Chapter 24, Problem 24.115P

(a)

Interpretation Introduction

Interpretation:

Safe level of radon of air has to be determined in $\text{Bq/L}.$

Concept Introduction:

Unit conversion:

  $\begin{array}{c}\text{1 Ci = 3}{\text{.70×10}}^{\text{10}}\text{ disintegrations per second}\\ \\ \text{1 Bq = 1 d/s}\end{array}$

(b)

Interpretation Introduction

Interpretation:

Activity of radon in $\text{Bq/L}$ remaining after 9.5 days in the room air has to be determined using the given information.

Concept Introduction:

The half–life period for first order reaction is as follows:

  $\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\ln \text{ 2}}{\text{k}}\\ \text{Where,}\\ \text{k = Rate constant}\\ {\text{t}}_{\text{1/2}}\text{= half-life}\end{array}$

Integrated rate law for a first order reaction is given below

  $\begin{array}{c}\ln A_t\text{ = }\ln A_0-\text{ kt}\\ \text{where,}\\ \text{ln}\text{=}\text{natural}\text{logarithm}\\ {\text{A}}_{\text{0}}\text{= Activity}\text{of}\text{A}\text{at}\text{time}\text{t}\text{=}\text{0}\\ {\text{A}}_{\text{t}}\text{= Activity}\text{of}\text{A}\text{after}\text{time, t}\\ \text{k}\text{=}\text{rate}\text{constant}\end{array}$

Radioactive decay is a first order reaction.

(c)

Interpretation Introduction

Interpretation:

Number of days more to takes for reaching the EPA recommended level after 9.5 days has to be determined using the given information.

Concept Introduction:

Radioactive decay is a first order reaction.

The half–life period for first order reaction is as follows:

  $\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\ln \text{ 2}}{\text{k}}\\ \text{Where,}\\ \text{k = Rate constant}\\ {\text{t}}_{\text{1/2}}\text{= half-life}\end{array}$

Integrated rate law for a first order reaction is given below

  $\begin{array}{c}t\text{ = }\frac{1}{k}\ln \frac{N_0}{N_t}\\ \text{where,}\\ \text{ln}\text{=}\text{natural}\text{logarithm}\\ {\text{N}}_{\text{0}}\text{= Amount}\text{of}\text{subsatnce}\text{at}\text{time}\text{t}\text{=}\text{0}\\ {\text{N}}_{\text{t}}\text{= Amount}\text{of}\text{subsatnce}\text{after}\text{time, t}\\ \text{k}\text{=}\text{rate}\text{constant}\end{array}$