Chapter 14.2, Problem 9SP

Interpretation Introduction

Interpretation: To determine the new volume when the temperature is.

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

Answer to Problem 9SP

The new volume will be 0.95 L

Explanation of Solution

Boyle's law, also known as the Boyle-Mariotte law and Mariotte's law, is a gas law that was discovered experimentally and explains how the pressure and volume of a fixed amount of gas relate to one another.

  $\text{PV=K}$

Where P is pressure, V is volume.

The given data:

  ${\text{V}}_{\text{1}}$ = 2.5L

  ${\text{V}}_{\text{2}}$ =?

  ${\text{P}}_{\text{1}}$ =40KPa

  ${\text{P}}_{\text{2}}$ = 105Kpa

According to Boyles law.

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

Put the values of the given data in the above equation.

  $\begin{array}{c}{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}{\text{=P}}_{\text{2}}{\text{V}}_{\text{2}}\\ {\text{V}}_{\text{2}}\text{=}\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{P}}_{\text{2}}}\\ {\text{V}}_{\text{2}}\text{=}\frac{\text{40×2}\text{.5}}{\text{105}}\\ {\text{V}}_{\text{2}}\text{=0}\text{.95L}\end{array}$

Therefore, the new volume will be 0.95 L.