Question

Suppose that you are travelling in the Space Shuttle Endeavor on a journey to Mars. The atmosphere (of the vehicle) consists of 20% oxygen and 80% helium by volume. It was noticed before take off from the Kennedy Space Center that there is a small leakage which if unchecked, would lead to a continual loss of gas at a rate of 0.05 atm/day through effusion. If the temperature in the space shuttle is maintained at 22°C and the volume of the vehicle is 15,000 liters. Calculate the amounts of helium and oxygen in grams that must be stored on a 5-day journey to allow for the leakage.

Answer 1

With loss rate of 0.05 atm/day, in 5 days there will be $0.05\times5=0.25\ atm$ lost. Since nothing is mentioned about the hypothetical consumption of oxygen by astronauts, the key assumption is that there should be minimum of 0.25 atm of the gas mixture initially. Since pressure and volume are proportional, there are 20% of O₂ and 80% of He by pressure, too. Therefore,

$P_{O_2}=0.25\ atm\times0.2=0.05\ atm$

$P_{He}=0.25\ atm\times0.8=0.2\ atm$

$n_{O_2}=\frac{P_{O_2}V}{RT}=\frac{0.05\ atm\times15000\ L}{0.08206\frac{L\cdot{atm}}{mol\cdot{K}}\times295\ K}=31.0\ mol$

$n_{He}=\frac{P_{He}V}{RT}=\frac{0.2\ atm\times15000\ L}{0.08206\frac{L\cdot{atm}}{mol\cdot{K}}\times295\ K}=124\ mol$

$m(O_2)=31.0\ mol\times\frac{32.00\ g}{1\ mol}=992\ g$

$m(He)=124\ mol\times\frac{4.003\ g}{1\ mol}=496\ g$

Answer: 992 g O₂; 496 g He