Chapter 7, Problem 7B.8E

(a)

Interpretation Introduction

Interpretation:

The time taken by $\text{A}$ to get reduced into $25\%$ of its initial concentration has to be determined.

Concept Introduction:

According to the integrated rate law for the first order reaction, the concentration of reactant is the exponential function of time.  The equation that represents the integrated rate law for the first order kinetics is shown below.

    ${\left[\text{A}\right]}_{\text{t}}={\left[\text{A}\right]}_0{\text{e}}^{-k_{\text{r}}t}$

The half-life of the particular chemical reaction is the time in which exactly half of the reactant gets consumed.  The mathematical expression for the half-life for a reaction follows first order kinetics is shown below.

  $t_{1/2}=\frac{\ln 2}{k_{\text{r}}}$

(b)

Interpretation Introduction

Interpretation:

The time taken by $\text{A}$ to get reduced into one-sixth of its initial concentration has to be determined.

Concept Introduction:

Same as part (a).