The molar volume in cm^3/mol of a binary liquid mixture at T and P is given by:
V~ = 120 x1 + 70 x2 + (15 x1 + 8 x2) x1 x2
a.) Find expressions for the partial molar volumes of species 1 and 2 at T and P.
b.) Show that when these expressions are combined in accord with Eqn 11.11 the given equation for V~ is recovered.
c.) Show that these expressions satisfy Eqn 11.14, the Gibbs-Duhem equation.
d.) Show that at constant T and P,
(dVbar1/dx1)@x1=1 = (dVbar2/dx1)@x1=0 = 0
e.) Plot values of V~, Vbar1, and Vbar2 calculated by the given equation for V~ and by the equations developed in part (a) vs. x1. Label points V~1, V~2, Vbar1 at infinite dilution and Vbar2 at infinite dilution.
Hints :
a.) This is similar to 11.8 Ans.: V2 = 14 x13 + x12 + 70
b.) Just a little bit of algebra here. Ans.: V = -7 x13 - x12 + 58 x1 + 70
c.) A bit of algebra with just a touch of differential calculus.
d.) Just a couple of derivatives and some plug-n-chug.
e.) A snap for you and your friend, Excel.
2 comments:
What are the two equations? Or what text book are you using?
I was using "Chemical Engineering Thermodynamics" by Smith and van Ness, 6th edition. The two equations are the answers to part (a). One equation gives the partial molar volume of species 1 as a function of x1 and x2. The other equation gives the partial molar volume of species 2 as a function of x1 and x2.
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