Chapter 13, Problem 40P

To determine

To Find: The volume of the helium gas using the ideal gas equation.

Answer to Problem 40P

The volume of the helium gas using the ideal gas equation.is $1.4$ times the original volume

Explanation of Solution

Given:

Final temperature, ${\text{T}}_{\text{2}}=5°\text{C}$

Initial temperature, ${\text{T}}_{\text{1}}=20°\text{C}$

Initial pressure, ${\text{P}}_{\text{1}}=1\text{atm}$

Final pressure, ${\text{P}}_{\text{2}}=0.\text{7}0\text{atm}$

Formula used:

Write the expression for the ideal gas equation.

  $\begin{array}{l}\mathrm{P}\mathrm{V}=\mathrm{n}\mathrm{R}\mathrm{T}\\ \frac{\mathrm{P}\mathrm{V}}{\mathrm{T}}=\mathrm{n}\mathrm{R}\end{array}$

Here, $\mathrm{P}$ is the pressure of the gas,

  $\mathrm{V}$ is the volume of the gas,

  $\mathrm{R}$ is the gas constant,

  $\mathrm{T}$ is the absolute temperature,

Calculation:

Suppose that helium gas is an ideal gas. Means the value is constant $\frac{\mathrm{P}\mathrm{V}}{\mathrm{T}}=\mathrm{n}\mathrm{R}$

  $\frac{\mathrm{P}\mathrm{V}}{\mathrm{T}}=\mathrm{n}\mathrm{R}$

Equate the initial and final state of the gas in the ideal gas equation.

  $\begin{array}{l}\frac{{\mathrm{P}}_1{\mathrm{V}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{P}}_2{\mathrm{V}}_2}{{\mathrm{T}}_2}\\ \frac{{\mathrm{V}}_2}{{\mathrm{V}}_1}=\frac{{\mathrm{P}}_1{\mathrm{T}}_2}{{\mathrm{P}}_2{\mathrm{T}}_1}\\ =\left(\frac{1.0}{0.70}\right)\frac{\left(273+5.0\right)\text{K}}{\left(273+20.0\right)\text{K}}\\ =1.4\end{array}$

Conclusion:

The volume of the helium gas using the ideal gas equation is $1.4$ times the original volume.