MULTICOMPONENT MARGULES EQUATIONS SIR: In recent work attempting t o apply multicomponent Margules equations to extraction calculations, some errors were discovered in published versions. To facilitate deriving constants from ternary data, differing forms of ternary Margules equations were reduced to the following form.
+
+ + + +
-k 2 X I X ? 4-X I X Z X ~ ] A I ~ [ X4? ‘/z x2x3 - 2 ~ 1 x 2 ’- x1x~x.31 A 3 1 [ + ‘/2 x2x3 -t 2 xIX3’ f x l X 2 x 3 1 A i 3 [ X 3 ’ + ’ / 2 x2xs -- 2 xix3’ - Xixzx31 A 3 2 [ - ”2 XZx3 -t2 xZx3’ xlXZx3] f A23[ ‘/2 x2x3 .- 2 X 2 x 3 ’ - xlx2%3]
log yi =
A 2 i [
‘/2
~ 2 x 3
+
+
The equations that were reduced to this form included those of Colburn and Pigford (1950), Gerster (1963), and Treybal (1963), without the ternary interaction term. The equation of Hanson et al. (1962), however, could not be put into this form. This led to the discovery that the subscripts had been reversed in the A-term of the fourth summation. This error occurs in Statement 17 of the computer program of this work. Other That is, “AVAL (Z, J)”should be “AVAL ( J , Z).” typographical errors in the equation, as reported by Hanson, have been corrected and are not part of the published program. T h e correct equation is:
5
L J=l *rJAJZ}]
-
I=1
2
IC
I=1
1
J=2
I#J
IZK J
