Chapter 13, Problem 76A

Interpretation Introduction

Interpretation:

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

Concept introduction:

The equation which helps to calculate density of a gas at given temperature and pressure is given by,

$\begin{array}{l}\text{D=}\frac{\text{PM}}{\text{RT}}\\ \text{where}\\ \text{D}\text{is}\text{the}\text{density}\text{of}\text{gas}\\ \text{M}\text{is}\text{the}\text{molecular}\text{mass}\text{of}\text{gas}\end{array}$

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

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

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

Answer to Problem 76A

The density of the gas is $\text{4}\text{.55}\text{g/L}$

Explanation of Solution

The formula to calculate density is given by:

$\text{D=}\frac{\text{PM}}{\text{RT}}$

According to the statement:

$\begin{array}{l}\text{P=5}\text{.30}\text{atm}\\ \text{M=28}{\text{gmol}}^{\text{-1}}\\ \text{R=0}\text{.0821}{\text{LatmK}}^{\text{-1}}{\text{mol}}^{\text{-1}}\\ {\text{T}}_{}\text{=125}\text{°C}\\ \text{=125+273}\\ \text{=398}\text{K}\end{array}$

Now substituting the values into formula,

$\begin{array}{c}\text{D=}\frac{\text{PM}}{\text{RT}}\\ =\frac{5.30\times 28}{0.0821\times 398}\\ \text{=4}\text{.55}\text{g/L}\end{array}$

Therefore density of the gas is $\text{4}\text{.55}\text{g/L}$

Conclusion

The density of the gas is $\text{4}\text{.55}\text{g/L}$.