My Math Forum Rearranging Langmuir equation

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 March 27th, 2017, 01:24 PM #1 Newbie   Joined: Mar 2017 From: New Zealand Posts: 2 Thanks: 0 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!
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 ...

 March 27th, 2017, 02:41 PM #3 Senior Member   Joined: Jun 2015 From: England Posts: 915 Thanks: 271 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
 April 1st, 2017, 11:34 PM #4 Newbie   Joined: Mar 2017 From: New Zealand Posts: 2 Thanks: 0 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
April 2nd, 2017, 02:57 AM   #5
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Quote:
 Originally Posted by zombean θ = KP / 1 + KP
Careful....
θ = KP / (1 + KP)

 November 7th, 2017, 05:02 PM #6 Newbie   Joined: Nov 2017 From: Malaysia Posts: 9 Thanks: 0 Langmuir Equation Hi all, I am Diana from Malaysia. I just join this forum I had problem regarding the derivation for langmuir equation for the reactions 2A(ads) --> B and 2A(ads) + B(ads) ---> C Please help, thank you
November 7th, 2017, 05:05 PM   #7
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Quote:
 Originally Posted by Audiana Hi all, I am Diana from Malaysia. I just join this forum I had problem regarding the derivation for langmuir equation for the reactions 2A(ads) --> B and 2A(ads) + B(ads) ---> C Please help, thank you
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