A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.35

Question

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.35 times 10^7 Pa and a temperature of 25.0 degree C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature (-78.5 degree C) to reduce the leak rate and pressure so that it can be safely repaired. What is the final pressure, in pascals, in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? What is the final pressure, in pascals, if one-tenth of the gas escapes during this process? To what temperature, in kelvins, must the tank be cooled from its initial state to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)?

Explanation / Answer

part(a)

at constant volume P2/P1 = T2/T1

P1 = 1.35*10^7 Pa

T1 = 25 + 273 = 298 K

T2 = -78.5+273 = 194.5 K

P2/(1.35*10^7) = 194.5/298

P2 = 0.88*10^7 Pa <<<<---------answer

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part(b)

for an ideal gas P1*V1/T1 = P2*V2/T2

V2 = V1 - V1/10 = V1*(9/10) = 0.9*V1

P2*V1*0.9/194.5 = 1.35*10^7*V1/298

P2*0.9/194.5 = 1.35*10^7/298

P2 = 0.98*10^7 Pa

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part(c)

if P2 = 1 atm = 10^5 pa

T2 = ?

at constant volume

P1/T1 = P2/T2

1.35*10^7/298 = 10^5/T2

T2 = 2.2 K <<<--answer

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