How long would it take for 2.2 x 10^-4 mol H2 to effuse through the same orifice as the 2.2x 10^-4 mol N2? (It takes 105s for N2 to effuse)
I was thinking of setting up the equation like: sqroot(28.014gN2/mol / 2.016g H2/mol) = 3.728
What should I do next? Also, when setting up the ratio of the molar masses, does the heavier molar mass always go on top?
If you call H2 = gas 1 and N2 = gas 2, then M1 = molar mass H2 and M2 = molar mass N2.
Then rate H2/rate N2 = (sqrt(M2/M1)
[(2.2E-4/x)/(2.2E-4/105)] = sqrt (28/14)
[(1/x)/(1/105)] = 3.728
1/x = 3.728*(1/105)
105 = 3.728*x
x = 105/3.728 = about 28 seconds which makes since. The lower molar mass will effuse faster than the higher molar mass material.
Oh, so to get the rate of a gas, you do moles divided by the time?
yes, rate is L/time or mols/time as so many liters/second or liters/min or liters/hr etc.
Well, let's juggle some numbers! You're on the right track with the molar mass ratio. But remember, to find the time it takes for H2 to effuse, you need to use Graham's law of effusion.
According to Graham's law, the rate of effusion is inversely proportional to the square root of the molar mass. So, based on the molar mass ratio, you have:
(sqrt(molar mass of N2 / molar mass of H2))^2 = (sqrt(28.014g/mol / 2.016g/mol))^2 = (sqrt(13.875))^2 ≈ 3.728^2
Now, to find the time it takes for H2 to effuse, you can set up a proportion:
(105s / x) = (3.728^2 / 1)
Cross-multiplying, you get:
105s = 3.728^2 * x
Now, solve for x:
x = (105s) / (3.728^2)
So, it would take about (105s) / (3.728^2) seconds for 2.2 x 10^-4 mol H2 to effuse through the same orifice as 2.2 x 10^-4 mol N2.
And don't worry, when setting up the ratio of molar masses, the heavier molar mass should always be on the bottom, not the top. Just like a clown's hat, the heavier things tend to be at the bottom!
To determine how long it would take for the given amount of H2 to effuse, you're on the right track with the formula for effusion. However, instead of using the ratio of molar masses, you should use the ratio of the square roots of the molar masses. This ratio is inversely proportional to the effusion rates.
To calculate the effusion rate of H2 relative to N2, use the formula:
(rate of H2)/(rate of N2) = sqrt(Molar mass of N2 / Molar mass of H2)
Now, substitute the given molar masses of N2 and H2:
(rate of H2)/(105 s) = sqrt((28.014 g/mol) / (2.016 g/mol))
Simplifying this equation yields:
(rate of H2) = (sqrt(2.016/28.014)) * (105 s)
Now, you can calculate the effusion time for H2 using the given equation. By substituting the calculated ratio and the given time for N2, you can find the time it takes for H2 to effuse through the same orifice as N2.