Consider a mixture of 3 gases (helium, argon, and nitrogen). helium has mole fraction of 0.28. argon has a partial pressure of 450 kpa. there are 7.5 moles of nitrogen. the total pressure is 1470 kpa. determine:

a. mole fraction of argon and nitrogen
b. partial pressure of helium and nitrogen
c. number of moles of helium and nitrogen

a. Mole fraction of Argon = 0.28

Mole fraction of N₂ = 0.414

b. Partial pressure He = 411.6 kPa

Partial pressure N₂ = 608.58 kPa

c. Mole of He = 5.54 mole

Mole of N₂ = 7.5 mole

Explanation:

There is a formula for mole fraction which has a relation with partial pressure in a mixture of gases

Mole fraction = Fraction for partial pressure

Mole of Ar / Total moles = Partial pressure Ar / Total pressure

Partial pressure Ar = 450kPa

450kPa / 1470kPa = 0.306

If mole fraction of He is 0.28 we can assume this:

Sum of mole fraction = 1

0.28 (He) + 0.306 (Ar) + Mole fraction N₂ = 1

1 - 0.28 - 0.306 = Mole fraction N₂ → 0.414

Now we can know partial pressure of He and N₂

0.28 = Partial pressure He / 1470kPa

1470kPa . 0.28 = 411.6 kPa

0.414 = Partial pressure N₂ / 1470kPa

1470kPa . 0.414 = 608.58 kPa

Mole fraction: Mole of gas / Total mole

0.414 = Mole of N₂ / Total Mole

0.414  . Total mole = 7.5 mole

7.5 mole / 0.414 = 18.11 Total mole

18.11 . 0.28 (Ar) = 5.07 mole

18.11 . 0.306 (He) =  5.54 mole