A high-pressure gas cylinder contains 30.0 L of toxic gas at a pressure of 1.50

Question

A high-pressure gas cylinder contains 30.0 L of toxic gas at a pressure of 1.50 x10^7 N/m2 and a temperature of 30.0°C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperatures (78.5°C), to reduce the leak rate and pressure so that it can be safely repaired.

(a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change?
(b) What is the final pressure if one-tenth of the gas escapes?
(c) To what temperature must the tank be cooled 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

1. Isochoric process
P1/T1 = P2/T2
1.5*10^7/303.16 = P2/194.66
P2 = 9.6315*10^6 Pa
2. P1V = nRT1
1.5*10^7*30*10^-3 = nR(303.16)
nR = 1484.36469

P2V = mRT2
P2*30*10^-3 = mR194.66
m = 0.9n
P2 = 0.9nR*194.66/30*10^-3 = 8.66839*10^6 Pa
3. 1.5*10^7/303.16 = 1.01*10^5/T
T = 2.04127 K

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