Chapter 15, Problem 49E

Interpretation Introduction

Interpretation:The time taken by DDT to reach $\text{1}{\text{.41×10}}^{\text{-7}}\text{ M}$ concentration needs to be calculated.

Concept Introduction: The integrated rate law for first order reaction (the rate of the reaction depends on one reactant only) is written as:

  ${\text{ln[A]}}_{\text{t}}{\text{ = -kt + ln[A]}}_{\text{o}}$

Where, ${\text{[A]}}_{\text{t}}$ represents concentration at time, $\text{t}$ , $\text{k}$ represents rate constant and ${\text{[A]}}_{\text{o}}$ represents initial concentration.

The time required for a reaction to reduce its initial concentration to half of its initial value is said to be half-life. The half-life, ${\text{t}}_{\frac{1}{2}}$ for first order rection is given as:

  ${\text{t}}_{\frac{\text{1}}{\text{2}}}\text{ = }\frac{\text{0}\text{.693}}{\text{k}}$