-4}Mmi{n}^{-1}}$.

Explanation of Solution

Explanation

The reaction between propionaldehyde and hydrocyanic acid has been studied in aqueous solution at $\text{25}{}^{\text{ο}}\text{C}$.

Concentrations of reactants as a function of time are shown in the table given below.

Time (min)	$\left[{\text{CH}}_3{\text{CH}}_2\text{CHO}\right]\left(\text{M}\right)$	$\left[\text{HCN}\right]\left(\text{M}\right)$
$3.28$	$0.0384$	$0.0657$
$11.12$	$0.0346$	$0.0619$
$24.43$	$0.0296$	$0.0569$
$40.35$	$0.0242$	$0.0515$
67.22	$0.0190$	$0.0463$

The average rate of consumption of $\text{HCN}$ from $\text{11}\text{.12}\text{min}$ to $\text{40}\text{.35}\text{min}$ is calculated by the formula,

$\text{Rate}=\frac{{\left[\text{HCN}\right]}_{\text{f}}-{\left[\text{HCN}\right]}_{\text{i}}}{\Delta t}$

Where,

• ${\left[\text{HCN}\right]}_{\text{f}}$ is the final concentration of $\text{HCN}$.
• ${\left[\text{HCN}\right]}_{\text{i}}$ is the initial concentration of $\text{HCN}$.
• $\Delta t$ is the difference in time.

The final concentration of $\text{HCN}$ at $\text{40}\text{.35}\text{min}$ is $\text{0}\text{.0515}\text{M}$.

The initial concentration of $\text{HCN}$ at $\text{11}\text{.12}\text{min}$ is $0.0619\text{M}$.

The value of $\Delta t$ is $\text{40}\text{.35}\text{min}-\text{11}\text{.12}\text{min}=29.23\min$.

Substitute the value of $\Delta t$, final concentration and initial concentration of $\text{HCN}$ in the above equation.

$\begin{array}{c}\text{Rate}=\frac{\text{0}\text{.0515}\text{M}-0.0619\text{M}}{29.23\min }\\ =\underset{\_}{-3.55\times 10^{-4}Mmi{n}^{-1}}\end{array}$

(b)

Interpretation Introduction

Interpretation: The average rate of consumption of $\text{HCN}$ from $\text{11}\text{.12}\text{min}$ to $\text{40}\text{.35}\text{min}$ and the average rate of consumption of propionaldehyde over the same period is to be calculated.

Concept introduction: Rate law of a chemical reaction describes the relationship between concentrations of reactants and the rate of that particular reaction.

To determine: The average rate of consumption of propionaldehyde from $\text{11}\text{.12}\text{min}$ to $\text{40}\text{.35}\text{min}$.

Answer to Problem 13.65QP

Solution

The average rate of consumption of propionaldehyde from $\text{11}\text{.12}\text{min}$ to $\text{40}\text{.35}\text{min}$ is $\underset{\_}{-3.55\times 10^{-4}Mmi{n}^{-1}}$.

Explanation of Solution

Explanation

The reaction between propionaldehyde and hydrocyanic acid has been studied in aqueous solution at $\text{25}{}^{\text{ο}}\text{C}$.

Concentrations of reactants as a function of time are shown in the table given below.

Time (min)	$\left[{\text{CH}}_3{\text{CH}}_2\text{CHO}\right]\left(\text{M}\right)$	$\left[\text{HCN}\right]\left(\text{M}\right)$
$3.28$	$0.0384$	$0.0657$
$11.12$	$0.0346$	$0.0619$
$24.43$	$0.0296$	$0.0569$
$40.35$	$0.0242$	$0.0515$
67.22	$0.0190$	$0.0463$

The average rate of consumption of propionaldehyde from $\text{11}\text{.12}\text{min}$ to $\text{40}\text{.35}\text{min}$ is calculated by the formula,

$\text{Rate}=\frac{{\left[{\text{CH}}_3{\text{CH}}_2\text{CHO}\right]}_{\text{f}}-{\left[{\text{CH}}_3{\text{CH}}_2\text{CHO}\right]}_{\text{i}}}{\Delta t}$

Where,

• ${\left[{\text{CH}}_3{\text{CH}}_2\text{CHO}\right]}_{\text{f}}$ is the final concentration of propionaldehyde.
• ${\left[{\text{CH}}_3{\text{CH}}_2\text{CHO}\right]}_{\text{i}}$ is the initial concentration of propionaldehyde.
• $\Delta t$ is the difference in time.

The final concentration of propionaldehyde at $\text{40}\text{.35}\text{min}$ is $0.0242\text{M}$.

The initial concentration of propionaldehyde at $\text{11}\text{.12}\text{min}$ is $\text{0}\text{.0346}\text{M}$.

The value of $\Delta t$ is $\text{40}\text{.35}\text{min}-\text{11}\text{.12}\text{min}=29.23\min$.

Substitute the value of $\Delta t$, final concentration and initial concentration of propionaldehyde in the above equation.

$\begin{array}{c}\text{Rate}=\frac{0.0242\text{M}-\text{0}\text{.0346}\text{M}}{29.23\min }\\ =\underset{\_}{-3.55\times 10^{-4}Mmi{n}^{-1}}\end{array}$

Conclusion

The average rate of consumption of propionaldehyde from $\text{11}\text{.12}\text{min}$ to $\text{40}\text{.35}\text{min}$ is $\underset{\_}{-3.55\times 10^{-4}Mmi{n}^{-1}}$.