Human body discharges 9.60x10^2 of CO2/day. Space craft has volume of 9.30x10^4

Question

Human body discharges 9.60x10^2 of CO2/day. Space craft has volume of 9.30x10^4 L.

Three astronauts are going to make a voyage lasting 6 days. The carbon dioxide that they exhale must be removed from the cabin of the space craft, and a human body discharges about 9.60 Times 10^2 g of CO_2/day. If the cabin of the space craft has a volume of 9.30 Times 10^4 L and the partial pressure of CO_2 must be maintained at not more than 4.1 torr at the cabin temperature of 27.0 degree C, what is the total weight of CO_2, expressed in kg, that must be removed from the cabin on this journey made by the three astronauts? Assume that the initial partial pressure of CO_2 (g) in the cabin is zero at the start of the journey.

Explanation / Answer

mass of CO2 discharged by a single person per day = 9.60x102 g CO2/day

Hence total mass of CO2 discharged by 3 astronauts in 6 days = 6 day x 3 person x 9.60x102 g CO2/day/person

= 1.73x104 g CO2

Volume of the space craft, V = 9.30x104 L

Maximum allowed partial pressure of CO2 inside the space craft = 4.1 torr = 0.005395 atm

temperature, T = 27 DegC = 27+273 = 300.0 K

Now we can calculate the maximum moles of CO2 that can remain inside the space craft from ideal gas equation

PV = nRT

=> n = PV/RT = (0.005395 atm x 9.30x104 L) / (0.0821 L.atm.mol-1K-1 x 300.0 K)

=> n = 20.37 mol CO2

molar mass of CO2 = 44.0 g/mol

Hence mass of CO2 that can lie inside space craft = 20.37 mol x 44.0 g/mol = 896 g CO2

Hence mass of CO2 need to be discharged = 1.73x104 g CO2 - 896 g CO2

= 16404 g = 16404 g x (1 Kg / 1000 g) = 16.4 Kg (answer)

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