Question

A gaseous mixture contains 426.0 Torr of H2(g), 362.9 Torr of N2(g), and 80.1 Torr of Ar(g). Calculate the mole fraction, X, of each of these gases.

X_N2

X_H2

X_Ar

Answer 1

Let P1 = partial pressure gas
X1 = mole fraction of gas
and Pt = total pressure

P1 = (X1)(Pt)
X1 = P1/Pt

This is derived from
equation of partial pressure gas over total pressure
P = nRT/V
P1 = n1RT/V over Pt = ntRT/V = P1/Pt = n1/nt
Therefore ratio of partial pressure gas/total pressure = mole fraction individual gas
Total pressure: 369.7 + 433 + 74.3 = 877 torr
X H2 = 433/877 = 0.494
X N2 = 369.7/877 = 0.422
X Ar = 74.3/877 = 0.0847

or other way of solving it

The total gas pressure for the mixtrues of the partial pressures of gasses is determined to be:

433.0 torr + 369.7 torr + 74.3 torr = 877.0 torr


X H2 433.0 torr/ 877.0 torr = 0.4940 = 49.4% hydrogen gas.

X N2 369.7 torr/ 877.0 torr = 0.4216 = 42.2% nitrogen gas.

X Ar 74.3 torr/ 877.0 torr = 0.0847 = 8.47% argon gas.