Questions: What is the molar volume of O2 gas under the conditions of temperature and pressure where its density is 0.832 g / L ?

Solution Steps

We are given:

• The density of \(\mathrm{O}_2\) gas: \(0.832 \, \mathrm{g/L}\)

The molar mass of \(\mathrm{O}_2\) can be calculated as follows:

• The atomic mass of oxygen (\(\mathrm{O}\)) is approximately \(16.00 \, \mathrm{g/mol}\).
• Since \(\mathrm{O}_2\) consists of two oxygen atoms, its molar mass is: \[ M_{\mathrm{O}_2} = 2 \times 16.00 \, \mathrm{g/mol} = 32.00 \, \mathrm{g/mol} \]

The density (\(\rho\)) of a gas is given by: \[ \rho = \frac{m}{V} \] where \(m\) is the mass and \(V\) is the volume. Rearranging this formula to solve for volume (\(V\)) gives: \[ V = \frac{m}{\rho} \]

The molar volume (\(V_m\)) is the volume occupied by one mole of the gas. Using the molar mass (\(M_{\mathrm{O}_2}\)) and the given density (\(\rho\)): \[ V_m = \frac{M_{\mathrm{O}_2}}{\rho} \] Substituting the values: \[ V_m = \frac{32.00 \, \mathrm{g/mol}}{0.832 \, \mathrm{g/L}} \] \[ V_m = 38.46 \, \mathrm{L/mol} \]

Final Answer