Chapter 10, Problem 81A

Interpretation Introduction

Interpretation: The method to determine the molar mass of a gaseous compound needs to be determined if the molecular formula is not known.

Concept Introduction: The relation between pressure, volume, number of moles, and temperature of a gas is as follows:

  $PV=nRT$

Here, P is pressure, V is volume, n is the number of moles, R is the Universal gas constant, and T is temperature.

Explanation of Solution

For a given gaseous compound, the molar mass is the mass of the compound in 1 mol. Now, if the molar volume of the compound is taken at STP, that is, 22.4 L and its mass is measured, that mass will be the molar mass of the compound. This relation can be represented as follows:

  $PV=nRT$

At STP, the value of pressure and temperature are 1 atm and 273.15 K respectively. If the molar volume is taken, the number of moles calculated will be 1 mol.

  $\begin{array}{c}n=\frac{PV}{RT}\\ =\frac{\left(1\text{ atm}\right)\left(22.4\text{ L}\right)}{\left(0.082\text{ L atm/mol K}\right)\left(273.15\text{ K}\right)}\\ =1\text{ mol}\end{array}$

Now, the number of moles is related to the mass and molar mass of the compound as follows:

  $n=\frac{m}{M}$

For 1 mol, the mass of the compound will be equal to its molar mass. Thus, if the mass of the gaseous compound under these conditions is measured it will be equal to the molar mass of the compound. This way, the molar mass of a gaseous compound can be determined without knowing the molecular formula.