Chapter 13, Problem 63A

Interpretation Introduction

Interpretation:

The volume occupied by one and two mol of a gas at STP is to be calculated.

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 63A

The volume occupied by one mol of a gas at STP is $22.4L$

The volume occupied by two mol of a gas at STP is $44.8L$

Explanation of Solution

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

$\mathrm{PV}=nRT$

Or

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

Given data for one mole is:

$\text{n=1}\text{mol}$

$\begin{array}{l}\mathrm{At}STP\\ \mathrm{P}=1atm\end{array}$

$\mathrm{T}=273K$

$\text{R=}0.0821Latm{K}^{-1}mo{l}^{-1}$

Now substituting the values into formula,

$\begin{array}{c}V=\frac{nRT}{P}\\ =\frac{1\times 0.0821\times 273}{1}\\ =22.4L\end{array}$

Given data for two moles is:

$\text{n=2}\text{mol}$

$\begin{array}{l}\mathrm{At}STP\\ \mathrm{P}=1atm\end{array}$

$\mathrm{T}=273K$

$\text{R=}0.0821Latm{K}^{-1}mo{l}^{-1}$

Now substituting the values into formula,

$\begin{array}{c}V=\frac{nRT}{P}\\ =\frac{2\times 0.0821\times 273}{1}\\ =44.8L\end{array}$

Conclusion

$1mol$ of each gas at STP occupies $22.4L$ and $2mol$ occupies $44.8L$