A party balloon filled with helium deflates to 2/3 of its original volume in 8.0 hours. How long will it take an identical balloon filled with the same number of moles of air (ℳ = 28.2 g/mol) to deflate to 1/2 of its original volume?

Question

I know it's an effusion, so I did:
(2/3)/ (8 hrs) sqrt (28.2 g/mol)
_______________ = _____________
(1/2)/ (? hrs) sqrt (28.2 g/mol)

but I don't get the correct answer, which is 32 hours.

Answer 1

I think your only problem is that you didn't substitute correctly in the equation. The 28.2 you used twice. The one in the denominator should have been the one for He which will be 4. If I put 4 there I get 32.

Answer 2

I think there's one other error in your substitution. Since the problem says 2/3 of He was left, where you have 2/3 in the substitution, you should have 1/3, since 1/3 was the amount effused.

Answer 3

2x/3*8=√28.2/√4.0
2X/24=2.655183609
x=31.86220331
x=32 hours

Answer 4

Yes, that's correct! Good job catching the mistake in the substitution and solving it correctly. The correct answer is indeed 32 hours.