Dalton's Law of Partial Pressure: Heliox Tank Mystery

What is the partial pressure of helium gas in the tank?

If the total pressure in a tank of heliox is 208 atm and the mole fraction of oxygen is 0.220, what is the partial pressure of helium in the tank?

Answer:

Partial pressure of helium gas in the tank is 162.24 atm.

Partial Pressure:

A partial pressure is the imaginary pressure that a gas would have if it were to occupy the complete volume of the initial mixture by itself at the same temperature. Each gas in a mixture of gases has a partial pressure.

Explanation:

Total pressure in Heloix (P) = 208 atm

The mole fraction of an individual gas component in an ideal gas mixture can be expressed in terms of the component's partial pressure or the moles of the component

Mole fraction of oxygen (X₀) = 0.220

The sum of the mole fractions of all the components present must equal 1.

Mole fraction of helium (Xₐ) = 1-(X₀) = 1- 0.220= 0.78

According to Dalton's law of partial pressure:

Partial pressure of oxygen gas in Heloix: P*X₀ = 208 * 0.22 = 45.76 atm

Partial pressure of helium gas in Heloix: P*Xₐ = 208 * 0.78 = 162.24 atm

Partial pressure of helium gas is 162.24 atm.