Chapter 14.3, Problem 26SP

Interpretation Introduction

Interpretation: The number of moles of helium does sphere contains is to be determined.

Concept introduction: Ideal gas, or a perfect gas, is a gas whose physical behavior corresponds to a specific idealized relation between pressure, volume, and temperature, known as the ideal or general gas law.

Answer to Problem 26SP

The number of moles of helium gas in a sphere contains is $250.7557\text{ mol}$ .

Explanation of Solution

The volume of the sphere is $685\text{ L}$ .

The pressure of the sphere is $1.89\times {10}^3\text{ kPa}$ .

The temperature of the sphere is $621\text{ K}$ .

The value of a gas constant is $8.314{\text{ kPa L K}}^{-1}{\text{ mol}}^{-1}$ .

The ideal gas is as follows:

  $PV=nRT$   ...... (1)

Where,

• $P$ is the pressure.
• $n$ is the number of moles.
• $T$ is the temperature.
• $V$ is the volume.
• $R$ is a gas constant.

Substitute the values of $P$ , $R$ , $T$ and $V$ in equation (1) to calculate the number of moles of helium gas in a sphere as follows:

  $\begin{array}{c}PV=nRT\\ n=\frac{PV}{RT}\\ =\frac{1.89\times {10}^3\bcancel{\text{kPa}}\times 685\bcancel{\text{L}}}{8.314\bcancel{\text{kPa}}\bcancel{\text{L }}\bcancel{{\text{K}}^{-1}}{\text{ mol}}^{-1}\times 621\bcancel{\text{K}}}\\ =250.7557\text{ mol}\end{array}$

Therefore, the number of moles of helium gas in a sphere contains is $250.7557\text{ mol}$ .

Conclusion

The number of moles of helium gas in a sphere contains is $250.7557\text{ mol}$ .