Chapter 13.2, Problem 27PP

Interpretation Introduction

Interpretation:

The volume of the gas is to be calculated when pressure, temperature and number of moles of the gas are given.

Concept introduction:

Ideal gas equation helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Where

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

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

$\mathrm{n}$ is the number of moles of the gas

$\mathrm{R}$ is the ideal gas constant

$\mathrm{T}$ is the temperature of the gas

Answer to Problem 27PP

The volume of the gas is $7.808L$

Explanation of Solution

Given information:

The number of moles of gas is $0.323mol$

The pressure of gas $\mathrm{P}=0.900atm$

Gas constant is $0.0821Latm{K}^{-1}mo{l}^{-1}$

The temperature of the gas $\mathrm{T}=265K$

Ideal gas equation helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Or

$\mathrm{V}=\frac{nRT}{P}$

Where

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

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

$\mathrm{n}$ is the number of moles of the gas

$\mathrm{R}$ is the ideal gas constant

$\mathrm{T}$ is the temperature of the gas

Now

Number of moles of gas is $0.323mol$

$\mathrm{P}=0.900atm$

Gas constant is $0.0821Latm{K}^{-1}mo{l}^{-1}$

$\mathrm{T}=265K$

Now substituting the values into formula,

$\begin{array}{c}V=\frac{nRT}{P}\\ =\frac{0.323\times 0.0821\times 265}{0.900}\\ =7.808L\end{array}$

Therefore, volume of the gas is $7.808L$

Conclusion

The volume of the gas is $7.808L$.