Chapter 10.3, Problem 10.13P

Interpretation Introduction

(a)

Interpretation:

The number of half-lives that have elapsed to form the sample in the diagram A should be determined:

 

Concept Introduction:

The order of reaction can be defined as the number raised as the power of reactant molecules in the rate law of the reaction. According to rate law, the rate of reaction is directly proportional to the concentration of the reactant molecule. On the basis of the order of reaction, the reactions can be classified as a zero-order reaction, first-order reaction and a second-order reaction. The rate constant for each type of reaction also depends on the initial concentration and half-life. A radioactive disintegration is a first-order reaction.

For zero order reaction:

For first order reaction: $\text{t1/2 = }\frac{\text{0}\text{.693 }}{\text{k}}$

For second order reaction: $\text{t1/2 = }\frac{\text{1 }}{\text{k[A]}}$

Interpretation Introduction

(b)

Interpretation:

The minutes that have elapsed to form the sample in the diagram A should be determined:

 Concept Introduction:

The order of reaction can be defined as the number raised as the power of reactant molecules in the rate law of the reaction. According to rate law, the rate of reaction is directly proportional to the concentration of the reactant molecule. On the basis of the order of reaction, the reactions can be classified as a zero-order reaction, first-order reaction and second-order reaction. The rate constant for each type of reaction also depends on the initial concentration and half-life. A radioactive disintegration is a first-order reaction.

For zero order reaction: $\text{t1/2 = }\frac{\text{[A]}}{\text{2k}}$

For first order reaction: $\text{t1/2 = }\frac{\text{0}\text{.693 }}{\text{k}}$

For second order reaction: $\text{t1/2 = }\frac{\text{1 }}{\text{k[A]}}$