Chapter 18, Problem 125A

Interpretation Introduction

Interpretation: The volume occupied by 24.5 g of carbon dioxide gas which has a volume of 88.8 kPa and temperature of ${\text{55}}^{\text{ο}}\text{C}$ is to be calculated.

Concept Introduction: The product of pressure (p) and volume (V) is equal to the product of the number of moles (n), temperature (T), and gas constant (R). This relation is called the ideal gas equation.

Answer to Problem 125A

The volume occupied by 24.5 g of carbon dioxide gas which has a volume of 88.8 kPa and a temperature of ${\text{55}}^{\text{ο}}\text{C}$ is 17.22 L.

Explanation of Solution

Given;

Mass of carbon dioxide is 24.5 g.

Temperature is ${\text{55}}^{\text{ο}}\text{C}$ .

Pressure is 88.8 kPa.

Using the ideal gas equation, for calculating the volume occupied by carbon dioxide gas as follows:

  $\begin{array}{c}\text{pV}=\text{nRT}\\ \text{V}=\frac{\text{nRT}}{\text{p}}\\ =\frac{\frac{\text{Given}\text{mass}}{\text{Molar}\text{mass}}\text{RT}}{\text{p}}\end{array}$

Now, plug the given values in the above equation as:

  $\begin{array}{c}\text{V}=\frac{\frac{\text{24}\text{.5 g}}{\text{44}\text{.01}\text{g/mol}}\times 8.314\frac{\text{L}\text{.kPa}}{\text{mol}\text{.K}}\times \left(55+273.15\right)\text{K}}{\text{88}\text{.8}\text{kPa}}\\ =\frac{\text{0}\text{.56}\text{mol}\times 8.314\frac{\text{L}\text{.kPa}}{\text{mol}\text{.K}}\times \left(328.5\right)\text{K}}{\text{88}\text{.8}\text{kPa}}\\ \text{V}=17.22\text{L}\end{array}$