Question

A common concept that crops up in a Dalton's Law context is mole fraction.

Suppose you had equal moles of two different gases in a mixture. Then the mole fraction for each would be 0.50.

The mole fraction for each gas is simply the moles of that gas divided by the total moles in the mixture.

Seems simple enough. How does it relate to Dalton's Law?

Answer: the mole fraction also gives the fraction of the total pressue each gas contributes. So if the mole fraction for a gas was 0.50, then it would contribute 50% of the total pressure. If the mole fraction of a gas was 0.15, then its partial pressure would be 0.15 times the total pressure.

The reverse is also true. If you divided the partial pressure of a gas by the total pressure, you would get the mole fraction for that gas.

By the way, mole fractions are unitless numbers. The mole (or pressure) units cancel out.

Use this to solve for the following questions.

A tank contains 480.0 grams of oxygen and 80.00 grams of helium at a total pressure of 7.00 atmospheres. Calculate the following.

         How many moles of O₂ are in the tank?  moles O₂

         How many moles of He are in the tank?  moles He

         Total moles of gas in the tank?  moles of gas

          Mole fraction of O₂?

          Mole fraction of He?

          Partial pressure of O₂?  atm

          Partial pressure of He?  atm

Answer 1

molar mass of O₂ = 31.9988 g/mole

molar mass of He = 4.0 g/mole

no. of mole = gm of compound/molar mass

no. of mole of  O₂​ = 480/31.9988 = 15 mole

no. of mole of He = 80/4.0 = 20 mole

no. of mole of  O₂​ = 15 mole

no. of mole of He = 20 mole

Total mole = sum of indivisual mole

total mole of gas = mole of  O₂​ + mole of He = 15 + 20 = 35 mole

mole fraction = no. of indivisual mole / total mole

mole fractin of  O₂​ = 15/35 = 0.4286

mole fraction of He = 20/35 = 0.5714

Partial pressure = mole fraction X total pressure

partial pressure of  O₂​ = 0.4286 X 7 = 3 atm

partial pressure of He = 0.5714 X 7 = 4 atm