Using the Wilson equation, calculate the activity coefficients for isopropyl alcohol (IPA) and water in a mixture of IPA, methanol, water, and ethanol; composition, all mol fraction:

Question

Methanol	Ethanol	IPA	Water
0.05	0.05	0.18	0.72

Accepted Answer

Use the binary Wilson A values given by Hirata (1975). The program “WILSON”, Table 8.9, is used to solve this example.

Table 8.9. Program for Wilson equation (Example 8.15)
100	REM WILSON EQUATION
110	REM CALCULATES ACTIVITY COEFFICIENTS FOR MULTICOMPONENT SYSTEMS
120	PRINT ‘‘DATA STATEMENTS LINES 410 TO 450’’
130	READ N
140	REM MAT READ A
150	FOR I = 1 TO N
160	FOR J = 1 TO N
170	READ A(I, J)
180	NEXT J
190	NEXT I
200	PRINT ‘‘TYPE IN LIQUID COMPOSITION, ONE COMPONENT AT A TIME’’
210	FOR P=1 TO N
220	PRINT ‘‘X’’;P;‘‘?’’
230	INPUT X(P)
240	NEXT P
250	FOR K=1 TO N
260	Q1=0
270	FOR J=1 TO N
280	Q1=Q1+X(J)*A(K,J)
290	NEXT J
300	Q2=0
310	FOR I=1 TO N
320	Q3=0
330	FOR J=1 TO N
340	Q3=Q3+X(J)*A(I,J)
350	NEXT J
360	Q2=Q2+(X(I)*A(I,K))/Q3
370	NEXT I
380	G(K) = EXP(1-LOG(Q1)-Q2)
390	PRINT ‘‘GAMMA’’;K;‘‘=’’;G(K)
400	NEXT K
410	DATA 4
420	DATA 1,2.3357,2.7385,0.4180
430	DATA 0.1924,1,1.6500,0.1108
440	DATA 0.2419,0.5343,1,0.0465
450	DATA 0.9699,0.9560,0.7795,1
460	END

The Wilson A-values for the binary pairs are [latex]A_{i, j}[/latex]

		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	0.9560	0.7795	1

Component 1 = MeOH

2 = EtOH

3 = IPA

4 = [latex]H _{2} O[/latex]

The output from the program for the concentrations given was:

[latex]\gamma_{3}=2.11, \quad \gamma_{4}=1.25[/latex]

Experimental values from Hirata (1975)

[latex]\gamma_{3}=2.1, \quad \gamma_{4}=1.3[/latex]

Question 8.15a: Using the Wilson equation, calculate the activity coefficien...

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