Question

It takes bromine vapor 4.73 min to effuse through a pinhole of a container. How long will it take CH4 gas to effuse under the same temperature and pressure?

Okay so, I tried using Graham's law for this problem. Rate A was 4.73. Molar Mass of bromine was 79.904 and the molar mass of gas B, CH4, is 16.04246. I plugged everything in and got 10.6 minutes for the rate of effusion for CH4 gas, but the answer is 1.5 minutes. Please tell me what I did wrong?

Answer 1

I can't duplicate your numbers although I tried several combinations; however, you have made at least two errors.
a)Error #1 is that you are calling rate the same as time. It isn't. The time it takes the gas to go through is obvious, the rate is the AMOUNT (such as 1 L) per time. Therefore, the rate for Br2 is 1 L/4.73 min. (The problem doesn't mention volume nor does it say the volume is the same for both gases but I assume it is.
b)Error #2 is that you have used the molar mass of Br as 79.9 but it is twice that or 159.8.

rate 1/rate 2 = sqrt(M2/M1)
rate 1 = rate Br2 = 1/4.73 min
rate 2 = rate CH4 = 1/x min
M1 = molar mass Br2 = 159.8
M2 = molar mass CH4 = 16

1/4.73/1/x = sqrt(16/159.8)
0.2114/1/x = 0.3164
0.2114 = 0.3164*(1/x)
(1/x) = 0.2114/0.3164 = 0.668 and
x = 1/0.668 = 1.496 min which rounds to 1.5 min which is the TIME it takes for CH4 to effuse under the same conditions, not the rate at which it does so.