(Callen 9.7-2)

The phase diagram of a solution of A in B, at a pressure of 1 atm, has a coexistence region in the $(X,T)$ plane (e.g., $X_A$ is a liquid molar fraction with $N=N_A+N_B$ and T temperature and $Y_A$ is a gas molar fraction). The upper bounding curve of the two phase region can be represented by


and the lower bounding curve of the two-phase region is represented by


Show that if a small fraction of the liquid $−dN/N$ is boiled off, the change in the fraction of the remaining liquid is,

$dX_A =-\left[(2X_A-X_A^2)^{\frac{1}{2}}-X_A \right]\frac{-dN}{N}$.

All I knew was that $dX_A$ could be obtained from $dN = dN_A+dN_B$

and from there

$dN_A+dN_B = N dX_A + X_A dN + N dX_B + X_B dN$... I previously found that, when temperature is such that $X_A=X_B=1/2$, $Y_A=0.8660$...

  • $\begingroup$ The solution is more geometry than chemistry - sketch the liquidus and solidus and do the math. $\endgroup$ – Jon Custer Sep 25 '15 at 12:39
  • $\begingroup$ I am not sure at all about which term in the desired answer should be $Y_A$ instead of $X_A$ given how I defined these guys... $\endgroup$ – NSERC Protester Sep 25 '15 at 15:30

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