Question

Stuck on Graham's Law. A sample of neon effuses from a container in 76 seconds. The same amount of an unknown noble gas requires 155 seconds. Identify the unknown gas. Please see below for the work that I have done so far.

Answer 1

Rate Ne=76 seconds. Rate unknown = 155 seconds (So, unknown will have a greater MM because it's moving slower). MM of Ne= 20.18 MM of unknown = ?
Rate 1: Ne MM1= 20.18 Rate 2: 155 MM2= x
\[\left( \frac{ 76 seconds }{ 155 seconds } \right)^{2} = \left( \frac{ MM unknown }{ 20.18 g/mol Ne } \right)\]
\[.20404162332 = \left( \frac{ MM unknown }{ 20.18 g/mol Ne } \right)\]
So, if you multiply .20404162332 by 20.18 you get 4.85 g/mol which is def. not correct because the MM of the unknown must be greater than Ne.

Answer 2

The formula DOES work if you set it up like this:
\[\left( \frac{ 155 seconds }{ 76 seconds } \right)^{2} = \frac{ MM unknown }{20.18 g/mol Ne } \] = 83.9 Krypton Which makes sense bc has a greater molar mass, which would mean it travels more slowly.

However, the equation set up would be that Ne's rate is 155 seconds which is not true. I'm stumped and I don't understand why it works this way, and not the true way. IF someone could help that would be great. Thanks!

Answer 3

bc krypton has*

Answer 4

That's because the SECOND formula you used IS actually correct - you just need to be clear on the variables you're working with.

Graham's Law shows a relationship between the RATE of effusion and the mass of the particles. Your first equation (where you got the funny answer) uses the TIME of effusion, not the RATE. One way you can consider rate in this particular question is by thinking about "units" of gas per second. We're told we have the same amount of each gas, which we can call a unit, so Ne effuses at a RATE of 1 unit/76 s and the unknown gas effuses at a rate of 1 unit/155 s.

If you plug in 1/76 and 1/155 into Graham's Law instead of just 76 and 155, it's equivalent to what you've written in the second equation!

Answer 5

HAH! That works! Seriously, thank you so much. I literally spent over an hour trying to figure this out after reading the text, reviewing my notes, watching videos and searching online. Whew.