Chapter 10.2, Problem 30LC

Interpretation Introduction

Interpretation: The molar mass of an element that has a density of 1.7824 g/L should be calculated.

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 30LC

The molar mass of an element that has a density of 1.7824 g/L is $\text{39}\text{.9 g/mol}$ .

Explanation of Solution

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 element and molar volume at STP, the molar mass of the compound 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:

  $\text{molar mass (g/mol) = }\frac{\text{1}\text{.7824 g}}{\text{L}}\text{×}\frac{\text{22}\text{.4 L}}{\text{1 mol}}\text{ = 39}\text{.9 g/mol}$

Hence, the molar mass of an element that has a density of 1.7824 g/L is $\text{39}\text{.9 g/mol}$ .