Solubility correlation of monocarboxylic acids in ... - ACS Publications

996

Ind. Eng. Chem. Process Des. Dev. 1986, 25, 996-1008

Kato, K.; Kubota, H.; Wen, C. Y. E P S y m . Ser. 1970, 86(105), 87. Kim, M. H. M.S. Thesls, Washington University, St. Louls, MO. 1981. Lu, H. S. M.S.Thesls. University of Wyomlng, Laramle, 1980. Merrick, D. Fuel 1983, 82. 553. Salam, L. M.S. Thesls, Washlngton University, St. Louis, MO, 1983. SenGupta, A.; Thodos, G. AIChE J . 1983, 9 , 751. Sergent, G. D.; Smlth, I. W. fuel 1973, 52, 1. Thorsness, C. B.; Rozsa. R. 8. SPE J. 1978, 18. 105. Westbrook, D.A. M.S. Thesis, University of Texas, Dallas, 1976.

Wheeler, A. Adv. Catal. 1951, 3 , 249. Yoon, H.; Wei. J.; Denn, M. M. AIChE J . 1978, 24, 885. Young, L. C.; Fiiniayson, B. A. Ind. Eng. C I ” . Fundam. 1973, 12, 412. Yu, W. C. RID.Thesis, Unlverslty of Delaware, Newark, 1981.

Received f o r review July 29, 1985 Revised manuscript received March 10, 1986 Accepted May 27, 1986

Sdubltfty Correlation of Monocarboxylic Acids in One-Component Solvents Ursruta Domaiidta’ and Tadeusz Hofman Department of Physhl Chemistty, Technical Unlversity of Warsaw, 00664 Warsaw, Poland

The solubility data of monocarboxylic acMs in one-component solvents reported in the literature were described by using f i e two-parameter correlation equations (namely the Redlich-Kister equation, the van Laar equation, and three vwsions of the Wilson equation). The description is found to be generally satisfactory when one of the Wilson equations taking into account the temperature dependence of A, parameters is employed.

The thermodynamic description of solid-liquid equilibrium (SLE) follows from the thermodynamic principle of equilibrium in multiphase and multicomponent systems. It requires the fugacities of each component in all coexisting phases to equal one another. For the solubility of one solid component in a solvent, the fugacity may be expressed as in eq 1 where f l is the fugacity of the solute i r solid (s) and liquid (L) phases, respectively. f i S=

flL

(1)

Introducing an activity coefficient (yl) and assuming that there exists no solid solution in the solid phase, one can obtain eq 2 and 3. Since the ratio of fugacities may

flL= X1TlLflOL(T,P)

(24

flS= f1OS(T,P)

(2b)

X1TlL

In

= flos/floL

(34

( ~ 1 ~ = 1 In ~ ) (fios/floL)

(3b)

be interrelated to the enthalpy of melting (fusion) - AHmlo, one can derive finally eq 4 where x1 is a mole fraction of

-R In (xlylL)=

LtAHmlo T

dT1

(4)

* Author to whom correspondence should be addressed. 0196-4305/86/ 1125-0996$01.50/0

solute and Ttis the temperature of the triple point; practically it is replaced by the melting-point temperature a t normal pressure (Tm). The description of solid-liquid equilibria may be considered as the special form of eq 4, having explicitly defined the dependences on T and xl. Thus, the following functions must be established to make the above equation applicable to numerical calculations: (i) the dependence of the enthalpy of melting on temperature, Mml0 = f(T); (ii) the relation between the solute activity coefficient and temperature and solute mole fraction, ylL = f(T,xl). In a majority of papers devoted to solid-liquid equilibria, it is assumed that AHmlois temperature independent. It is generally the result of the lack of experimental data concerning heat capacities (C,). However, it seems that the influence of this parameter is rather negligible as was discussed by Domaiiska (1985). For the activity coefficients, when one assumes that ylL = 1for each x1 and T considered, the well-known Schriider equation expressing the so-called ideal solubility is obtained. Since the concept of the ideal solubility may be applied to the limited number of systems only, the more sophisticated formula for ylL= f(xl,7‘)must be generally used. The relationships for the activity coefficient are most frequently derived from the so-called correlation equations, which describe the Gibbs excess free energy of mixing (GE) with respect to x1 and are commonly applied in vaporliquid equilibrium calculations. The Wilson equation with the TX, parameter independent from temperature (Morimi 0 1986 American Chemical Society

Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986 997

and Nakanishi, 1977; Muir and Howat, 1982) and the Redlich-Kister, van Laar, and UNIQUAC equations (Szafraiiski and Choliiiski, 1980) are used for this purpose. In this paper three different versions of the Wilson equation, the Redlich-Kister equation, and the van Laar equation are applied to correlate more than 350 set of solubility data of monocarboxylic acids in one-component solvents. The literature data by different authors and our results published earlier were taken into consideration in calculations. The correlations are a very convenient form of accumulating data for process design calculations. An attempt to predict the solubility in multicomponent solvents from binary parameters was also made (Muir and Howat, 1982; Domaiiska and Hofman, 1985). Moreover, the correlation methods presented may be applied to estimate the values of the solute activity coefficients.

Calculations The following two-parameter equations were used to represent the activity coefficient (rlL) vs. temperature (T) and the solute mole fraction (xl; x 2 = 1 - xl): 1. Redlich-Kister equation with two constants In ylL = xZ2[Al+ A2(4X1 - l)]

(5)

2. van Laar equation In ylL = x22AlA22/(Alxl+ A2x2)2

(6)

3. Wilson equation (Wilson, 1964)

In ylL= a - In (xl

+ x2A12) + 1 - xl/(xl + xZAl2)x2AZl/(xlAzl

+ x 2 ) (7)

Three versions of the Wilson equation were tested: Aij # f ( T )

gij - gii # f(T) g.. 1J - gIL = aij/T

(Wilson 1) (Wilson 2)

aij # f(T)

(74 (7b)

(Wilson 3) ( 7 ~ )

where for (7b) and ( 7 4 Aij = exp[-kij - gii)/RTl

(8)

Equation 8 results from the original Wilson equation with an additional assumption as to the equality of molar volumes of pure liquid components ( Vio = Vjo). The assumption must be set up since no volume data of supercooled liquid are available. It is equivalent to the Hiranuma (1972) reformulation of the Wilson equation. The temperature dependence of gii - gii introduced in version 7c is analogical to that of Schotte (1984), applied in the UNIQUAC equation. The parameters of above relationships were fitted by the optimization technique. The objective function was as in eq 9 where In ali is an "experimental" value of the loga-

(10) According to the above formulation, the objective function is consistent with the Maximum Likelihood principle, provided that the fiist-order approximation (eq 10) is valid. Neau and Peneloux (1981) called such a procedure the Observed Deviation method. The experimental errors of temperature and solute mole fraction were fixed for all cases and set to A T = 0.5 K and Ax1 = 0.001. The appropriate values of temperature and enthalpy of melting for acids Clo-Cz0were taken from Schaake et al. (1982). The values for CZ2,AHml' = 76.400 kJ-mol-' and Tml= 353.8 K, were obtained by linear extrapolation of even-numbered normal alkanoic acids derived from the paper mentioned above. These data for octadecenoic acids were taken from Jalal et al. (1982). The temperatures and enthalpies of melting were taken, respectively, for benzoic acid and 3-chloro- and 4-chlorobenzoic acid from the work of Yalkowsky and Valvani (1980),for 2-methylbenzoic acid from Domaiiska (19861, and for 3-methyl- and 4-methylbenzoic acid, 4-methoxy- and 2-chlorobenzoic acid, and 3-phenyl-2-propynoic acid from Domaiiska et al. (1982). The calculations concern experimental data of different ranges of concentrations and temperature. The mole fraction of solute in water was of the order of x1 = lo-', whereas in better solvents x1 = 0.01 + 0.8 in the range of temperatures from 290 to 340 K for aliphatic acids and from 300 to 505 K for benzoic acids. Results a n d Discussion The results of calculations for aliphatic acids and benzoic acids are collected in Table I and 11, successively. There are only the resulta obtained with the Wilson equation (eq 7c) as the best version of calculations. The remaining results of calculations including the parameters of the Redlich-Kister, van Laar, and two other versions of the Wilson equations (eq 7a and 7b), and the corresponding measures of deviations as well are listed for each system being computed in Tables I and I1 of the supplementary material. The number of experimental points presented in the tables does not include the solute melting points (TmJ* Two measures of the goodness of correlation are shown, namely, 1, root mean-square deviation of temperature u1 = [?(T~& - Ti)2/(n

C wi-'[ln xliyli(Ti, x l i , AI, A,) - In a1il2 (9)

i=l

rithm of the solute activity taken as the left side of eq 4 with AHmlo# f(T),i.e., -In aIi = (AHmlo/R)(T;l - Tm1-l); W iis the weight of the experimental point; Al and A2 are two adjustable parameters of the Redlich-Kister, van Larr, and Wilson equations; i denotes the ith experimental point; and n is the number of experimental data. The weights were calculated by means of the error propagation formula (eq 10) where A T and Axl are the estimated errors of T and xl, respectively.

(11)

where T,Cd and TI are the calculated and experimental temperatures of the ith point and 2, relative root meansquare deviation of a logarithm of the solute activity n

u2 = [ C WL2(lnxlIyli - In a l J 2 / ( n- 1)]ll2= r=l

n

J'(A1, A,) =

- 1)11/2

1=1

[J'(-&, & / ( n

a,

- 1)1'/' (12)

where A, and are parameters of the correlation equation which minimize the objective function F (eq 9). If the estimates of experimental errors are appropriate, the u2 parameter should be equal to one. The literature data include solubility values of some investigated acids in a series of more than 50 one-compound solvents. The discrepancy of solubility values, obtained by various investigators, is due to the differences in purity of used components and different methods of measurements, which has an effect on the mathematical

908

Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986

Table I. Parameters and Values of Mean-Square Deviations of the Data Correlated by the Wilson Equation (Equation 7c)" w3

solvent acetonitrile benzene butanol 2-butanone butyl acetate chlorobenzene cyclohexane 1,2-dichloroethane 1,2-dimethylbenzene N,N-dimethylacetamide N,N-dimethylformaide ethyl acetate 2-furancarboxaldehyde methanol methylbenzene nitrobenzene nitroethane 2-propanol 2-propanone tetrachloromethane trichloromethane

no. of pts W3, 10-3a,2/10-3a21,kJ-degmol-' ul, K 1. Decanoic Acid (Capric Acid, C10H2002) 4 1.1186 0.98 1.394 2 3.4320 3 0.40 -0.404 67 4 -0.242 95 0.56 1.0707 4 9.480 5 1.59 -0.533 92 4 9.304 6 1.06 -0.458 54 5 2.204 3 0.53 -0.426 96 3 5.202 7 0.41 -0.239 47 4 1.320 1 0.18 -0.13808 5 1.9716 0.44 -0.442 32 11 -0.528 80 6.05 0.363 33 13 -0.651 09 9.10 0.485 36 4 0.708 39 0.37 -0.167 51E-01 4 1.4229 0.31 0.727 45 4 0.23 0.213 03 0.626 63 5 1.1848 0.16 -0.386 82 3 1.2938 0.21 0.277 13 4 1.0435 2.24 1.0612 4 -0.844 29E-01 0.17 0.652 27 4 0.17 0.565 38 0.15584 4 0.59 0.948 03 -0.242 85 4 0.77 -0.245 68 0.201 16

acetonitrile

3

butanol

3

2-butanone

3

butyl acetate

3

ethyl acetate

3

methanol

3

nitroethane

3

2-propanol

3

2-propanone

3

tetrachloromethane

3

trichloromethane

3

acetic acid

3

acetonitrile

5

benzene

4

62

ref

1.97

Hoerr and Ralston, 1944

0.79

Ralston and Hoerr, 1942

1.12


3.07


8.03


1.01

Hoerr et al., 1946

0.81


0.36

Hoerr et al., 1946

0.81

Hoerr et al., 1946

10.06

Harris et al., 1968

12.54

Harris et al., 1968

0.73


0.59

Hoerr e t al., 1946

0.52


0.31

Hoerr et al., 1946

0.42

Hoerr et al., 1946

5.23


0.36


0.35


1.17


1.52


2.40


0.08


3.15


1.28


0.75


0.67


4.76


0.71


0.15


0.34


0.79


Cl9Hz4O2) 0.32

0.65


2.61

1.09


0.08

0.15


2. Undecanoic Acid (CllH2202) 1.680 0 1.31 0.867 78 -0.661193-01 0.04 0.926 97 10.326 1.63 -0.385 77 4.165 4 0.65 -0.342 22 0.642 10 0.36 0.17277 0.144 09 0.30 0.915 36 1.360 1 1.98 0.913 35 -0.418923-01 0.33 0.759 23 0.733 27 0.07 0.193 04 0.578 45 0.17 -0.228 32E-01 2.648 4 0.41 -0.501 19 3. Dodecanoic Acid (Lauric Acid, 1.3579 -0.222 52 1.9026 0.968 21 1.5648 -0.417 15

-

Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986 999 Table I (Continued) ~~~

~

~~

w3

solvent butanol 2-butanone butyl acetate chlorobenzene cyclohexane 1,2-dichloroethane Nfl-dimethylacetamide 1,2-dimethylbenzene N,N-dimethylformamide l,4-dioxane ethanol ethyl acetate 2-furancarboxaldehyde methanol methylbenzene nitrobenzene nitroethane nitromethane 2-propanol 2-propanone tetrachloromethane trichloromethane water

no. of pts W3, 10-3~12/10-3~zl, kJ.deg.mo1-' 5 -0.116 25 0.703 44 5 1.666 2 -0.553 29 5 1.0485 -0.395 31 2.641 1 6 -0.577 25 4 1.4708 -0.292 55 5 2.1504 -0.239 84 5 12.724 -2.562 3 2.161 2 6 -0.567 46 8 5.962 6 -0.748 99 3 0.221 79 -0.108 94 5 0.389 39 0.293 79 5 0.930 41 -0.10035 4 2.196 3 0.418 53 5 1.167 1 -0.060 68 1.8934 6 -0.559 65 4 1.734 0 0.15992 5 1.5705 1.2590 3 3.070 9 25.201 5 0.097 03 0.418 23 5 0.953 40 0.646003-01 5 1.277 5 -0.451 02 5 0.822 06 -0.511 79 5 6.6520 18.649

acetic acid

3

acetonitrile

5

benzene

4

butanol

5

2-butanone

5

butyl acetate

5

cyclohexane

4

ethyl acetate

5

methanol

5

nitroethane

5

2-propanol

5

2-propanone

5

tetrachloromethane

5

ul, K

0.65

1.29

ref Hoerr and Ralston, 1944

1.49

2.86


0.89

1.74


0.93

1.85

Hoerr et al., 1946

0.15

0.29


1.54

1.20

Hoerr et al., 1946

1.38

2.73

Harris et al., 1968

0.79

1.41

Hoerr et al., 1946

5.56

5.12

Harris et al., 1968

0.08

0.15

Hoerr et al., 1946

0.56

1.17


1.99

3.96


7.30

1.23

Hoerr et al., 1946

1.24

2.27


0.27

0.53

Hoerr et al., 1946

0.12

0.23


3.18

2.52

Hoerr et al., 1946

3.12

2.41


0.41

0.84


0.22

0.47


0.68

1.31


1.07

2.08


12.02

0.00


0.97


0.83


1.01


1.28


3.19


2.09


1.11


1.26


2.91


1.75


1.37


15.83


1.84


4. Tridecanoic Acid (C13H2802) 1.1207 0.49 -0.436 06E-01 2.321 2 2.30 0.994 49 1.052 9 0.51 -0.240 54 0.257 76 0.60 0.348 51 2.256 3 1.69 -0.505 30 1.2880 1.07 -0.381 83 1.3706 0.56 -0.254 73 0.61 0.963 17 -0.108943-01 1.3334 1.59 -0.260 67E-01 2.82 1.9782 1.0593 0.477 11 0.65 0.147 13 2.013 6 8.65 -0.283 30 1.449 4 0.95 -0.429 37

02

1000


Table I (Continued) w3

solvent trichloromethane

no. of pts W3, 10-3alz/10-3azl,kJ-degmol-l 5 1.6683 -0.621 92

K

1.53

ref Hoerr and Ralston. 1944

0.46

0.90


5.69

0.93


0.23

0.43


0.86

1.37


1.60

2.95


1.25

2.33


1.95

1.75

Hoerr et al., 1946

0.30

0.58


1.58

0.92

Hoerr et al., 1946

9.19

9.25

Harris et al., 1968

3.81

1.45

Hoerr et al., 1946

6.36

6.80

Harris et al., 1968

0.06

0.12

Hoerr et al., 1946

2.21

2.89


1.05

1.39


0.00

0.01

Hoerr et al., 1946

0.94

0.90


2.51

0.94

Hoerr et al., 1946

1.00

1.06

Hoerr et al., 1946

2.96

0.97


7.61

2.87

Hoerr et al., 1946

0.75

1.17


0.13

0.25


1.32

2.34


0.90

1.54


21.92

0.00

Ralston and Hoerr. 1942

0.33


0.39


1.17


1.50


2.85


1.58


1.08


0.59


ul,

0.80

02

5. Tetradecanoic Acid (Myristic Acid, Cl,H,Oz)

acetic acid

4

acetonitrile

6

benzene

5

butanol

6

2-butanone

6

butyl acetate

6

chlorobenzene

7

cyclohexane

5

1,2-dichloroethane

5

N,N-dimethylacetamide 1,2-dimethylbenzene N,”-dimethy lformamide

11

7 14

l,4-dioxane

4

ethanol

6

ethyl acetate

6

2-furancarboxaldehyde

3

methanol

6

methylbenzene

7

nitrobenzene

5

nitroethane

6

nitromethane

4

2-propanol

6

2-propanone

5

tetrachloromethane

6

trichloromethane

6

water

5

acetonitrile

6

acetic acid

4

benzene

5

butanol

6

2-butanone

6

butyl acetate

6

cyclohexane

5

ethyl acetate

6

2.1413 -0.332 40 2.455 3 0.944 93 2.274 0 -0.592 61 0.901 04E-01 0.413 79 1.3056 -0.532 22 1.180 2 -0.492 35 2.421 6 -0.659 78 2.1300 -0.535 61 2.564 5 -0.383 78 -0.866 19 0.569 35 2.339 9 -0.663 04 8.4230 -0.863 30 2.489 9 -0.658 72 0.970 57 -0.586 94E-01 0.92777 -0,986 58E-01 3.060 8 0.260 28 1.7910 -0.179 77 2.151 2 -0.648 57 1.4928 0.362 04 2.285 3 0.741 25 3.386 6 23.757 0.399 17 0.142 87 0.886 10 0.221 44 1.7109 -0.622 93 1.476 2 -0.706 01 6.254 9 32.642

6. Pentadecanoic Acid (CI6HS0O2) 2.803 6 4.02 1.216 4 2.322 7 0.19 -0.218 82 1.958 5 0.62 -0.470 68 0.388 59 0.92 0.375 17 1.52 1.332 9 -0.442 45 1.0554 0.83 -0.285 73 1.8697 0.57 -0.402 09 1.1988 0.45 -0.587 17E-01

Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1980 1001

Table I (Continued) ~~~~~

~

w3t

solvent methanol

no. of pta 6

nitroethane

6

2-propanol

6

2-propanone

5

tetrachloromethane

6

trichloromethane

6

acetamide

13

acetic acid

5

acetonitrile

6

benzene

6

butanol

7

2-butanone

7

butyl acetate

7

chlorobenzene

6

cyclohexane

6

1,2-dichloroethane

5

l,2-dichloroethylene

5

NJV-dimethylacetamide

6

1,2-dimethylbenzene

6

NJV-dimethylformamide

8

1,4-dioxane

5

ethanol

7

ethyl acetate

7

ethyl acetate

4

heptane

4

methanol

4

methanol

15

methanol

7

methylbenzene

5

methylbenzene

6

methylbenzene

15

nitrobenzene

5

nitroethane

4

nitromethane

5

1,l’-oxybis(ethane)

4

2,2’-oxybis(propane)

15

10-3a12/lo%,,, kJ-degmol-’ 1.860 8 -0.181 58E-01 2.786 3 0.709 16 0.771 02 0.44600E-01 1.313 1 0.144 82 1.305 6 -0.437 04 0.871 07 -0.457 22

w3

K

1.00

1.44


1.57

0.37


0.73

1.48


0.87

1.69


0.92

1.76


0.57

1.01


gi,

g2

7. Hexadecanoic Acid (Palmitic Acid, Cl8H31O& 15.402 5.64 11.54 30.000 0.30 0.44 2.456 5 -0.383 02 0.12 2.766 0 2.05 1.474 4 2.020 4 3.83 2.98 -0.604 47 1.165 1 0.61 0.87 -0.409 50 1.055 1 0.92 0.65 -0.21492 1.579 5 0.68 1.22 -0.641 26 2.741 8 6.60 0.79 -0.766 08 1.79 2.730 2 0.87 -0.708 82 2.549 7 3.56 0.92 -0.444 65 13.32 2.428 1 0.37 -0.421 18 0.59 12.596 1.17 -2.142 9 8.00 2.443 7 0.75 -0.733 01 13.45 0.486 57E-01 1.18 -0.574 63 0.24 1.874 8 0.45 -0.685 53 2.11 1.548 5 1.44 -0.310 28 1.300 0 0.61 0.57 -0.323 67 1.742 8 0.10 0.00 -0.378 59 1.70 3.9080 0.01 -0.745 40 1.4172 0.01 0.33 0.898 78 2.566 1 1.21 1.36 -0.327 14 2.240 5 0.92 1.88 -0.276 61 2.720 1 3.85 0.53 -0.722 51 2.313 1 6.04 0.84 -0.711 43 2.34 2.577 3 0.68 -0.736 16 2.201 5 1.09 7.47 0.81656E-01 0.24 0.85 2.631 8 0.793 50 3.722 0 12.10 3.59 25.339 0.12 1.745 9 0.81 -0.745 86 1.072 8 1.31 0.39 -0.415 33

Magne and Skau, 1952 Ralston and Hoerr, 1942 Hoerr and Ralston, 1944 Ralston and Hoerr, 1942 Hoerr and Ralston, 1944 Ralston and Hoerr, 1942 Hoerr and Ralston, 1944 Hoerr et al., 1946 Hoerr and Ralston, 1944 Hoerr et al., 1946 Preckshot and Nouri, 1957 Harris et al., 1968 Hoerr et al., 1946 Harris et al., 1968 Hoerr et al., 1946 Ralston andd Hoerr, 1942 Hoerr and Ralston, 1944 Kolb, 1959 Kolb, 1959 Kolb, 1959 Bailey et al., 1969 Hoerr and Ralston, 1944 Kolb, 1959 Hoerr et al., 1946 Bailey et al., 1969 Hoerr et al., 1946 Hoerr and Ralston, 1944 Hoerr et al., 1946 Kolb, 1959 Bailey et al., 1969

1002


Table I (Continued) solvent 2-propanol

7

2-propanone

5

2-propanone

6

2-propanone

18

tetrachloromethane

7

tetrachloromethane

4

trichloroethylene

4

trichloromethane

7

water

5

acetic acid

5

acetonitrile

6

benzene

6

butanol

7

2-butanone

7

butyl acetate

7

cyclohexane

6

ethanol

7

ethyl acetate

7

methanol

3

meth an o1

7

methylbenzene

3

nitroethane

4

2,2’-oxybis(propanej

3

2-propanol

7

2-propanone

6

2-propanone

3

tetrachloromethane

7

trichloromethane

7

water

5

acetic acid

5

acetonitrile

4

benzene

5

benzene

6

benzene

6

butanol

6

1.040 1 -0.294 24 0.697 52 18.178 1.6166 -0,26891 1.714 3 -0.302 58 2.697 2 -0.797 12 2.3416 -0.748 79 1.144 1 0.517 86 2.157 9 -0.865 64 23.464 -0.919 37

1.20

1.25


1.71

0.05

Kolb, 1959

0.68

0.26


0.96

0.83

Bailey et al., 1969

1.49

2.53


0.47

0.41

Preckshot and Nouri, 1957

1.17

2.15


0.99

1.55


37.18

0.00


0.42


0.35


0.70


1.04


2.18


0.69


0.86


1.72


0.91


0.62

Bailey et al., 1969

0.98


0.41

Bailey et al., 1969

0.34


0.16

Bailey et al., 1969

1.81


0.42


0.29

Bailey et al., 1969

1.81


0.99


0.00


0.25


0.19


0.31

Domaiiska, 1985

0.40


0.29


1.64

Hoerr and Ralston. 1944

8. Heptadecanoic Acid (C17H3402j 2.733 8 1.15 -0.310 23 3.005 6 2.37 2.1140 2.808 3 0.74 -0.681 98 1.1288 0.63 -0.225 08 1.9162 1.73 -0.633 99 1.5092 0.53 -0.516 54 2.521 9 1.18 -0.646 91 1.724 7 2.79 -0.248 55 1.5283 2.64 -0.273 97 2.9914 3.53 -0.290 64 2.443 1 4.43 -0.143 69 2.5735 4.15 -0.702 06 3.133 5 4.92 0.706 69 1.4485 1.52 -0.500 44 1.5433 1.84 -0.397 83 1.955 3 1.39 -0.261 77 1.967 5 1.73 -0.281 72 2.539 8 1.09 -0.730 70 1.7994 0.64 -0.783 56 24.705 37.19 -0.879 89 9. Octadecanoic Acid (Stearic Acid, C18HM02j 2.836 2 5.95 -0.398 62 2.07 3.579 2 1.0745 2.79 3.002 2 -0.834 34 3.032 4 3.96 -0.834 10 3.035 0 3.94 -0.834 37 2.146 8 6.46 -0.645 19


1003

Table I (Continued) w 3 9

solvent 2-butanone

no. of pts 7

butyl acetate

7

chlorobenzene

4

cyclohexane

10

cyclohexane

6

cyclohexanone

7

1,2-dibromo-l,1,2,2-tetrafluoroethane

3

1,2-dichloroethane

4

1,2-dichloroethylene

4

dichloromethane

3

N,N-dimethylacetamide

16

1,2-dimethylbenzene

4

2,2-dimethylbutane

3

N,N-dimethylformamide

16

l,4-dioxane

5

ethanol

9

ethanol

I

ethanol

6

ethyl acetate

4

ethyl acetate

5

heptane

3

heptane

13

methanol

4

methanol

15

methanol

5

methylbenzene

3

methylbenzene

4

methylbenzene

18

2-methylbutane

3

methylcyclohexane

4

2-methylheptane

4

2-methylpentane

4

4-methyl-2-pentanone

10

nitrobenzene

3

nitroethane

3

nitromethane

5

1,l'-oxybis(ethane)

5

10-~a,~/ kJ-deg-mol-' 1.216 4 -0.251 05 2.828 9 -0.804 29 2.968 1 -0.85801 3.571 9 -0.861 77 2.843 7 -0.810 15 1.920 4 -0.648 19 3.254 1 -0.662 47 3.177 7 -0.571 13 2.930 7 -0.545 55 2.851 6 -0.780 27 11.759 -1.046 5 2.878 6 -0.813 08 2.752 7 0.343 82 12.196 -1.034 9 2.525 6 -0.848 49 1.047 5 0.877 14 1.6720 -0.223 31 2.955 7 -0,603 38 1.4337 -0.169 69 2.044 5 -0.537 75 2.607 2 -0.12302 2.483 8 -0.607 94 2.288 3 1.365 8 2.579 5 -0,275 30 2.359 1 -0.162 71 5.598 6 -0.852 39 2.537 4 -0.773 04 2.917 5 -0.834 26 2.182 3 0.405 59 2.290 5 -0.323 21 2.308 8 0.418 71 2.331 2 0.18093 1.656 1 -0.483 31 2.309 7 0.724 89E-01 2.959 6 0.869 37 3.344 3 30.264 2.045 8 -0.804 65

w3

K 1.66

0.62

ref Ralston and Hoerr, 1942

3.93

0.95


0.06

0.11

Hoerr et al., 1946

0.75

1.19

Domadska and Hofman, 1985

4.90

0.46


0.52

0.87

Domaiiska, 1985

0.81

0.34

Brandreth and Johnson, 1971

1.24

1.21

Hoerr et al., 1946

1.14

1.33


0.35

0.49


5.01

6.98

Harris et al., 1968

0.43

0.55

Hoerr et al., 1946

0.56

0.00

Kolb, 1959

7.07

4.24

Harris et al., 1968

0.04

0.08

Hoerr et al., 1946

1.24

0.68

Domaiiska and Hofman, 1985

2.06

1.77


0.47

0.11


5.00

0.08

Kolb, 1959

5.37

1.21


1.95

0.01

Kolb, 1959

0.76

0.78

Domadska and Hofman, 1985

3.17

0.01

Kolb, 1959

1.84

1.08

Bailey et al., 1969

9.93

1.81


0.82

0.00

Kolb, 1959

1.19

1.34

Hoerr et al., 1946

4.76

0.73

Bailey et al., 1969

3.34

0.03

Kolb, 1959

0.73

0.01

Kolb, 1959

4.66

0.02

Kolb, 1959

2.66

0.01

Kolb, 1959

0.40

0.47

Domadska, 1985

2.34

1.89

Hoerr et al., 1946

5.08

0.44


11.76

2.15

Hoerr et al., 1946

0.70

0.02

Kolb, 1959

011

UZ

1004


Table I (Continued) w3,

solvent 2,2'-oxybis(propane) pentane

no. of pts 6 3

2-propanol

13

2-propanol

7

2-propanone

5

2-propanone

4

2-propanone

6

2-propanone

15

2-propanone

12

1,1,2,2-tetrachloro-1,2-difluoroethane

4

tetrachloroethylene

12

tetrachloromethane

4

tetrachloromethane

6

tetrachloromethane

6

1,2,3,4-tetrahydronaphthalene l,l,l-trichloroethane

15 3

trichloroethylene

11

trichloroethylene

5

trichloromethane

7

l,l,l-trichloro-2,2,2-trifluoroethane

3

1,1,2-trichloro-1,2,2-trifluoroethane

5

triethyl phosphate

5

water

3

methanol methylbenzene 2,2'-oxybis(propane) 2-propanone

methanol methylbenzene 2-propanone

methylbenzene 2,2'-oxybis(propane) 2-propanone

10-3412/10-3cZ21, kJ-degmol-' 1.2796 -0.502 05 2.833 3 -0.182 50 1.03000 -0.253 48 1.774 5 -0.517 05 1.8932 -0.311 44 2.019 2 -0.340 70 1.6956 -0.214 38 1.845 1 -0.301 07 1.5510 -0.262 81 2.303 6 -0.646 39 3.083 7 -0.908 32 2.7809 -0.895 38 12.591 -0.983 64 4.221 7 -0.948 46 2.682 0 -0.762 08 2.280 3 -0.795 32 -0.365 97 0.221 91 2.565 5 -0.878 28 2.9416 -0.970 23 3.0048 -0.529 20 2.847 7 -0.502 82 8.778 1 -1.071 2 5.943 4 51.175

w3

K

0.46

0.23

ref Bailey et al., 1969

3.76

0.01

Kolb, 1959

1.46

2.28

Domaiiska and Hofman, 1985

6.81

1.68


1.36

0.37


5.11

0.05

Kolb, 1959

1.18

0.51


0.81

0.75

Bailey et al., 1969

1.74

0.85

Domadska, 1985

0.10

0.16


0.32

0.70

DomaAska, 1985

0.01

0.02


3.49

3.67


1.61

2.83


1.32

1.69

DomaAska, 1985

0.06

0.09


5.62

1.16

Domadska, 1985

1.39

0.80


1.77

1.49


0.35

0.25


1.89

0.72


3.63

5.03

DomaAska, 1985

32.76

0.00


01,

02

10. @)-6-Octadecenoic Acid (Petroselaidic Acid, C18Hu02) 15 2.1520 0.87 1.34 -0.33009 12 2.944 4 1.20 0.80 -0.865 59 6 1.3886 0.23 0.35 -0.662 14 15 1.492 1 0.55 0.37 -0.349 53 11. (Z)-6-Octadecenoic Acid (Petroselinic Acid, C18Hu02) 3 1.9213 2.17 1.45 -0.216 72 3 2.405 0 0.27 0.40 -0.672 64 3 1.617 5 0.16 0.04 -0.270 73 12. (E)-9-Octadecenoic Acid (Elaidic Acid, C18HuOZ) 12 2.713 2 1.14 0.53 -0.804 13 6 1.3470 1.97 0.33 -0.599 28 6 1.3208 1.44 0.87 -0.19651

Bailey et al., 1969 Bailey et al., 1969 Bailey et al., 1969 Bailey et al., 1969

Bailey et al., 1969 Bailey et al., 1969 Bailey et al., 1969

Bailey et al., 1969 Bailey et al., 1969 Bailey et al., 1969

Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986 1005 Table I (Continued) w3,

solvent 2,2’-oxybis(propane) tetrachloromethane

butanol butyl acetate cyclohexane cyclohexanone diiodomethane ethanol heptane 4-methyl-2-pentanone 2-propanol

1,2,3,4-tetrahydronaphthalene l,l,l-trichloroethane trichloroethylene

1,1,2-trichloro-1,2,2-trifluoroethane triethyl phosphate

butyl acetate cyclohexane ethanol methanol methylbenzene 2,2’-oxybis(propane) 2-propanol 2-propanone l,l,l-trichloroethane trichloroethylene

w3 10-3a12/ no. of pts kJ-degmol-’ 01, K 02 13. (2)-9-Octadecenoic Acid (Oleic Acid, Cl8HUO2) 3 1.0140 0.17 0.32 -0.385 04 8 7.930 8 1.29 1.91 -0.475 15

14. Eicosanoic Acid (Arachidic Acid, CzoHroOz) 7 1.890 1 1.44 1.01 -0.608 32 6 2.2100 0.27 0.48 -0.727 24 16 3.4610 0.88 0.77 -0.958 31 9 1.9334 0.60 0.85 -0.733 80 9 5.0319 0.93 0.13 0.955 66 11 2.526 9 0.96 0.72 -0,572 01 13 2.043 3 5.34 3.49 -0.477 38 12 2.2237 0.89 1.03 -0.699 88 8 1.9175 0.70 1.22 -0.579 32 9 3.199 7 0.64 1.13 -0.899 58 12 3.155 1 0.25 0.38 -0.978 03 7 3.960 5 0.18 0.29 -1.065 7 9 3.164 0 2.24 0.59 -0.6733 34 8 10.430 4.08 6.33 -1.1346 15. Docosanoic Acid (Behenic Acid, CZ2HuO2) 10 1.9384 0.87 1.05 -0.610 99 15 3.026 2 3.88 0.99 -0.93822 15 2.555 3 1.07 1.03 -0.513 04 3 3.842 8 1.29 0.18 -0.409 69 3 3.733 3 1.92 0.26 -1.043 6 3 13.647 8.44 10.64 -1.234 7 16 1.9725 1.11 0.90 -0.508 87 3 2.578 2 0.85 0.19 -0.515 13 9 4.306 0 0.66 0.93 -1.0685 12 3.515 8 0.35 0.60 -1.1136

ref Bailey et al., 1969 Preckshot and Nouri, 1957

Domaiiska and Hofman, 1985 Domaiiska, 1986 Domaiiska and Hofmann, 1985 Domaiiska, 1986 Domaiiska, 1986 Domaiiska and Hofman, 1985 Domaiiska and Hofman, 1985 Domaiiska, 1986 Domaiiska and Hofman, 1985 Domaiiska, 1986 Domaiiska, 1986 Domaiiska, 1986 Domafiska, 1986 Domaiiska, 1986

Domaiiska, 1985 Domadska and Hofman, 1985 Domaiiska and Hofman, 1985 Domaiiska, 1985 Domaiiska, 1985 Domaiiska, 1985 Domaiiska and Hofman, 1985 Domaiiska, 1985 Domaiiska, 1985 Domaiiska, 1985

OThe notation E-01 means X10-*.

description of solubility phenomena. The big discrepancy of the standard deviations in case where the same solute is in different solvents is observed. For example, the standard deviations (al)for octadecanoic acid in benzene from the Redlich-Kister equation are 9.76,9.72, and 8.46 K and from the van Laar equation are 3.06,4.29, and 4.27 K or in ethanol are, respectively, 2.95,1.60, and 4.31 K and 10.11, 2.57, and 2.44 K (see Table I of the supplementary material). The mathematical description of fatty acids-water systems of the extremely small solubility values ( x , = 0.2 X 10-9 is very bad and unacceptable as well. The average

computed values of standard deviations (al)from all of the equations used are from 0.31 to 62.65 K in five tested systems. The values of relative root mean-square deviations (az)are about 0.00 which confirms the above conclusion. There are some numerical restrictions which affect such big values of standard deviations (a1). Namely the derivative dTldxl has a big value in the case of small solubility systems, and it can be led with a big error, while it goes into the objective function through the weight of each experimental point. The investigated methods of correlations cannot be recommended to the systems of such a small solubility as


1006

Table 11. Parameters and Values of Mean-Square Deviations of the Benzoic Acids Data Correlated by the Wilson Equation (Equation 7c) w3

solvent

no. of pts

acetamide

6

acetic acid

5

benzene

13

benzene

7

butanol

7

methylbenzene

13

naphthalene

6

nitrobenzene

6

phenol

4

1-phenylethanone

6

2-propanone

4

tetrachloromethane

4

tetrachloromethane

7

trichloroethylene

7

trichloromethane

6

benzene

8

bromobenzene

9

chlorobenzene

7

cyclohexane

8

1,2-dichlorobenzene

7

diiodomethane 1,3-dimethylbenzene

15 9

ethanol

10

heptane

12

hexane

7

nitrobenzene

7

2-propanol

10

10-3a12/10-3azl,kJ.deg"l-' ul, K 1. Benzoic Acid (C,He02) 22.630 3.22 -1.788 1 0.292 31E-01 1.66 1.232 0 0.868 04 0.28 0.469673-02 16.628 5.21 -0.545 93 -0.259 31 6.06 30.379 0.685 12 1.07 0.127 55 14.605 0.70 -0.406 52 0.634 45E-01 1.59 0.586 16 -0.136 29 0.57 0.84066 -0.361 14E-02 0.41 0.997 50E-01 39.434 2.65 -0.874 53 0.998 25 0.51 0.137 26 0.340 26E-01 5.88 20.607 15.961 4.17 -0.504 47 -0.544 60 3.25 1.7315

62

ref

5.46

Timmermans, 1959

3.03

Mortimer, 1923

0.43

Chipman, 1924

7.40

Mokitra et al., 1974

9.67

Hradil et al., 1970

1.45

Chipman, 1924

1.25

Timmermans, 1959

2.65

Mortimer, 1923

1.18

Mortimer, 1923

0.80

Mortimer, 1923

3.15

Mortimer, 1923

0.49

Mortimer, 1923

9.18


6.09


4.89


2. 2-Methylbenzoic Acid (o-Toluic Acid, C8H802) 1.0118 0.87 1.92 -0.360 18E-01 1.0534 0.51 1.08 -0.157 85 3.1166 3.04 5.36 -0.587 38 1.6675 1.25 1.43 0.365 17 1.0892 0.40 0.83 -0.22902 2.471 9 1.02 0.55 0.591 16 0.993 68 0.47 1.05 -0.598673-01 -0.296 01 0.29 0.58 1.211 70 1.4988 1.03 1.63 0.846 53 0.44 1.8867 0.54 0.486 58 0.953 92 0.45 1.01 -0.263 58E-01 -0.378 08 0.60 1.11 1.1631 1.1290 0.53 1.19 -0.240 22E-01

Domaiiska et al., 1982 Domaiiska, 1986 Domadska, 1986 Domaiiska and Hofman, 1985 Domaiiska, 1986 Domaiiska, 1986 Domaiiska, 1986 Domaiiska and Hofman, 1985 Domaiiska and Hofman, 1985 Domaiiska, 1986 Domaiiska, 1986 Domaiiska and Hofman, 1985

tetrachloromethane

6

benzene

8

3. 3-Methylbenzoic Acid (m-Toluic Acid, C8Hs02) 0.850 51 0.96 2.16 0.139 24

Domaiiska et al., 1982

benzene

6

4. 4-Methylbenzoic Acid (p-Toluic Acid, C8H802) 2.044 1 0.50 0.30 -0.428 49

Domadska et al., 1982

benzene

8

5. 4-Methoxybenzoic Acid (Anisic Acid, C8H80s) 3.198 9 1.53 0.13 -0.666 25

Domaiiska et al.. 1982

benzene

11

6. 3-Phenyl-2-propynoic Acid (Phenylpropiolic Acid, CBHS02) 0.523 73 0.88 1.03 1.1006

Domaiiska, 1986



1007

Table I1 (Continued)

WS solvent

no. of pts

benzene

9

benzene

7

benzene

7

benzene

7

10-3a12/10-3azl,kJ-deg-mol-' 01, K 7. 2-Chlorobenzoic Acid (C7H502C1) 1.8008 0.31 -0.117 24 1.559 7 1.48 -0.224 45E-01

02

ref

0.28


2.04

Timmermans, 1959

8. 3-Chlorobenzoic Acid (C7H502C1) 1.9449 0.77 -0.377 88

1.32

Timmermans, 1959

9. 4-Chlorobenzoic Acid (C7H502C1) 1.794 4 3.01 0.659 95

3.56

Timmermans, 1959

Table 111. Mean Value of the Root Mean-Square Deviation (a,) and the Relative Root Mean-Square Deviation (a,) for Some Solvents with Different Alkanoic and Benzoic Acids Tested w3

alcohols ketones alkanes aromatic hydrocarbons water nitrogen compounds halohydrocarbons

no. of systems Alkanoic Acids 47 36 22 31 5 27 45

alcohols alkanes aromatic hydrocarbons halohydrocarbons

Benzoic Acids 3 3 14 8

solvent

q,K

82

1.41 0.86 2.13 1.89 28.21 4.08 1.06

1.17 1.09 0.63 0.99 0.00 1.61 0.96

2.32 0.91 1.09 2.29

3.79 1.20 1.56 3.64

fatty acids-water, furthermore, when the dissociation of solute into ions can take place additionally. In spite of the better solubility of aliphatic acids in N,N-dimethylacetamide and N,N-dimethylformamide than in water, the mathematical description is unsatisfying too. For example, the standard deviations obtained for all of the tested equations are ul = 6.72-9.10 K and u2 = 12.03-13.48, when the mole fractions of decanoic acid change from 0.04 to 0.75. It seems to be sensible to present the mean values of standard deviations of investigated systems with regard to the chemical character of solvents, what is shown in Table 111. Table I11 of the text contains the mean statistical results of calculations obtained with the Wilson equation in version Wilson 3 (eq 712). The remaining results of the statistical analysis of other tested correlation equations as well as the Wilson 3 method for various solvents, for example, for butanol, ethanol, and so on, are listed in Table I11 of the supplementary material. It can be noticed that the mean values of the standard deviations in systems of aliphatic acids with alcohols, ketones, alkanes, and aromatic hydrocarbons decrease in the direction RK VL W1 W2 W3 In case of benzoic acids, the application of the Redlich-Kister and van Laar equations to the calculations of the solute activity coefficient gives the comparable results. However, the smallest mean standard deviations for the most tested systems are obtained by the Wilson equation in version 7c. Benzoic acids-alcohols systems, however, are described the best by the van Laar equation. Perhaps this can be explained by the high and nearly ideal solubility of benzoic acids, especially, 2-methylbenzoic acid in alcohols.

- - - -

The mathematical description of the monocarboxylic acids solubility becomes worse with the decrease of solubility in tested solvents. For example, the mean values of 2 acids in cyclohexanone are alRK= 1.11, alVL= 0.57, and aIw3= 0.56K, whereas the mean values of 19 systems with 2-propanone, which is the worst solvent, are alRK= 3.22 and aIw3= 1.47 K. Cyclohexanone and cyclohexane have similar dissolving power probably due to the comparable size of molecules, but because of the possibility of forming hydrogen bonding with solute, cyclohexanone is a little better solvent. So the mathematical description of solubility in cyclohexane is worse than for cyclohexanone. The mean values of standard deviations of 12 systems are alRK = 4.13, alvL= 2.06, and i71w3 = 1.34 K. The solubility of alkanoic acids in heptane is smaller than in cyclohexane, so the standard deviation values increase (see the supplementary material, Table 111). The average values of the standard deviations for some solutes in all tested solvents are presented in Table IV of the supplementary material. It can be noticed that for certain acids, for example, eicosanoic and docosanoic, the mean values of standard deviations decrease in the order R-K VL W1- W2 W3. Some systems of a very bad mathematical description make mean values of the standard deviations worse. The standard deviations become smaller after rejection of these systems, what is shown in Table IV of the supplementary material. For example, the mean values of the standard deviations (a,) of decanoic acid in 21 solvents for all the correlation equations are 0.97-1.28 K and in 19 solvents decrease to 0.56-0.62 K. The solubilities of alkanoic acids in different solvents decrease with the number of carbon atoms increment, so the mathematical description gets worse especially for fatty acids (Cl6-CZ2). -+

4

+

Conclusions 1, The best results of the correlation of experimental points in binary systems of monocarboxylic acids in alcohols, ketones, alkanes, aromatic hydrocarbons, and halohydrocarbons are obtained by means of the Wilson equation utilizing temperature-dependent hi.parameters in version Ai, = exp[-(gij - gii)/RT],where - gii) = a i j / T and a,ij # f(T). The worst results are given by Wilson 2, Wilson 1, van Laar, and Redlich-Kister equations, successively. Other widely used equations such as NRTL and UNIQUAC are not tested, because of ambiguities in the determination of the a parameter for the former and difficulties in estimation of the structural parameters for the latter one. 2. The solubility of acids in various solvents decreases

Gij

1008


with the rise in the acid‘s molecular weight in a homologous series, and the mathematical description of the system becomes worse. 3. The mathematical description of the system by means of applied equations changes for the better when an inactive solvent is replaced by a polar one in which the better dissolving power causes the rupture of hydrogen bonds of acid dimers. Acknowledgment We thank the Institute of Physical Chemistry, Polish Academy of Sciences, for ita financial aid of Project 03.10.1. Nomenclature A = parameter in the correlation equation a = activity f = fugacity g = molar energy of interaction AH = enthalpy of fusion n = number of experimental data p = pressure R = gas constant T = solid-liquid equilibrium temperature V = molar volume z. = liquid-phase mole fraction W = weight of experimental point Greek Letters y = activity coefficient A = parameter of the Wilson equation ul, u2 = standard deviation parameters defined by eq 11and 12

Literature Cited Bailey, A. V.; Harris, J. A.; Skau, E. L. J. Am. 011 Chem. SOC. 1989, 46, 583-587. Brandreth, D. A.; Johnson, R. E. J. Chem. Eng. Data 1971, 16,325-327. Chlpman, J. J. Am. Chem. Soc. 1924. 46,2445-2448. Domatiska. U. Pol. J. Chem., in press. Domatiska, U. FluMPhase Equlllb. 1988, 26, 201-220. Domaiiska, U., submitted for publlcatlon In Ind. Eng . C b m . Fundam. DomaAska, U.; Buchowskl, H.; Pietrzyk, S . Pol. J. Chem. 1982, 5 6 , 1491-1499. Domatiska, U.; Hofman, T. J. Solution Chem. 1985, 14, 532-547. Harris, J. A.; Bailey, A. V.; Skau, E. L. J. Am. 011 Chem. SOC. 1988. 4 5 , 183- 184. Hiranuma, M. I n d . Eng. Chem. Process D e s . D e v . 1972, 11, 631-633. Hoerr, C. W.; Ralston, A. W. J. Org. Chem. 1944, 9 ,329-337. Hoerr, C. W.; Sedgwick, R. S.;Raiston, A. W. J. Org. Chem. 1948, 1 1 . 603-609. Hradii, J.; Malek, J.; B a h t . V. Chem. R u m . 1970, 2 0 , 117-120. Jalai, J. M.; Zografi, G.; Raksht, A. K.; Gunstone, F. D. Chem. Phys. LipMs 1982, 31,395-404. Koib, D. K. Diss. Abstr. 1959, 20, 82-86. Magne. F. C.; Skau, E. L. J. Am. Chem. SOC. 1952, 74,2628-2630. Makitra, R. G.; Mokrll, E. M.; Parada, A. Vlsn. L’vlv. Polkekh. Inst. 1974, 82, 52-56. Morimi, J.; Nakanishi, K. FluM Phase Equilib. 1977, I , 153-160. Mortimer, F. S . J. Am. Chem. Soc. 1923, 45,633-641. Mulr, R. F.;Howat, C. S., 111. Chem. Eng. 1982, 22, 89-92. Neau, E.; Peneloux, A. Fluid Phase Equilb. 1981, 6 , 1-19, Preckshot, G. W.; Nourl, F. J. J. Am. 011 Chem. Soc.1967, 34, 151-155. Ralston, A. W.; Hoerr, C. W. J. Org. Chem. 1942, 7 , 546-555. Rakton, A. W.; Hoerr. C. W. J. Org. Chem. 1945, IO, 170-179. Schaake, R. C . F.; Miltenburg. J. C.; Kruif, C. G. J. Chem. Therm@n. 1982, 14,771-778. Schotte, W. Chem. Eng. Sci. 1984, 39, 190-192. Szafraiiski, A.; ChoiiAski, J. Commun .-Czech .-Pol. Colloq. Chem. Thermodyn. Phys. Org. Chem. 1980, 106-108. Timmermans, J. The Physico-Chemical Constants of Binary System in Concenfrated Solutions; Interscience: New York, 1959; Vol. 2. Wilson, 0.M. J. Am. Chem. SOC.1984, 86, 127-130. Yaikowsky, S.H.; Valvani, S . C. J. Pharm. Sci. 1980, 69, 912-922.

Receiued for reuieul July 11, 1985 Revised manuscript received April 9, 1986 Accepted May 4, 1986

Superscripts

L = liquid phase O = pure component s = solid phase Subscripts 1, 2 = solute and solvent, respectively i, j = component i and j m = melting point t = triple point

Supplementary Material Available: Tables I and I1 specifying parameters and standard deviations of RedlichKister, van Laar,and versions 7a and 7b of Wilson equations for aliphatic and benzoic acids successively, Table I11 containing mean standard deviations, obtained with all the equations for different acids in the same solvent, and Table IV comprising mean-square deviations for some solutes in different solvents (32 pages). Ordering information is given on any current masthead page.

Solubility correlation of monocarboxylic acids in ... - ACS Publications

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