Question

When silent electric discharge is passed through $O_2$ gas, it converts into $O_3$. If the density of final sample is 20 times the density of hydrogen gas under similar conditions, calculate the mass percent of $O_2$ in the final sample.

Answer 1

40%

Answer 2

The density of a gas is directly proportional to its molar mass under similar conditions. Using this, the average molar mass of the final $O_2/O_3$ mixture is calculated as 40 g/mol. By setting up an equation for the average molar mass in terms of the mole fractions of $O_2$ (32 g/mol) and $O_3$ (48 g/mol), the mole fraction of $O_2$ is found to be 0.5. Assuming 1 mole of the mixture, this translates to 0.5 moles of $O_2$ (16 g) and 0.5 moles of $O_3$ (24 g). The total mass is 40 g. The mass percent of $O_2$ is then (16 g / 40 g) * 100 = 40%.