A high-pressure gas cylinder contains 30.0 L of toxic gas at a pressure of 1.60

Question

A high-pressure gas cylinder contains 30.0 L of toxic gas at a pressure of 1.60 107 N/m2 and a temperature of 29.0°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?

______N/m2 ?

(b) What is the final pressure if one-tenth of the gas escapes?

______ N/m2 ?

(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)?

_______ K?

Explanation / Answer

(A) P V = n R T

there is no leakage then  

P / T = constant

(1.60 x 10^7) / (273 + 29) = P / (273 -78.5)

P = 1.03 x 10^7 N/m^2

(B) now P / n T = constant

n' = 9 n/10 = 0.9 n

(1.60 x 10^7) / (n) (273 + 29) = P / (0.9n)(273 -78.5)

P = 9.27 x 10^6 N/m^2

(C) (1.60 x 10^7) / (273 + 29) = (1 x 101325) / Tf

Tf = 1.9 K

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