Using the compositions and Wilson coefficients given in Example 8.15a, determine the activity coefficient for methanol.

Question

Accepted Answer

Matrix of coefficients

		j
		1	2	3	4
i	1	1	2.3357	2.7385	0.4180
	2	0.1924	1	1.6500	0.1108
	3	0.2419	0.5343	1	0.0465
	4	0.9699	0.956	0.7795	1

	k		1		2		3		4
		MeOH		EtOH		IPA		H2O
comp			0.05		0.05		0.18		0.71

[latex]Q 1= x ( j )^{*} A ( k , j )[/latex]

k = 1		0.05
,j = 1	[latex]Q 1=[/latex]	0.116785
j = 3		0.4929
j = 4		0.30096
[latex] ext { sumQ1 }[/latex]		0.960675

[latex]Q 3=x(j)^{*} A(i, j)[/latex]

		i = 1	i = 2	i = 3	i = 4
j = 1	[latex]Q 3=[/latex]	0.05	0.00962	0.012095	0.048495
j = 2		0.116785	0.05	0.026715	0.0478
j = 3		0.49293	0.297	0.18	0.14031
j = 4		0.30096	0.079776	0.03348	0.72
sum		0.960675	0.436396	0.25229	0.956605

[latex]Q 2= x ( i )^{*} A ( i , k ) / \operatorname{sumQ} 3[/latex]

	[latex]Q 2=[/latex]	k D=1
i = 1		0.052047
i = 2		0.022044
i = 3		0.17258
i = 4		0.730007
sum		0.976685

[latex] ext { Gamma } k=\exp (1-\operatorname{Ln}(\operatorname{sumQ} 1)-\operatorname{sumQ} 2)[/latex]

[latex] ext { gamma } 1=1.06549[/latex]

Non-random two liquid equation (NRTL) equation

The NRTL equation developed by Renon and Prausnitz overcomes the disadvantage of the Wilson equation in that it is applicable to immiscible systems. If it can be used to predict phase compositions for vapour-liquid and liquid-liquid systems.

Universal quasi-chemical (UNIQUAC) equation

The UNIQUAC equation developed by Abrams and Prausnitz is usually preferred to the NRTL equation in the computer aided design of separation processes. It is suitable for miscible and immiscible systems, and so can be used for vapour-liquid and liquid-liquid systems. As with the Wilson and NRTL equations, the equilibrium compositions for a multicomponent mixture can be predicted from experimental data for the binary pairs that comprise the mixture. Also, in the absence of experimental data for the binary pairs, the coefficients for use in the UNIQUAC equation can be predicted by a group contribution method: UNIFAC, described below.

The UNIQUAC equation is not given here as its algebraic complexity precludes its use in manual calculations. It would normally be used as a sub-routine in a design or process simulation program. For details of the equation consult the texts by Reid et al. (1987) or Walas (1984).

The best source of data for the UNIQUAC constants for binary pairs is the DECHEMA vapour-liquid and liquid-liquid data collection, DECHEMA (1977).

Question 8.15b: Using the compositions and Wilson coefficients given in Exam...

Related Answered Questions