In two separate experiments, researchers used laser beams to confine 400 atoms (each) of Na and K in a volume 1.0 x 10-15 m3 (for a fraction of a second) at a temperature of 0.00024K. How

Question

In two separate experiments, researchers used laser beams to confine 400 atoms (each) of Na and K in a volume 1.0 x 10^-15 m³ (for a fraction of a second) at a temperature of 0.00024K. How many times faster/slower would K atoms be effusing than Na atoms?

1) K atoms effuse 0.77x slower

2) K atoms effuse 1.3x faster

3)K atoms effuse 0.77x faster

4) K atoms effuse at the same rate than Na atoms

5) K atoms effuse 1.3x slower

I know K atoms will effuse slower because potassium's molar mass is larger than sodium's. However, I do not know how to calculate how much slower it will be. Does it have something to do with the formula Rate₁/Rate₂ = sqrt(M_2/M₁) (with the capital M representing molar mass)? If so, what numbers would I plug in for Rate₁ and Rate₂? Also, if I'm completely off, can someone please tell me the correct reasoning and show steps to get to the right answer?

Answer 1

Yes, this is Graham’s Law of effusion. The values for rate 1 and rate 2 are relative and not really needed. You are only looking for a ratio of rates. So set rate of K as 1 and rate of Na as x.

1/x = sqrt (23/39) = 0.77

x = 1.3

So Na effuses 1.3 x faster, or put another way K effuses 1.3x slower = K effuses 0.77x as fadt as Na. There are many ways to express the answer.