Question

Assume the volume of the crew cabin is 74,000 L. The pressure is maintained at around 1.00 atm, ideally with an 80% nitrogen and 20% oxygen mix monitored by two gas systems. Assume that the temperature of the cabin is around 20ºC. How many moles of oxygen gas are present in the crew cabin at any given time? *

Answer 1

The number of moles of oxygen present in the crew cabin at any given time is 615.309 moles

Step-by-step explanation:

The given parameters are;

Volume of the crew cabin = 74,000 L

Pressure of the crew cabin = 1.00 atm

Percentage of nitrogen in the mixture of gases in the cabin = 80%

Percentage of oxygen in the mixture of gases in the cabin = 20%

Temperature of the cabin = 20°C = 293.15 K

Therefore, volume of oxygen in the crew cabin = 20% of 74,000 L

Hence, volume of oxygen in the crew cabin =
`(20)/(100) * 74,000 \, L = 14,800 \, L`

From the universal gas equation, we have;

`n = (P * V)/(R * T)`

Where:

n = Number of moles of oxygen

P = Pressure = 1.00 atm

V = Volume of oxygen = 14,800 L

T = Temperature = 293.15 K

R = Universal Gas Constant = 0.08205 L·atm/(mol·K)

Plugging in the values, we have;

`n = (1 * 14,800 )/(0.08205 * 293.15 ) = 615.309 \, moles`

The number of moles of oxygen present in the crew cabin at any given time = 615.309 moles.