A high-pressure gas cylinder contains 60.0 L of toxic gas at a pressure of 1.38

Question

A high-pressure gas cylinder contains 60.0 L of toxic gas at a pressure of 1.38 107 N/m2 and a temperature of 19.0°C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature (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 in pascals, assuming a negligible amount of gas leaks while being cooled and that there is no phase change?

9.19e6Pa

(b)

What is the final pressure in pascals if one-tenth of the gas escapes?

  ?Pa

(c)

To what temperature in kelvins 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)?

2.143 K

Explanation / Answer

. a) also assuming the cylinder has a negligible volume shrinkage as it is cooled.

universal gas law .. P1.V1/T1 = P2.V2/T2 .. .. V1 = V2

Final pressure P2 = P1.T2 / (T1) .. T in Kelvin

P2 = (1.38*10^7)(273-78.50) / (273+19) .. .. -------P2 = 9.192*10^6 Pa

b) From PV = nRT .. .. R (constant) = PV / nT
So .. P1.V1 / (n T1) = P2.V2 / (0.9n T2) .. .. again V1 = V2, n cancels

P2 = P1*0.9*T2 / T1 = 0.9 ans (a) .. 0.9*9.192*10^6 .. ------P2' = 8.27*10^6 Pa

c) P1/T1 = P2/T2 .. (VI = V2)(P2 = 1atm = 1*10^5 Pa)

T2 = P2.T1 / P1 .. (10^5Pa x 292K) / 1.38*10^7Pa ..

T2 = 2.143 K

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