Question

Almost all gaseous systems that we use are gas mixtures, air is the most obvious example. Air is composed of 78% nitrogen, 20% oxygen, 1 % argon, 1% water vapor, 0.3% carbon dioxide. Chemists often express the composition of a gas not with percent, but with a fraction. The mole fraction of nitrogen,Χ_N2 , in air is defined as

Χ_N2= n_N2 ⁄ n_Total = 0.78

The pressure of a gas mixture is the sum of the partial pressures of each gas. In a mixture of three gases (A, B, & C) the pressure is:

P_Total = P_A + P_B + P_C

The mole fraction can also be determined from the partial pressures. The mole fraction of gas A can be found from the relationship.

Χ_A= P_A ⁄ P_Total

A 4.4 L scuba tank is filled to a total pressure of 220 atm at room temperature (298 K) with three gasses:

Oxygen at a partial pressure of P_O2 = 34.4 atm.

Nitrogen at a partial pressure of P_N2 = 55.1 atm.

Helium* at a partial pressure of P_He = 130.5 atm.

From the pressure of the tank determine the total number of moles of gas in the tank. Use the partial pressures to determine the mole fraction of oxygen in the tank. Finally, report the moles of O₂(g) in the scuba tank.

Answer 1

Using ideal gas equation

PV = nRT

P =pressure

V= volume

n = total moles

n = PV/RT

= 220×4.4/0.0821×298

= 39.6 moles

Total miles of cases = 39.6 moles

Mole fraction of O2 = 34.4/220

=> 0.156

Moles of oxygen = PV/RT

=34.4×4.4/0.0821×298

= 6.19 moles