Computation of Volume and Surface Area Fractions for Use in the UNIQUAC Model

One mole each of benzene and 2,2,4-trimethyl pentane are mixed together. Using the data in Table 9.5-2, compute the volume fraction and surface area fractions of benzene and 2,2,4-trimethyl pentane in this mixture.

Question

Computation of Volume and Surface Area Fractions for Use in the UNIQUAC Model

One mole each of benzene and 2,2,4-trimethyl pentane are mixed together. Using the data in Table 9.5-2, compute the volume fraction and surface area fractions of benzene and 2,2,4-trimethyl pentane in this mixture.

Accepted Answer

Benzene consists of six aromatic CH (ACH) groups. Therefore,

[latex]\begin{array}{l}r_{B}=6 imes 0.5313=3.1878 \q_{B}=6 imes 0.4000=2.4000\end{array}[/latex]

The structure of 2,2,4-trimethyl pentane is

[latex]\begin{matrix} & &\underset{|}{CH_3}&&&&\underset{|}{CH_3} \ CH_3 &-&C &-&CH_2&-&CH&-&CH_3\ && \overset{|}{CH_3} \end{matrix}[/latex]

This molecule consists of five [latex]CH _{3}[/latex] groups, one [latex]CH _{2}[/latex] group, one CH group, and one C group. Thus

[latex]r_{ TMP }=5 imes 0.9011+0.6744+0.4469+0.2195=5.8463[/latex]

and

[latex]q_{ TMP }=5 imes 0.8480+0.5400+0.2280+0.0=5.0080[/latex]

Consequently,

[latex] heta_{B}=\frac{0.5 imes 2.4000}{0.5 imes 2.4000+0.5 imes 5.0080}=0.324 \quad heta_{ TMP }=0.676[/latex]

[latex]\phi_{B}=\frac{0.5 imes 3.1878}{0.5 imes 3.1878+0.5 imes 5.8463}=0.353 \quad \phi_{ TMP }=0.647[/latex]

Table 9.5-2 The Group Volume and Surface Area Parameters, R and Q, for Use with the UNIQUAC and UNIFAC Models*
Main Group	Subgroup	R	Q	Example Assignments
[latex]CH _{2}[/latex]	[latex]CH _{3}[/latex]	0.6325	1.0608	n-Hexane: [latex]4 CH _{2}, 2 CH _{3}[/latex]
	[latex]CH _{2}[/latex]	0.6325	0.7081	n-Heptane:[latex]5 CH _{2}, 2 CH _{3}[/latex]
	CH	0.6325	0.3554	2-Methylpropane:[latex]1 CH , 3 CH _{3}[/latex]
	C	0.6325	0	Neopentane: [latex]1 C , 4 CH _{3}[/latex]
C=C	[latex]CH _{2}= CH[/latex]	1.2832	1.6016	1-Hexene: [latex]1 CH _{2}= CH , 3 CH _{2}, 1 CH _{3}[/latex]
	CH=CH	1.2832	1.2489	2-Hexene: [latex]1 CH = CH , 2 CH _{3}, 2 CH _{2}[/latex]
	[latex]CH _{2}= C[/latex]	1.2832	1.2489	2-Methyl-1-butene: [latex]1 CH _{2}= C , 1 CH _{2}, 2 CH _{3}[/latex]
	CH=C	1.2832	0.8962	2-Methyl-2-butene: [latex]1 CH = C , 2 CH _{3}[/latex]
	C=C	1.2832	0.4582	12,3-Dimethyl-2-butene: [latex]1 C = C , 4 CH _{3}[/latex]
ACH	ACH	0.3763	0.4321	Benzene: 6 ACH
	AC	0.3763	0.2113	Styrene: [latex]1 CH _{2}= C , 5 ACH _{2}, 1 ACH[/latex]
[latex]ACCH _{2}[/latex]	[latex]ACCH _{3}[/latex]	0.91	0.949	Toluene: [latex]5 ACH _{1}, 1ACCH _{2}, 1 CH _{3}[/latex]
	[latex]ACCH _{2}[/latex]	0.91	0.7962	Ethylbenzene: [latex]5 ACH , 1 ACCH _{2}, 1 CH _{3}[/latex]
	ACCH	0.91	0.3769	Isopropylbenzene: [latex]5 ACH , 1 ACCH , 2 CH _{3}[/latex]
OH	OH(p)	1.2302	0.8927	1-Propanol: [latex]1 OH ( p ), 1 CH _{3}, 2 CH _{2}[/latex]
	OH(s)	1.063	0.8663	2-Propanol: [latex]1 OH ( s ), 2 CH _{3}, 1 CH[/latex]
	OH(t)	0.6895	0.8345	tert-Butanol: [latex]1 OH ( t ), 3 CH _{3}, 1 C[/latex]
[latex]CH _{3} OH[/latex]	[latex]CH _{3} OH[/latex]	0.8585	0.9938	Methanol
Water	[latex]H _{2} O[/latex]	1.7334	2.4561	Water
ACOH	ACOH	1.08	0.975	Phenol: 1 ACOH, 5 ACH
[latex]CH _{2} CO[/latex]	[latex]CH _{3} CO[/latex]	1.7048	1.67	2-Butanone: [latex]1 CH _{3} CO , 1 CH _{3}, 1 CH _{2}[/latex]
	[latex]CH _{2} CO[/latex]	1.7048	1.5542	2-Pentanone: [latex]1 CH _{2} CO , 2 CH _{3}, 1 CH _{2}[/latex]
CHO	CHO	0.7173	0.771	Propionic aldehyde: [latex]1 CHO , 1 CH _{3}, 1 CH _{2}[/latex]
CCOO	[latex]CH _{3} COO[/latex]	1.27	1.6286	Butyl acetate: [latex]1 CH _{3} COO , 1 CH _{3}, 3 CH _{2}[/latex]
	[latex]CH _{2} COO[/latex]	1.27	1.4228	Methyl propionate: [latex]1 HCOO , 1 CH _{3}, 1 CH _{2}[/latex]
HCOO	HCOO	1.9	1.8	Ethyl formate: [latex]1 HCOO , 1 CH _{3}, 1 CH _{2}[/latex]
[latex]CH _{2} O[/latex]	[latex]CH _{3} O[/latex]	1.1434	1.6022	Dimethyl ether: [latex]1 CH _{3} CO , 1 CH _{3}[/latex]
	[latex]CH _{2} O[/latex]	1.1434	1.2495	Diethyl ether: [latex]1 CH _{2} O , 2 CH _{3}, 1 CH _{2}[/latex]
[latex]CNH _{2}[/latex]	[latex]CH _{3} NH _{2}[/latex]	1.1434	0.8968	Diisopropyl ether: [latex]1 CHO , 4 CH _{3}, 1 CH[/latex]
	[latex]CH _{2} NH _{2}[/latex]	1.6607	1.6904	Methylamine: [latex]CH _{3} NH _{2}[/latex]
	[latex]CHNH _{2}[/latex]	1.6607	1.3377	Ethylamine: [latex]1 CH _{2} NH _{2}, 1 CH _{3}[/latex]
	[latex]CNH _{2}[/latex]	1.6607	0.985	Isopropylamine: [latex]1 CHNH _{2}, 2 CH _{3}[/latex]
CNH	[latex]CH _{3} NH[/latex]	1.6607	0.985	tert-Butylamine: [latex]1 CNH _{2}, 3 CH _{3}[/latex]
	[latex]CH _{2} NH[/latex]	1.368	1.4332	Dimethylamine: [latex]CH _{3} NH , 1 CH _{3}[/latex]
	CHNH	1.368	1.0805	Diethylamine: [latex]1 CH _{2} NH , 2 CH _{3}, 1 CH _{2}[/latex]
[latex]( C )_{3} N[/latex]	[latex]CH _{3} N[/latex]	1.368	0.7278	Diisopropylamine: [latex]1 CHNH , 4 CH _{3}, 1 CH[/latex]
	[latex]CH _{2} N[/latex]	1.0746	1.176	Trimethylamine: [latex]1 CH _{3} N , 2 CH _{3}[/latex]
[latex]ACNH _{2}[/latex]	[latex]ACNH _{2}[/latex]	1.0746	0.824	Triethylamine: [latex]1 CH _{3} N , 2 CH _{3}[/latex]
Pyridines	[latex]AC _{2} H _{2} N[/latex]	1.1849	0.8067	Aniline: [latex]1 ACNH _{2}, 5 ACH[/latex]
	[latex]AC _{2} HN[/latex]	1.4578	0.9022	Pyridine: [latex]1 AC _{2} H _{2} N , 3 ACH[/latex]
	[latex]AC _{2} N[/latex]	1.2393	0.633	2-Methylpyridine: [latex]1 AC _{2} HN , 3 ACH , 1 CH _{3}[/latex]
CCN	[latex]CH _{3} CN[/latex]	1.0731	0.3539	2,5-Methylpyridine: [latex]1 AC _{2} N , 3 ACH , 2 CH _{3}[/latex]
	[latex]CH _{2} CN[/latex]	1.5575	1.5193	Acetonitrile
COOH	COOH	1.5575	1.1666	Propionitrile: [latex]1 CH _{2} CN , 1 CH _{3}[/latex]
HCOOH	HCOOH	0.8	0.9215	Acetic acid: [latex]1 COOH , 1 CH _{3}[/latex]
		0.8	1.2742	Formic acid
CCl	[latex]CH _{2} Cl[/latex]	0.9919	1.3654	1-Chlorobutane: [latex]1 CH _{2} Cl , 1 CH _{3}, 2 CH _{2}[/latex]
	CHCl	0.9919	1.0127	2-Chloropropane: [latex]1 CHCl , 2 CH _{3}[/latex]
	CCl	0.9919	0.66	tert-Butyl chloride: [latex]1 CHCl , 3 CH _{3}[/latex]
[latex]CCl _{2}[/latex]	[latex]CH _{2} Cl _{2}[/latex]	1.8	2.5	Dichloromethane: [latex]1 CH _{2} Cl _{2}[/latex]
	[latex]CHCl _{2}[/latex]	1.8	2.1473	1,1-Dichloroethane: [latex]1 CHCl _{2}, 1 CH _{3}[/latex]
	[latex]CCl _{2}[/latex]	1.8	1.7946	2,2-Dichloropropane: [latex]1 CCl _{2}, 2 CH _{3}[/latex]
[latex]CCl _{3}[/latex]	[latex]CHCl _{3}[/latex]	2.45	2.8912	Chloroform
	[latex]CCl _{3}[/latex]	2.65	2.3778	1,1,1-Trichloroethane: [latex]1 CCl _{3}, 1 CH _{3}[/latex]
[latex]CCl _{4}[/latex]	[latex]CCl _{4}[/latex]	2.618	3.1836	Tetrachloromethane
ACCl	ACCl	0.5365	0.3177	Chlorobenzene: 1 ACCl, 5 ACH
[latex]CNO _{2}[/latex]	[latex]CH _{3} NO _{2}[/latex]	2.644	2.5	Nitromethane
	[latex]CH _{2} NO _{2}[/latex]	2.5	2.304	1-Nitropropane: [latex]1 CH _{2} NO _{2}, 1 CH _{3}, 1 CH _{2}[/latex]
	[latex]CHNO _{2}[/latex]	2.887	2.241	2-Nitropropane: [latex]1 CHNO _{2}, 2 CH _{3}[/latex]
[latex]ACNO _{2}[/latex]	[latex]ACNO _{2}[/latex]	0.4656	0.3589	Nitrobenzene: [latex]1 ACNO _{2}, 5 ACH[/latex]
[latex]CS _{2}[/latex]	[latex]CS _{2}[/latex]	1.24	1.068	Carbon disulfide
[latex]CH _{3} SH[/latex]	[latex]CH _{3} SH[/latex]	1.289	1.762	Methanethiol
	[latex]CH _{2} SH[/latex]	1.535	1.316	Ethanethiol: [latex]1 CH _{2} SH , 1 CH _{3}[/latex]
Furfural	furfural	1.299	1.289	Furfural
Diol	[latex]\left( CH _{2} OH ight)_{2}[/latex]	2.088	2.4	1,2-Ethanediol (ethylene glycol)
I	I	1.076	0.9169	Ethyl iodide: [latex]1 I , 1 CH _{3}, 1 CH _{2}[/latex]
Br	Br	1.209	1.4	Ethyl bromide: [latex]1 Br , 1 CH _{3}, 1 CH _{2}[/latex]
[latex]C \equiv C[/latex]	[latex]CH \equiv C[/latex]	0.9214	1.3	1-Hexyne: [latex]1 CH \equiv C , 1 CH _{3}, 3 CH _{2}[/latex]
	[latex]C \equiv C[/latex]	1.303	1.132	2-Hexyne: [latex]1 C \equiv C , 2 CH _{3}, 2 CH _{2}[/latex]
DMSO	DMSO	3.6	2.692	Dimethyl sulfoxide
ACRY	ACRY	1	0.92	Acrylonitrile
[latex]Cl ( C = C )[/latex]	[latex]Cl ( C = C )[/latex]	0.5229	0.739	Trichloroethylene: 3 Cl(C=C), 1 CH=C
ACF	ACF	0.8814	0.7269	Hexafluorobenzene: 6 ACF
DMF	DMF	2	2.093	N,N-Dimethylformamide
	[latex]HCON \left( CH _{2} ight)_{2}[/latex]	2.381	1.522	N,N-Diethylformamide: [latex]1 HCON \left( CH _{2} ight)_{2}, 2 CH _{3}[/latex]
[latex]CF _{2}[/latex]	[latex]CF _{3}[/latex]	1.284	1.266	1,1,1-Trifluoroethane: [latex]1 CF _{3}, 1 CH _{3}[/latex]
	[latex]CF _{2}[/latex]	1.284	1.098	Perfluorohexane: [latex]4 CF _{2}, 2 CF _{3}[/latex]
	[latex]CF[/latex]	0.8215	0.5135	Perfluoromethylcyclohexane: [latex]1 CF , 5 CF _{2}, 1 CF _{3}[/latex]
COO	COO	1.6	0.9	Methyl acrylate: [latex]1 COO , 1 CH _{3}, 1 CH _{2}= CH[/latex]
[latex]cy - CH _{2}[/latex]	[latex]cy - CH _{2}[/latex]	0.7136	0.8635	Cyclohexane: [latex]6 cy - CH _{2}[/latex]
	[latex]cy - CH[/latex]	0.3479	0.1071	Methylcyclohexane: [latex]1 cy - CH , 5 cy - CH _{2}, 1 CH _{3}[/latex]
	cy-C	0.347	0	1,1-Dimethylcyclohexane: [latex]1 cy - C , 5 cy - CH _{2}, 2 CH _{3}[/latex]
[latex]cy - CH _{2} O[/latex]	[latex]cy - CH _{2} OCH[/latex]	1.7023	1.8784	Tetrahydrofuran: [latex]1 cy - CH _{2} OC H _{2}, 2 cy - CH _{2}[/latex]
	[latex] ext { cy-CH } C _{2} O \left( CH _{2} ight)_{1 / 2}[/latex]	1.4046	1.4	1,3-Dioxane: [latex]2 cy - CH _{2} O \left( CH _{2} ight)_{1 / 2}, 1 ext { cy-CH } CH _{2}[/latex]
	[latex] ext { cy- }\left( CH _{2} ight)_{1 / 2} O \left( CH _{2} ight)_{1 / 2}[/latex]	1.0413	1.0116	1,3,5-Trioxane: [latex]3 cy -\left( CH _{2} ight)_{1 / 2} O \left( CH _{2} ight)_{1 / 2}[/latex]
cy-CON-C	[latex]cy - CON - CH _{3}[/latex]	3.9819	3.2	N-Methylpyrrolidone: [latex]1 cy - CON - CH _{3}, 3 cy - CH _{2}[/latex]
	[latex]cy - CON - CH _{2}[/latex]	3.7543	2.892	N-Ethylpyrrolidone: [latex]1 ext { cy-CON-CH }{ }_{2}, 3 ext { cy- } CH _{2}, 1 CH _{3}[/latex]
	cy-CON-CH	3.5268	2.58	N-Isopropylpyrrolidone: [latex]1 ext { cy-CON-CH, } 3 ext { су-CH } H _{2}, 2 CH _{3}[/latex]
	cy-CON-C	3.2994	2.352	N-tert-Butylpyrrolidone: [latex]1 ext { cy-CON-C, } 3 ext { cy-CH } CH _{2}, 3 CH _{3}[/latex]
ACS	[latex]AC _{2} H _{2} S[/latex]	1.7943	1.34	Thiophene: [latex]1 AC _{2} H _{2} S , 2 ACH[/latex]
	[latex]AC _{2} HS[/latex]	1.6282	1.06	2-Methylthiophene: [latex]1 AC _{2} HS , 2 ACH , 1 CH _{3}[/latex]
	[latex]AC _{2} S[/latex]	1.4621	0.78	2,5-Dimethylthiophene: [latex]1 AC _{2} S , 2 ACH , 2 CH _{3}[/latex]
Note: A (as in ACH) denotes a group in an aromatic ring, cy- denotes a group in a cyclic structure, and functional groups in bold without any example assignments, such as water, formic acid, etc. are specific to that molecule.

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