Chapter 22, Problem 92A

a.

Interpretation Introduction

Interpretation: To calculate the number of liters occupied by gas.

Concept Introduction: The volume of a gas at standard temperature pressure conditions is $22.4{\text{ L mol}}^{-1}$ .

Answer to Problem 92A

The volume occupied by a gas is $13.9\text{ L}$ .

Explanation of Solution

The moles of chlorine gas is given that is $6.20\times {10}^{-1}{\text{ mol Cl}}_2\left(g\right)$ .

The volume of a gas at standard temperature pressure conditions is $22.4{\text{ L mol}}^{-1}$ .

So, the number of liters occupied by a chlorine gas can be calculated as follows:

  $\begin{array}{l}6.20\times {10}^{-1}{\cancel{\text{mol Cl}}}_2\times \frac{22.4\text{ L}}{1\cancel{{\text{mol Cl}}_2}}\\ =13.9\text{ L}\end{array}$

Thus, the volume occupied by a gas is $13.9\text{ L}$ .

b.

Interpretation Introduction

Interpretation: To calculate the volume occupied by gas.

Concept Introduction: As per Boyle’s law, the volume of gas is in inverse relation to the pressure of a gas for a given mass of a gas at a constant temperature.

It can be expressed as follows:

  ${\text{V}}_{\text{2}}\times {\text{P}}_{\text{2}}={\text{P}}_{\text{1}}{\text{×V}}_{\text{1}}$

Answer to Problem 92A

The volume of a gas is $1\text{ L}$ .

Explanation of Solution

The pressure of a gas is $\text{3 kPa}$ .

The volume of a gas is $\text{6 L}$ at $\text{0}\text{.5 kPa}$

Thus, using Boyle’s law, the volume can be calculated as follows:

  $\begin{array}{c}{\text{V}}_{\text{2}}=\frac{{\text{P}}_{\text{1}}{\text{×V}}_{\text{1}}}{{\text{P}}_{\text{2}}}\\ =\frac{\text{0}\text{.5 }\cancel{\text{kPa}}\text{×6 L}}{\text{3 }\cancel{\text{kPa}}}\\ =1\text{ L}\end{array}$

Thus, the volume of a gas is $1\text{ L}$ .

c.

Interpretation Introduction

Interpretation: To calculate the partial pressure of a gas.

Concept Introduction: The total pressure is the sum of the partial pressure of gases in a mixture of gases.

Answer to Problem 92A

The partial pressure of X gas is $\text{20 kPa}$

Explanation of Solution

Three gases are given, i.e., X, Y, and Z.

The total pressure of a gas is $\text{50 kPa}$ .

The sum of the partial pressures of gases Y and Z is $\text{30 kPa}$ .

Calculation for the partial pressure of X gas is as follows:

  $\begin{array}{c}{P}_X+P_Y+P_Z=P_{Total}\\ P_X+3\text{0 kPa}=\text{50 kPa}\\ P_X=\left(50-30\right)\text{kPa}\\ P_X=20\text{ kPa}\end{array}$