A high-pressure gas cylinder contains 70.0 L of toxic gas at a pressure of 1.50x
ID: 1352541 • Letter: A
Question
A high-pressure gas cylinder contains 70.0 L of toxic gas at a pressure of 1.50x10^7 N/m2 and a temperature of 24.0°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
P1 =1.5x10^ N/m^2, T1 =24°C =24+273 = 297 K
T2 = -78.5°C = -78.5+273 = 194.5 K
(a) V1=V2, n1 =n2
From ideal gas equaiton
PV =nRT
P2/P1 = T2/T1
P2 = P1(T2/T1) = (1.5x107)(194.5/297)
P2 = 9.8x106 N/m2
(b) V1=V2, n2 =n1/10
From ideal gas equaiton
PV =nRT
P2/P1 = (T2/T1)(n2/n1)
P2 = P1(T2/T1) (n2/n1)= (1.5x107)(194.5/297)(1/10)
P2 = 9.8x105 N/m2
(c) V1=V2, n1=n2
P1 =1 atm =1.01x105 N/m2
From ideal gas equaiton
PV =nRT
P2/P1 = T2/T1
T2 = T1(P2/P1) = (297)(1.01x105 /1.5x107 )
T2 = 1.998K
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