Chapter 10.2, Problem 31LC

Interpretation Introduction

Interpretation: The molar masses of given gases A, B and C should be calculated and must be identified as ammonia, ${\text{NH}}_{\text{3}}$ , sulfur dioxide, ${\text{SO}}_2$ , chlorine, ${\text{Cl}}_2$ , nitrogen, ${\text{N}}_2$ , or methane, ${\text{CH}}_4$ .

Concept Introduction: A factor that uses one set of units to change it to another set of units is said to be a conversion factor.

Answer to Problem 31LC

The molar masses of given gases A, B and C is 28.0 g/mol, 64.1 g/mol and 16.0 g/mol respectively.

Gas A represents nitrogen, ${\text{N}}_2$ , gas B represents sulfur dioxide, ${\text{SO}}_2$ and gas C represents methane, ${\text{CH}}_4$ .

Explanation of Solution

Given:

The density of gases A, B and C at STP are 1.25 g/L, 2.86 g/L and 0.714 g/L respectively.

The molar volume of any compound at STP is 22.4 L for 1 mol of the compound.

Now, using the value of density of the given gases and molar volume at STP, the molar mass of the gases can be calculated.

The required conversion factor is:

  $\text{molar mass (g/mol) = }\frac{\text{g}}{\text{L}}\text{×}\frac{\text{22}\text{.4 L}}{\text{1 mol}}$

On substituting the value of density and solving:

For gas A:

  $\text{molar mass (g/mol) = }\frac{\text{1}\text{.25 g}}{\text{L}}\text{×}\frac{\text{22}\text{.4 L}}{\text{1 mol}}\text{ = 28 g/mol}$

For gas B:

  $\text{molar mass (g/mol) = }\frac{\text{2}\text{.86 g}}{\text{L}}\text{×}\frac{\text{22}\text{.4 L}}{\text{1 mol}}\text{ = 64}\text{.1 g/mol}$

For gas C:

  $\text{molar mass (g/mol) = }\frac{\text{0}\text{.714 g}}{\text{L}}\text{×}\frac{\text{22}\text{.4 L}}{\text{1 mol}}\text{ = 16}\text{.0 g/mol}$

The molar masses of:

ammonia, ${\text{NH}}_{\text{3}}$ : 17 g/mol

sulfur dioxide, ${\text{SO}}_2$ : 64.1 g/mol

chlorine, ${\text{Cl}}_2$ : 35.4 g/mol

nitrogen, ${\text{N}}_2$ : 28 g/mol

methane, ${\text{CH}}_4$ : 16 g/mol

On comparing the values of molar masses, it can be concluded that gas A represents nitrogen, ${\text{N}}_2$ , gas B represents sulfur dioxide, ${\text{SO}}_2$ and gas C represents methane, ${\text{CH}}_4$ .