A high-pressure gas cylinder contains 70.0 L of toxic gas at a pressure of 1.80

Question

A high-pressure gas cylinder contains 70.0 L of toxic gas at a pressure of 1.80 Times 10^7 N/m^2 and a temperature of 28.0 degree C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperatures (-78.5 degree C), to reduce the leak rate and pressure so that it can be safely repaired. 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? What is the final pressure if one-tenth of the gas escapes? How many moles are in the tank compared to the original number of moles? N/m^2 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)? Review the values for initial and final pressure for this situation. K

Explanation / Answer

b)

nf = final number of moles

ni = initial number of moles

given 1/10th of gas escape

hence nf = ni - ni/10 = 0.9 ni

nf = 0.9 ni

Pi = initial pressure = 1.80 x 107

Pf = final pressure

Ti = initial Temperature = 28 c = 273 + 28 = 301 K

Tf = final Temperature = - 78.5 c = 273 - 78.5 = 194.5 K

Using the formula

Pi Vi /(ni Ti) = Pf Vf /(nf Tf)

given Vi = Vf

(1.80 x 107) / (ni (301)) = Pf / ((0.9 ni) 194.5)

Pf = 1.05 x 107 N/m2

c)

at constant Volume

Pf/Tf = Pi/Ti

(1.01 x 105 )/ Tf = (1.80 x 107) / 301

Tf = 1.689 K

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