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.
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?
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