The enclosed cabin of a submarine has a volume of 2.4 x 105 liters, a temperature of 312 K, and a pressure of 116 kPa. As people in the cabin breathe, carbon dioxide gas, CO2(g), can build up to unsafe levels. Air in the cabin becomes unsafe to breathe when the mass of CO2(g) in this cabin exceeds 2156 grams. State what happens to the average kinetic energy of the gas molecules if the cabin temperature decreases.

Question:

1 State what happens to the average kinetic energy of the gas molecules if the cabin

temperature decreases.

2 Show a numerical setup for calculating the pressure in the submarine cabin if the cabin

temperature changes to 293 K.

3 Determine the number of moles of CO₂(g) in the submarine cabin at which the air

becomes unsafe to breathe. The gram-formula mass of CO₂ is 44.0 g/mol.

4 Convert the original air pressure in the cabin of the submarine to atmospheres.

1) The average kinetic energy of the gas molecules will decrease

2) P₂ = 293 K × 116 kPa/312 K = 108.94 kPa

3) 49 mols

4) 116 kPa  = 1.145 atm

Explanation:

(1) When the cabin temperature decreases, the pressure within the cabin will decrease because the average kinetic energy of the gas molecules will decrease. That is the gas particles will have a lower speed.

(2) P₁V₁/T₁ = V₂P₂/T₂

Since the volume is constant we have

116 kPa/312 K = P₂/293 K

P₂ = 293 K × 116 kPa/312 K = 108.94 kPa

(3)  

Since CO₂ is 44.0 g/mol, we have

2156/44 = 49 mols

(4) 1 atm = 101325 Pa

Therefore 116 kPa = 1/101325 ×116000 = 1.145 atm