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Pressure in cylinder, find moles of air entered. Please help! :)
The inside of the cylindrical can shown above has cross-sectional area 0.0044 m2 and length 0.28 m. The can is filled with an ideal gas and covered with a loose cap. The gas is heated to 385 K and some is allowed to escape from the can so that the remaining gas reaches atmospheric pressure (1.0 x 105 Pa). The cap is now tightened, and the gas is cooled to 296 K.
(a) What is the pressure of the cooled gas? 1Your answer is correct. Pa
(b) Determine the upward force exerted on the cap by the cooled gas inside the can. 2Your answer is correct. N
(c) If the cap develops a leak, how many moles of air would enter the can as it reaches a final equilibrium at 296 K and atmospheric pressure?
3Your answer is incorrect. moles (Assume that air is an ideal gas.)
I got parts a and b. I can't get part c, the number of moles of air that would enter.
I've tried some different things and basically got the same answers within the range .01207-.01208 mol.
One method i tried:
find initial number of moles by PV=nRT, where P=76883.1169 (found for part a), V=.001232, R=8.315, and T=296...I got initial moles (ni)=.03848
Then, I did PV/nRT = PV/nRT which simplifies down to Pi/ni = Pf/nf.
Plug in Pi=76883.1169, ni=.03848, Pf=1.01e5 and nf is unknown.
Solve for nf and get .05055.
Finally, do nf-ni = .05055-.03848 = .01207 moles.
Unfortunately, that is not correct.
Can you tell me where I'm going wrong or if perhaps I am on the entirely incorrect track here?
Thanks so much,
--aweg
Homework Statement
The inside of the cylindrical can shown above has cross-sectional area 0.0044 m2 and length 0.28 m. The can is filled with an ideal gas and covered with a loose cap. The gas is heated to 385 K and some is allowed to escape from the can so that the remaining gas reaches atmospheric pressure (1.0 x 105 Pa). The cap is now tightened, and the gas is cooled to 296 K.
(a) What is the pressure of the cooled gas? 1Your answer is correct. Pa
(b) Determine the upward force exerted on the cap by the cooled gas inside the can. 2Your answer is correct. N
(c) If the cap develops a leak, how many moles of air would enter the can as it reaches a final equilibrium at 296 K and atmospheric pressure?
3Your answer is incorrect. moles (Assume that air is an ideal gas.)
Homework Equations
The Attempt at a Solution
I got parts a and b. I can't get part c, the number of moles of air that would enter.
I've tried some different things and basically got the same answers within the range .01207-.01208 mol.
One method i tried:
find initial number of moles by PV=nRT, where P=76883.1169 (found for part a), V=.001232, R=8.315, and T=296...I got initial moles (ni)=.03848
Then, I did PV/nRT = PV/nRT which simplifies down to Pi/ni = Pf/nf.
Plug in Pi=76883.1169, ni=.03848, Pf=1.01e5 and nf is unknown.
Solve for nf and get .05055.
Finally, do nf-ni = .05055-.03848 = .01207 moles.
Unfortunately, that is not correct.
Can you tell me where I'm going wrong or if perhaps I am on the entirely incorrect track here?
Thanks so much,
--aweg