Given the one parameter Margules equation, eq 4.28, obtain eq 4.29 partial molar

Question

Given the one parameter Margules equation, eq 4.28, obtain eq 4.29

partial molar excess free volume, G, as 4.27) on Jr.pn, The one-parameter Margules equation for a binary mixture (4.28) is suitable when components of the liquid mixture are similar in size and chemical nature. Equation (4.28) is sometimes also called the two-suffix equation because it is quadratic in composition. It follows that (see Problem 4-2) (4.29) and (4.30) The two-parameter or three-suffix Margules equation for GE and the are given as corresponding expression for ri and (4.31)

Explanation / Answer

GE= Ax1x2, since x1= n1/(n1+n2), where n1= no of moles of 1st species, n2=no of moles of species -2

x2=n2/(n1+n2)

GE= A*n1n2/(n1+n2)2,

nGE= An1n2*(n1+n2)/(n1+n2)2= An1n2/(n1+n2)

differentitaing the equstion with respect to n1

d/dn1(nGE)= An2[ n1+n2-n1)/(n1+n2)2= A{(n2/(n1+n2)}2= Ax22

RT lnY1= Ax22

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