Chapter 14.2, Problem 22LC

Interpretation Introduction

Interpretation: To determine the volume if the temperature does not change.

Concept Introduction: Ideal gas equation give the relation between temperature, pressure, and volume. The ideal gas equation can be shown as $\text{PV}\text{=}\text{nRT}$

Answer to Problem 22LC

The final volume will be 1.48kPa.

Explanation of Solution

The formula which gave the relation between the pressure, volume, temperature as well as the number of moles, is named an ideal gas equation.

It can be represented by $\text{PV}\text{=}\text{nRT}$ .

Where P is pressure, V is volume, T is temperature and n is the number of moles.

When the temperature will be kept constant then the new expression will be

  ${\text{P}}_{\text{1}}{\text{V}}_{\text{1}}\text{=}{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}\mathrm{......}\text{(i)}$

Where, ${\text{P}}_{\text{1}}$ is initial pressure, ${\text{P}}_{\text{2}}$ is final pressure, ${\text{V}}_{\text{1}}$ is initial volume, ${\text{V}}_{\text{2}}$ is the final volume.

Given data:

Initial volume ( ${\text{V}}_{\text{1}}$ ) = 6 L.

Initial pressure ( ${\text{P}}_{\text{1}}$ ) = 25kPa

Final pressure ( ${\text{P}}_{\text{2}}$ ) = 101kPa

Final volume ( ${\text{V}}_{\text{2}}$ ) = ?

Now, put the values of the given data in equation (i).

  $\begin{array}{c}{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}\text{=}{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}\\ {\text{V}}_{\text{2}}\text{=}\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{P}}_{\text{2}}}\\ {\text{V}}_{\text{2}}\text{=}\frac{\text{25×6}}{\text{101}}\\ \text{=1}\text{.48}{\text{kP}}_{\text{a}}\end{array}$

Therefore, the volume will be 1.48kPa