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?

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.

To determine the time it takes for CH4 gas to effuse, we can use Graham's law, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

Here's how you can correctly solve the problem:

1. Determine the ratio of the molar masses:
Molar Mass of bromine (MBr) = 79.904 g/mol
Molar Mass of CH4 (MCH4) = 16.04246 g/mol

Square the ratio of the molar masses:
(MBr / MCH4)^2 = (79.904 / 16.04246)^2 ≈ 24.6

2. Use the given rate of effusion (4.73 min for bromine) and the ratio of molar masses to find the rate of effusion for CH4 gas:

Rate of effusion of CH4 (RCH4) = Rate of effusion of Br2 (RBr2) / (MBr / MCH4)^0.5
RCH4 = 4.73 / √(24.6) ≈ 0.9548 min

Therefore, the correct answer is approximately 0.95 minutes, not 10.6 minutes.

It seems there was an error in the calculation of the square root in your calculation. Double-check your calculations to ensure you used the correct values and performed the square root correctly.