Question

A gas mixture consists of 320 mg of methane, 175 mg of argon, and 225 mg of neon. the partial pressure of neon at 300k is 8.87 kpa. calculate (i) the volume and (ii) the total pressure of the mixture.

Answer 1

To determine the volume of the gas mixture, we first need to determine the total pressure of the mixture. To do this, we use the definition of the partial pressure of a component in the gas mixture. The partial pressure is the pressure of a component as if it were alone in the container. It is equal to  the mole fraction of the component times the total pressure of the system. From this, we determine total pressure.

Pneon = xneonP
P = Pneon / xneon
P = 8.87 kPa / (225 / (225 + 320 + 175))
P = 8.87 kPa / 0.3125 = 28.384 kPa

Assuming ideal gas, we use PV=nRT to calculate for the volume,
PV = nRT
V = nRT / P

n = 225 mg ( 1 mmol / 20.18 mg) + 320 mg ( 1 mmol / 16.05 mg ) + 175 mg ( 1 mmol / 39.95 mg ) = 35.47 mg = 35467.0 g 

V = 35467.0 (8.314) (300) / (28384) = 3116.68 m^3