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

Answer 1

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