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  
Math Team Joined: Jul 2011 From: Texas Posts: 2,624 Thanks: 1305  Quote:
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: 662 Thanks: 187 
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 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,475 Thanks: 693  

Tags 
equation, langmuir, rearranging 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
rearranging an equation  lysdexic  Algebra  3  December 17th, 2015 09:28 AM 
Help rearranging equation  kategg  Algebra  4  June 9th, 2014 07:53 AM 
Help Rearranging an Equation  jwalker  Algebra  2  November 16th, 2013 09:10 PM 
Need help rearranging this equation  dmm  Algebra  2  September 26th, 2009 07:08 PM 