A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.40

Question

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.40 107 N/m2 and a temperature of 19.0°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

T1= 19+273 = 292K

T2=-78.5 + 273 = 194.5

P = P (T/ T) since volume is constant.

P = 1.4e7* (194.5/ 292) = 9.33e7 N/m2

(b) P1V1/T1 = P2V2/T2

V1= 50 L   

since 1/10th of gas escapes , so V2= 50 - (1/10 )50 = 45L

P2= (P1V1/T1)(T2/V2)

P2= (1.4e7 * 50/ 272) (194.5/45)

P2= 1.11e 7 N/m2

(c)P/ T = P /T) since volume is constant.

P2= 1 atm =101325 N/m2


101325/ T = 1.4e7 / 292

T2= 101325/47945.2

T2= 2 K

T2= 2-273 = -271 o C

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