All regular solutions with positive enthalpies of mixing have the same value of the activity of its components (A or B ) at the critical point of the miscibility gap. Calculate the activity aA and aB at TC for a regular solution with regular solution constant α.

Question

All regular solutions with positive enthalpies of mixing have the same value of the activity of its components (A or B ) at the critical point of the miscibility gap. Calculate the activity [latex]a_A[/latex] and [latex]a_B[/latex] at [latex]T_C[/latex] for a regular solution with regular solution constant α.

Accepted Answer

At the critical temperature,

[latex]RT_c\ln a_B=\bar{G}_B(0.5) =\Delta G^M(0.5)=\Delta H^M(0.5)-T_c\Delta S^M(0.5)[/latex]

[latex]RT_c\ln a_B(0.5)=\Delta H^M(0.5)-T_c\Delta S^M(0.5)[/latex]

[latex]R\left\lgroup\frac{\alpha }{2R} \right\rgroup \ln a(0.5)=\frac{\alpha }{4}-\left\lgroup\frac{\alpha }{2R} \right\rgroup R\ln 2 [/latex]

[latex]a_B(0.5)=0.824 [/latex]

Question 10.11.2: All regular solutions with positive enthalpies of mixing hav...

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