A high-pressure gas cylinder contains 60.0 L of toxic gas at a pressure of 1.49

Question

A high-pressure gas cylinder contains 60.0 L of toxic gas at a pressure of 1.49 ? 107 N/m2 and a temperature of 24.0°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?

(b)

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

(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)?

Explanation / Answer

Answers:

a) Final pressure in the gas Pf = 9.75 x 106 Pa

b) Final pressure in the gas Pf = 9.75 x 105 Pa

c) Temperature should be 2.01 K

Explaination:

a) We will use ideal gas equation to solve this problem: PV = nRT

PiVi/Ti = PfVf/Tf

volume is constant so it got cancelled

Pf = Pi (Tf/Ti)

Substituting the given values

Pf = 9.75 x 106 Pa

b) PV = nRT

PiVi = nRTi

PfVf = (n/10)RTf

volume is constant so it got cancelled and one tenth gas is leaked so we

Pf = (1/10)Pi (Tf/Ti)

Substituting the given values

Pf = 9.75 x 105Pa

c) Tf =(Pf/Pi) x Ti

={ (1.013 x 105 N/m2)/ (1.49 x 107 N/m2)} x 297 K

= 2.01K

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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