Chapter 13, Problem 68A

Interpretation Introduction

Interpretation:

The number of molecules 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 68A

The number of molecules of the gas is $3.03\times {10}^{4}molecules$

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

$\mathrm{V}=1L$

${\text{P=1×10}}^{\text{-15}}\text{mmHg}$

$\text{R=}\text{62}\text{.4}{\text{LmmHgK}}^{\text{-1}}{\text{mol}}^{\text{-1}}$

$\mathrm{T}=22C$

To convert temperature into Kelvin ,

$\begin{array}{c}\mathrm{T}\left(K\right)=T\left(C\right)+273\\ =22+273\\ =295K\end{array}$

Now substituting the values into formula,

$\begin{array}{c}n=\frac{PV}{RT}\\ =\frac{1\times {10}^{-15}\times 1}{62.4\times 295}\\ =5.43\times {10}^{-20}mol\end{array}$

Further number of molecules is calculated by multiplying number of moles with Avogadro’s number.

$\begin{array}{c}Numberofmolecules=6.022\times {10}^{23}\times 5.43\times {10}^{-20}\\ =3.03\times {10}^{4}molecules\end{array}$

Therefore number of molecules of the gas is $3.03\times {10}^{4}molecules$

Conclusion

The number of molecules of the gas is $3.03\times {10}^{4}molecules$.