A gas sample contains 4.0 g of CH₄ and 2.0 g of He. What is the volume of the sample at STP?

Question

Quizplus · Accepted Answer

1) Convert the masses of CH₄ and He to moles using their respective molar masses:
4.0 g CH₄ x 1 mol CH₄/16.04 g CH₄ = 0.2498 mol CH₄
2.0 g He x 1 mol He/4.00 g He = 0.5000 mol He

2) Use the mole ratio of CH₄ to total moles to find the mole fraction of CH₄:
Mole fraction of CH₄ = 0.2498 mol CH₄ / (0.2498 mol CH₄ + 0.5000 mol He) = 0.3329

3) Use the mole fraction and the total moles to find the volume at STP using the ideal gas law:
PV = nRT
P = 1 atm (at STP)
R = 0.08206 L atm/mol K
T = 273 K (at STP)
Total moles = 0.2498 mol CH₄ + 0.5000 mol He = 0.7498 mol
V = nRT/P = (0.7498 mol)(0.08206 L atm/mol K)(273 K)/(1 atm) = 16.99 L
(Note: Some sources may use 22.4 L/mol as the volume at STP, but this is only valid for an ideal gas. Real gases deviate from ideal behavior, and this value is only an approximation for a gas like He that is close to ideal.)

A Gas Sample Contains 4