Chapter 13, Problem 77A

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 77A

The number of moles of the gas at $35°C$ is $2.7mol$

Explanation of Solution

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

Now

$\mathrm{V}=22L$

$\text{P=3}\text{.1}\text{atm}$

$\text{R=}0.0821{\text{LatmK}}^{\text{-1}}{\text{mol}}^{\text{-1}}$

$\mathrm{T}=35C$

To convert temperature into Kelvin,

$\begin{array}{c}\mathrm{T}\left(K\right)=T\left(C\right)+273\\ =35+273\\ =308K\end{array}$

Now substituting the values into formula,

$\begin{array}{c}n=\frac{PV}{RT}\\ =\frac{3.1\times 22}{0.0821\times 308}\\ =2.7mol\end{array}$

Conclusion

The number of moles of the gas at $35°C$ is $2.7mol$