Chapter 13.2, Problem 29PP

Interpretation Introduction

Interpretation:

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

Concept introduction:

Ideal gas equation helps to calculate number of the moles of a gas at given temperature, volume 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 29PP

The number of moles of the gas is $0.0068mol$

Explanation of Solution

Given information:

The volume of the gas $\mathrm{V}=0.044L$

The pressure of the gas $\mathrm{P}=3.81atm$

The temperature of the gas $\mathrm{T}=25C$

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

$\mathrm{PV}=nRT$

Or

$\mathrm{n}=\frac{PV}{RT}$

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

To convert temperature into Kelvin,

$\begin{array}{c}\mathrm{T}\left(K\right)=T\left(C\right)+273\\ =25+273\\ =298K\end{array}$

Now substituting the values into formula,

$\begin{array}{c}n=\frac{PV}{RT}\\ =\frac{3.81\times 0.044}{0.0821\times 298}\\ =0.0068mol\end{array}$

Therefore, number of moles of the gas is $0.0068mol$

Conclusion

The number of moles of the gas is $0.0068mol$.