Question

A neon – dioxygen mixture contains 70.6 g dioxygen and 167.5 g neon. If the pressure of the mixture of gases in the cylinder is 25 bar, what is the partial pressure of oxygen and neon in the mixture?

Answer 1

Hint: The partial pressure of any substance in a mixture is equal to the mole fraction of the same substance in the mixture multiplied by the total pressure. Partial pressure has the same units as that of pressure.

Complete step by step answer:
In a mixture of gases, each constituent gas has a partial pressure which is the theoretical pressure of that constituent gas if it alone occupied the entire volume of the original mixture at the same temperature. It is the measure of the thermodynamic activity of the gas molecules. The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture.
In the given question:
Moles of dioxygen = $\dfrac{{70.6}}{{32}}$ = 2.21 moles

And the moles of neon = $\dfrac{{167.5}}{{20}}$ = 8.38 moles

Thus, total number of moles in the mixture = 2.21 + 8.38 = 10.59 moles

Mole fraction of dioxygen = $\dfrac{{2.21}}{{10.59}}$ = 0.21

And the mole fraction of neon = $\dfrac{{8.38}}{{10.59}}$ = 0.79

Now,
Partial pressure of dioxygen = 0.21 $\times$ 25 bar = 5.25 bar
And the partial pressure of neon = 0.79 $\times$ 25 bar = 19.75 bar

Hence, the partial pressure of dioxygen and neon is equal to 5.25 bar and 19.75 bar respectively.

Note: Remember that the sum of partial pressures of all the constituents of a mixture is equal to the total pressure. This can be used to verify if the partial pressures found are correct.