A high-pressure gas cylinder contains 30.0 L of toxic gas at a pressure of 2.20

Question

A high-pressure gas cylinder contains 30.0 L of toxic gas at a pressure of 2.20 107 N/m2 and a temperature of 12.0°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? Incorrect: Your answer is incorrect. . Apply the ideal gas law for the initial and final situations. 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)

P = P (T/ T) /since volume is constant.

T = 273 - 78.5 = 194.5 K

T = 273 + 12 =285 K

P = 2.2e7* (194.5/ 285) = 1.50e+7 Pa

b)

The pressure will be reduced to 0.9 P = 0.9*1.50e+7 = 1.35*10^7   Pa

c)
since volume is constant, using Charles Law

P/ T = P /T

Now, P = 1 atm = 101325 Pa

P = 2.20*10^7 Pa

T = 12 oC = 285 K

101325/ T = 2.20*10^7 / 285

T = 1.3126 K

The tank shoud be cooled upto the temp = 1.3126 - 273 = - 271.69 oC

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