A gas mixture being used to simulate the atmosphere of another planet consists of 305 mg of methane, 186 mg of argon, and 267 mg of nitrogen.

Question

The partial pressure of nitrogen at 292 K is 7 kPa. Calculate the total pressure of the mixture. Calculate the volume.

Answer 1

Dalton's Law of Partial Pressures

The mole fraction of a gas times the total pressure = partial pressure of that gas

Total pressure = sum of partial pressures of all the gases present

moles methane (16 g/mol) = 305 mg x 1 g/1000 mg x 1 mol/16 g = 0.0191 mols

moles argon (40 g/mol) = 186 mg x 1 g/1000 mg x 1 mol/40 g = 0.00465 mols

moles nitrogen (28 g/mol) = 267 mg x 1 g/1000 mg x 1 mol/28 g) = 0.00954 mols

Total moles = 0.03329 moles

Mole fraction nitrogen = 0.00954 / 0.03329 = 0.287

0.287 P_total = 7 kPa

P_total = 7 kPa / 0.287 = 24.4 kPa ... total pressure of the mixture

To find the volume we can use the ideal gas law PV = nRT

P = pressure = 24.4 kPa

V = volume = ? liters

n = total moles = 0.03329 mols

R = gas constant = 8.314 L-kPa/Kmol

T = temp in K = 292K

Solving for V (volume) we have..

V = nRT/P = (0.03329)(8.314)(292) / 24.4

V = 3.31 liters