Chapter 24, Problem 103AP

Interpretation Introduction

Interpretation:

The density of gaseous $\text{HF}$ at its normal boiling point is to be calculated and the discrepancy between the calculated and experimental results is to be discussed.

Concept introduction:

Density is calculated as follows:

$d=\frac{m}{V}$

Here, $d$ is the density, $m$ is the mass of the gas, and $V$ is the volume of the gas.

The ideal gas law is as follows:

$PV=n\text{R}T$

Here, $P$ is the pressure, $V$ is the volume of the gas, $T$ is the temperature, $\text{R}$ is the gas constant, and $n$ is the number of moles.

$n$ is calculated as follows:

$n=\frac{\text{Mass}}{\text{Molar Mass}}$

The density formula for an ideal gas is derived by substituting the value of $n$ in ideal gas lawequation as follows:

$\begin{array}{c}PV=n\text{R}T\\ PV=\left(m/M\right)\text{R}T\end{array}$

$\begin{array}{c}PM=\left(m/V\right)\text{R}T\\ PM=d.\text{R}T\\ d=\frac{PM}{\text{R}T}\end{array}$

Here, R is the gas constant, $d$ is the density, $T$ is the temperature, $P$ is the pressure, and $M$ is the molar mass.