A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 2.10

Question

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 2.10 107 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?
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) V = 50 L = 50 x 10^-3 m^3 = 0.050 m^3

Pi = 2.10 x 10^7 Pa

Ti = 273 + 19 K = 292 K

final Temp, Tf = 273 - 78.5 = 194.5 K

V and amount of gas is constant.

Using Gas equation, P V = n R T

P / T = nR /V = constant

(2.10 x 10^7) / (292) = P / (194.5)

P = 1.40 x 10^7 Pa

b) Initially there are n moles then finally there will ne 0.1n moles.

now P / nT = constant

(2.10 x 10^7) / (292 x n ) = P / (194.5 x 0.1n)

P = 1.40 x 10^6 Pa

c) final Pressre, P = 1atm = 101325 Pa

(2.10 x 10^7 ) / (292) = 101325 / Tf

Tf = 1.41 K = - 271.6 deg C

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.