Calculate the mole fraction, partial pressures of each gas, and the total pressure in the tank.

Question

A 12.5 L tank is filled with helix mixture containing 24.2 g of He and 4.32 g of O₂ at 298 K. Calculate the mole fraction, partial pressures of each gas, and the total pressure in the tank.

Answer 1

Hi Berryl,

Let's review some basic ideas:

Use the ideal gas law (PV = nRT) when you are asked about a property of a gas (pressure, volume, temperature, amount of moles) and you know three of those properties.

Mole fraction is the fraction of the total moles that a particular substance is contributing to that total:

mole fraction = moles substance / total moles

Think of partial pressure as the pressure a gas would exert if it was the only gas there. Partial pressure is proportional to the number of moles so: partial pressure = total pressure x mole fraction.

Let's calculate total pressure first.

We know the volume in liters and the temperature. We can also find the number of moles of each gas by conversion. So this is a good question for the ideal gas law. Make sure that your units match the idea gas constant, R.

V = 12.5 liters; T = 298 Kelvin; let's use R = 0.0821 L atm / mol K.

Now we want the total moles in the container.

Convert grams to moles by taking grams and dividing by molar mass:

24.2 grams Neon * 1 mol Neon / 20.18 g Neon = 1.199 mol Neon

4.32 grams Oxygen * 1 mol Oxygen / 31.998 g O2 = 0.135 mol Oxygen

Total moles equals the sum of those: 1.334 mol gas

Note that we can combine the moles of gas because according to ideal gas behavior, all ideal gases behave the same way regardless of chemical identity.

Solving for P:

P = nRT/V = 1.334*0.0821*298/12.5 = 2.611 atm.

Moles fractions:

Apply the equation given above: moles Neon/ divided by total moles = 1.199 mol/1.334 mol = 0.899

Oxygen: 0.135/1.334 = .101

Note that the mole fractions should add up to 1.

Partial pressures:

Apply the equation given above:

P_Ne = mole fraction_Ne * P_tot = 0.899 * 2.611 atm = 2.35 atm

P_O2 = mole fraction * P_tot = 0.101*2.611 atm = 0.264 atm

Just like the mole fractions, the partial pressures should add up to the total pressure.

Hope that helps! You should run through the calculations on your own to be sure you understand.