Chapter 17, Problem 113A

Interpretation Introduction

Interpretation: The number of hydrogen molecules in 44.8 L H₂(g) at STP should be calculated.

Concept Introduction: 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 113A

The number of hydrogen molecules in 44.8 L H₂(g) at STP is $\text{1}\text{.2}\times {\text{10}}^{24}\text{ molecules}$

Explanation of Solution

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

The required conversion factor is:

  $\frac{\text{1 mol}}{\text{22}\text{.4 L}}\text{× }44.8\text{ L}$

On solving,

  $\frac{\text{1 mol}}{\text{22}\text{.4 L}}\text{× }44.8\text{ L = 2 mol}$

Thus, the number of moles for $\text{44}\text{.8 L}$ of ${\text{H}}_{\text{2}}\text{(g)}$ at STP is $\text{2 mol}$ .

Now, to determine the number of hydrogen molecules in $\text{2 mol}$ Avogadro’s number is used as:

  $\text{2 mol}\times \frac{\text{6}\text{.02}\times {\text{10}}^{23}\text{ molecules}}{1\text{ mol}}\text{ = 1}\text{.2}\times {\text{10}}^{24}\text{ molecules}$

Hence, the number of hydrogen molecules in 44.8 L H₂(g) at STP is $\text{1}\text{.2}\times {\text{10}}^{24}\text{ molecules}$