Chapter 22, Problem 22.22QP

(a)

Interpretation Introduction

To determine: The concentration of cobalt expressed in parts per million.

Interpretation: The concentration of cobalt in grams per kilogram of solvent. Its concentration is to be calculated in parts per million.

Concept introduction: Parts per million by mass is the amount of solute in milligrams present in one kilogram of the substance.

Therefore, the concentration in $\text{ppm}$ is calculated by the formula,

$\text{Concentration}\text{in}\text{ppm}=\frac{\text{Mass}\text{of}\text{solute}\text{in}\text{milligrams}}{\text{Mass}\text{of}\text{solvent}\text{in}\text{kilograms}}$

Answer to Problem 22.22QP

The concentration of cobalt expressed in parts per million is $\underset{\_}{4.3\times 10^{-2}ppm}$.

Explanation of Solution

Given

The concentration of cobalt in grams per kilogram is $4.3\times {10}^{-5}\text{g}/\text{kg}$.

Parts per million by mass is the amount of solute in milligrams present in one kilogram of the substance.

One gram is equal to $1000$ milligram.

Therefore, $4.3\times {10}^{-5}\text{g}/\text{kg}$ is equal to $4.3\times {10}^{-2}\text{mg}/\text{kg}$.

Thus, the concentration of cobalt is $\underset{\_}{4.3\times 10^{-2}ppm}$.

(b)

Interpretation Introduction

To determine: The concentration of boron expressed in parts per million.

Interpretation: The amount of boron in grams is given to be present in given mass in kilogram. Its concentration is to be calculated in parts per million.

Concept introduction: Parts per million by mass is the amount of solute in milligrams present in one kilogram of the substance.

Therefore, the concentration in $\text{ppm}$ is calculated by the formula,

$\text{Concentration}\text{in}\text{ppm}=\frac{\text{Mass}\text{of}\text{solute}\text{in}\text{milligrams}}{\text{Mass}\text{of}\text{solvent}\text{in}\text{kilograms}}$

Answer to Problem 22.22QP

The concentration of boron expressed in parts per million is $\underset{\_}{0.14ppm}$.

Explanation of Solution

Given

The mass of boron is $0.014\text{g}$.

The mass of the body is $100\text{kg}$.

One gram is equal to $1000$ milligram.

Therefore, $0.014\text{g}$ is equal to $14\text{mg}$.

The concentration in $\text{ppm}$ is calculated by the formula,

$\text{Concentration}\text{in}\text{ppm}=\frac{\text{Mass}\text{of}\text{solute}\text{in}\text{milligrams}}{\text{Mass}\text{of}\text{solvent}\text{in}\text{kilograms}}$

Substitute the value of mass of boron and body in the above equation.

$\begin{array}{c}\text{Concentration}\text{in}\text{ppm}=\frac{14\text{mg}}{100\text{kg}}\\ =0.14\text{ppm}\end{array}$

Therefore, the parts per million of boron is $\underset{\_}{0.14ppm}$.

(c)

Interpretation Introduction

To determine: The concentration of chromium expressed in parts per million.

Interpretation: The amount of chromium in milligrams is given to be present in given mass. Its concentration is to be calculated in parts per million.

Concept introduction: Parts per million by mass is the amount of solute in milligrams present in one kilogram of the substance.

Therefore, the concentration in $\text{ppm}$ is calculated by the formula,

$\text{Concentration}\text{in}\text{ppm}=\frac{\text{Mass}\text{of}\text{solute}\text{in}\text{milligrams}}{\text{Mass}\text{of}\text{solvent}\text{in}\text{kilograms}}$

Answer to Problem 22.22QP

The concentration of chromium expressed in parts per million is $\underset{\_}{0.07ppm}$.

Explanation of Solution

Given

The mass of cooper is $5\text{mg}$.

The mass of the body is $70\text{kg}$.

The concentration in $\text{ppm}$ is calculated by the formula,

$\text{Concentration}\text{in}\text{ppm}=\frac{\text{Mass}\text{of}\text{solute}\text{in}\text{milligrams}}{\text{Mass}\text{of}\text{solvent}\text{in}\text{kilograms}}$

Substitute the value of mass of chromium and body in the above equation.

$\begin{array}{c}\text{Concentration}\text{in}\text{ppm}=\frac{5\text{mg}}{70\text{kg}}\\ =0.07\text{ppm}\end{array}$

Therefore, the parts per million of chromium is $\underset{\_}{0.07ppm}$.

Conclusion

1. a. The concentration of cobalt expressed in parts per million is $\underset{\_}{4.3\times 10^{-2}ppm}$.
2. b. The concentration of boron expressed in parts per million is $\underset{\_}{0.14ppm}$.
3. c. The concentration of chromium in parts per million is $\underset{\_}{0.07ppm}$.