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March 27th, 2017, 01:24 PM   #1
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Rearranging Langmuir equation

Hi all,

I am tearing my hair out trying to complete this rearrangement:

Starting from the Langmuir equation given as (1)

θ = KP / 1 + KP (1)

where K = the equilibrium constant for the surface reaction = the ratio of rate constants = ka / kd
P = pressure of the adsorbate gas molecule

Rearrange (showing all working) the above equation to get the following expression (2)

P/V = P/V∞ + 1/KV∞ (2)

In doing the rearrangement, please use θ = V/V∞
Where V= volume of adsorbate and V∞=the volume of adsorbate at full (monolayer) coverage


I've tried what feels like a million different ways to get from (1) to (2), but always seem to end up with things up the wrong way or missing.

I'm hoping someone can perhaps point me in the right direction?

Thanks!
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March 27th, 2017, 01:52 PM   #2
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Quote:
P/V = P/V∞ + 1/KV∞ (2)
going backwards ...

P = PV/V∞ + V/KV∞

P = Pθ + θ/K

P = θ(P + 1/K)

θ = P/(P+1/K) = KP/(KP + 1)

reverse the process ...
skeeter is offline  
March 27th, 2017, 02:41 PM   #3
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Surely this is a straight substitution followed by some simple algebraic manipulation?

let T = theta and Vi = Vinfinity

T = KP/(1+KP)

Substitute given

V/Vi = KP/(1+KP)

V(1+KP) = ViKP

(1+KP) = (ViKP)/V

(1+KP)/ViK = P/V

1/ViK + KP/ViK = P/V

1/ViK + P/Vi = P/V
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April 1st, 2017, 11:34 PM   #4
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Oh man now I feel really daft...

Thank you so much - I was substituting the V/V∞ in right from the beginning, so I think that's what was getting me very muddled and frustrated.

Thanks again
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April 2nd, 2017, 02:57 AM   #5
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Quote:
Originally Posted by zombean View Post
θ = KP / 1 + KP
Careful....
θ = KP / (1 + KP)
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