Chapter 16.1, Problem 12SSC

Interpretation Introduction

Interpretation: The average reaction rate of the reaction needs to be determined.

Concept introduction: The average rate of an action or process is defined as the change in a given quantity during a specific period of time. In equation form, the average rate is expressed as follows:

  $\text{Average}\text{rate=}\frac{\Delta \text{Quantity}}{\Delta t}$

Answer to Problem 12SSC

The average reaction rate of the reaction is $0.25\text{mol}/(\text{L}·\text{s})$ .

Explanation of Solution

Given that A and B react and concentration of A changes from 1.00 M to 0.50 M in 2 seconds. Decrease of concentration means the rate of expression is negative.

So, the expression of the average reaction rate is,

  $\begin{array}{c}\text{Average}\text{reaction}\text{rate=}-\frac{\Delta [\text{A}]}{\Delta t}\\ =-\frac{[\text{A}]\text{at}\text{time}{t}_2-[\text{A}]\text{at}\text{time}{t}_1}{t_2-t_1}\\ =-\frac{0.50\text{M}-1.00\text{M}}{2s}\\ =\frac{0.50\text{M}}{2s}\\ =0.25\text{mol}/(\text{L}·\text{s})\end{array}$

Conclusion

The negative sign in reaction expression indicates that the concentration of the compound decreases as the reaction proceeds but the reaction rate is always positive.