I'm trying to find online the derivation for the 2 parameter margules equation but cant find it anywhere.

basically need to prove $$ \frac{d}{dn1} (x_{1}x_{2}(A_{21}x_{1} + A_{12}x_{2})) = x_2^2(A_{12} + 2(A_{21}-A_{12})x_{1}) $$

but everytime I try just end up with a page full of rubbish. I've searched online for the derivation but cant find it anywhere.

EDIT: the A values are functions of temperature only and can be considered constants

  • $\begingroup$ @J.Ari is it not the model itself x1x2(Ax1 + Bx2) that is a power series fit? the activity coefficient equation can then be derived from that model using first principles $\endgroup$
    – SimpleJack
    Apr 17, 2017 at 16:03
  • $\begingroup$ You're right, my first comment was mixing concepts so I deleted it. What I meant to say was the the 2 parameter excess Gibbs model is a curve fit and not formed from first principles, which is what I thought you were trying to find. The activity coefficients are found by differentiating the first term only while using the Gibbs-Duhem equation. $\endgroup$
    – J. Ari
    Apr 17, 2017 at 16:55
  • $\begingroup$ This question is a matter of going through the calculus rigorously, I don't think there is a trick you are missing. $\endgroup$
    – J. Ari
    Apr 17, 2017 at 17:01
  • $\begingroup$ You should rather post this question on chemistry.stackexchange.com or physics.stackexchange.com. It is more likely that you will get a quick answer. $\endgroup$
    – MrYouMath
    Apr 18, 2017 at 11:53

1 Answer 1


Hope this helps!

Hope it makes a lil more sense. Be careful to multiply your excess gibbs by n & xlx2 from the activity coefficient relationship with gibbye! Also, be super grateful you didn't have to do the same thing for the Margules 3 parameter that I literally just worked out like 15 minutes before I saw this!

  • $\begingroup$ If possible, please edit your answer replacing the image with text and MathJax (allows proper math formatting such as $\ln\gamma_1 = 0$). $\endgroup$
    – Wasabi
    Apr 20, 2017 at 14:22

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