Chapter 13, Problem 13.1P

Interpretation Introduction

Interpretation:

The rate of change in the concentration of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\left(\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]/\Delta t\right)$ and ${\text{I}}_3^{-}\left(\Delta \left[{\text{I}}_3^{-}\right]/\Delta t\right)$ for the given reaction during the given time interval is to be predicted.

Concept introduction: The rate of a reaction is defined as the change in concentration of the reactants or the products per unit time.

To determine: The rate of change in the concentration of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\left(\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]/\Delta t\right)$ and ${\text{I}}_3^{-}\left(\Delta \left[{\text{I}}_3^{-}\right]/\Delta t\right)$ during the given time interval.

Answer to Problem 13.1P

Solution:

The rate of change in the concentration of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\left(\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]/\Delta t\right)$ is $-4.40\times {10}^{-3}\text{M/s}$ and the rate of change in the concentration of ${\text{I}}_3^{-}\left(\Delta \left[{\text{I}}_3^{-}\right]/\Delta t\right)$ is $+4.40\times {10}^{-3}\text{M/s}$ .

Explanation of Solution

Given information:

The average rate of a reaction is $4.40\times {10}^{-3}\text{M/s}$ .

The given chemical reaction is,
  ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\left(aq\right)+3{\text{I}}^{-}\left(aq\right)+2{\text{H}}^{\text{+}}\left(aq\right)\stackrel{}{\to }{\text{I}}_3^{-}\left(aq\right)+2{\text{H}}_{\text{2}}\text{O}\left(l\right)$

The rate of a reaction is,
  $\text{Rate}=-\frac{\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]}{\Delta t}=-\frac{1}{3}\frac{\Delta \left[{\text{I}}^{-}\right]}{\Delta t}=-\frac{1}{2}\frac{\Delta \left[{\text{H}}^{\text{+}}\right]}{\Delta t}=+\frac{\Delta \left[{\text{I}}_3^{-}\right]}{\Delta t}=+\frac{1}{2}\frac{\Delta \left[{\text{H}}_{\text{2}}\text{O}\right]}{\Delta t}$

The rate of change in the concentration of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\left(\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]/\Delta t\right)$ is given by the expression,
$\text{Rate}=-\frac{\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]}{\Delta t}$

Substitute the value of average rate of a reaction in the above expression to calculate the rate of change in the concentration of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\left(\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]/\Delta t\right)$ .
  $\begin{array}{c}4.40\times {10}^{-3}\text{M/s}=-\frac{\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]}{\Delta t}\\ \frac{\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]}{\Delta t}=-4.40\times {10}^{-3}\text{M/s}\end{array}$

Hence, the rate of change in the concentration of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\left(\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]/\Delta t\right)$ is $-4.40\times {10}^{-3}\text{M/s}$ .
The rate of change in the concentration of ${\text{I}}_3^{-}\left(\Delta \left[{\text{I}}_3^{-}\right]/\Delta t\right)$ is given by the expression,
  $\text{Rate}=+\frac{\Delta \left[{\text{I}}_3^{-}\right]}{\Delta t}$

Substitute the value of average rate of a reaction in the above expression to calculate the rate of change in the concentration of ${\text{I}}_3^{-}\left(\Delta \left[{\text{I}}_3^{-}\right]/\Delta t\right)$ .
  $\begin{array}{c}4.40\times {10}^{-3}\text{M/s}=+\frac{\Delta \left[{\text{I}}_3^{-}\right]}{\Delta t}\\ \frac{\Delta \left[{\text{I}}_3^{-}\right]}{\Delta t}=+4.40\times {10}^{-3}\text{M/s}\end{array}$

Hence, the rate of change in the concentration of ${\text{I}}_3^{-}\left(\Delta \left[{\text{I}}_3^{-}\right]/\Delta t\right)$ is $+4.40\times {10}^{-3}\text{M/s}$ .

Conclusion

The rate of change in the concentration of ${\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\left(\Delta \left[{\text{H}}_{\text{2}}{\text{O}}_{\text{2}}\right]/\Delta t\right)$ is $-4.40\times {10}^{-3}\text{M/s}$ .

The rate of change in the concentration of ${\text{I}}_3^{-}\left(\Delta \left[{\text{I}}_3^{-}\right]/\Delta t\right)$ is $+4.40\times {10}^{-3}\text{M/s}$ .