Chapter 10, Problem 103A

Interpretation Introduction

Interpretation: The number of oxygen molecules in a 75.0 g sample of air needs to be determined.

Concept Introduction: The number of moles of a substance is related to mass and molar mass as follows:

  $n=\frac{m}{M}$

Here, m is mass and M is the molar mass of the substance.

Also, the number of moles is related to the pressure of the gas 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

The percentage of oxygen by volume in dry air is given 20.95%.

Thus, the relation between the volume of oxygen and air is:

  $\begin{array}{c}{V}_{{\text{O}}_2}=\frac{20.95}{100}{\text{V}}_{\text{air}}\\ =0.2095{\text{V}}_{\text{air}}\end{array}$

The mass of the air is given 75 g and the density of air is 1.19 g/L. thus, the volume of air can be calculated as follows:

  $\begin{array}{l}d=\frac{m}{\text{}V}\\ V=\frac{m}{d}\end{array}$

Substitute the values,

  $\begin{array}{c}{V}_{\text{air}}=\frac{75\text{ g}}{1.19\text{ g/L}}\\ =63\text{ L}\end{array}$

Now, the volume of oxygen in the air will be:

  $\begin{array}{c}{V}_{{\text{O}}_2}=0.2095{\text{V}}_{\text{air}}\\ =0.2095\left(63\text{ L}\right)\\ =13.20\text{ L}\end{array}$

Therefore, the volume of oxygen gas is 13.20 L.

Now, at STP the value of temperature is 273.15 and pressure is 1 atm. Thus, the number of moles of oxygen gas can be calculated as follows:

  $PV=nRT$

Or,

  $n=\frac{PV}{RT}$

Substitute the values,

  $\begin{array}{c}n=\frac{\left(1\text{ atm}\right)\left(13.20\text{ L}\right)}{\left(0.082\text{ L atm/K mol}\right)\left(273.15\text{ K}\right)}\\ =0.5893\text{ mol}\end{array}$

Therefore, the number of moles of oxygen gas is 0.5893 mol.

Now, the mass of oxygen gas can be calculated as follows:

  $m=n\times M$

Molar mass of oxygen gas is 32 g/mol.

  $\begin{array}{c}m=\left(0.5893\text{ mol}\right)\left(32\text{ g/mol}\right)\\ =18.86\text{ g}\end{array}$

Thus, the mass of oxygen gas is 18.86 g.