Line Coordinate Representation of SOLUBILITY CURVES FRANK E. E. GERMANN AND RICHARD P. GERiMANNl University of Colorado, Boulder, Colo.
T
which is then solved for X , the mole fraction of the solute in1 equilibrium with the solvent a t the given temperature. Since. this calculation takes some effort, the authors decided to make a. graph of the data on line coordinates, as was done in the case of' vapor pressure curves by Germann and Knight (1). Values of -log X and of 1/T were used as uniform scales on t h e two parallel lines. The equation was then solved for -log X at tlyo widely separated temperatures, and straight lines were drawn connecting the two pairs of values of -log X and 1/T. The point of intersection of these two lines represents all possible. solutions of the given equation and really is the graph of t h e equation. The point of intersection of the straight lines is recorded on the graph rather than the lines. Afler a large number of equations were located in this way, it became obvious that the points were grouping themselves along straight lines. All points along a given straight line were seen to. belong to systems having the same solute but different solvents. Moreover, it was observed that the two ends of the line had a special significance, since the one corresponded to the melting: point of the pure solute and the other to a mole fraction of 1 (or. -log 1 = 0). The simple interpretation of the above fact is that most organic chemicals are miscible in all proportions in t h e liquid state. Thus, when the melting temperature of the solute is reached, we may make up a solution in which its concentration,. reaches 100 per cent or a mole fraction of 1. Many of the points lie very close to, but not exactly on, the, straight lines. I n most cases this is due to the fact that the melt-ing points of the solute obtained by different experimenters do, not agree. I n Mortimer's original -log X us. 1/T curves froma which he calculated the equations, the experimental values of t h e melting points given by the experimenter were used. I n the case of acenaphthene, for example, some authors gave 92.5" C. and others 95' C. as the melting point. Mortimer's equations for, these systems would therefore lie on lines pointing to 92.5" a n d 95" C., respectively. I n numerous cases solubilities were deter-. mined over a limited range of temperature far below the melting: point. In these cases values of constants a and b were determined from data which did not include the melting point of t h e solute. I n the case of system 385 (3, page 174) for acetone-anthracene, the range studied was from 15" to 55" C. If the equa-tion for this system,
WO-component systems, consisting of solid, liquid, and vapor phases in equilibrium with each other, usually comprise a single homogeneous liquid solution and a solid phaw consisting of either one of the pure components or a compound of both. When water is the solvent and small amounts of a solid nonvolatile solute are added, the freezing point of the water is lowered. Accordingly we are accustomed t o speak of this as the freezing point curve. When larger amounts of the solid are added, so that even at room temperature solution is not complete, we speak of the liquids being saturated with the solute. As the temperature is varied, the solubility changes, and we have what is known as the solubility curve. Since the latter represents the solubility of the phase appearing as a solid in excess, the former curve must be the solubility curve of the solid phase ice. Thus in the case of solutions of salt and water, if for high concentrations of salt we speak of the solubility of salt in water, for low concentrations we should speak of the solubility of water in salt. Stated another way, if salt lowers the melting point of water in the one curve, then water lowers the melting point of salt in the other. Le Chatelier (9)and Schroder (4) developed equations for solubility curves which still form the basis of all subsequent work, although they are now frequently derived from more fundamental considerations. The equation of Schrader may be written in the form,
where X', X = mole fractions of solute in solution a t temperatures T' and T AH = molal latent heat of fusion of solute if solution is ideal
A t the melting point of the solute, T ' , X' becomes unity if the liquids are completely miscible. Hence we may write
1 logs =
or
AH 2.303 X 8.315 T
+
= 0.05223 AH
T
+c
(3)
Equation 3 has been used by Mortimer (3) in the form, -1ogx
1 X
= log -
z=
0.05223
-a + b
(4)
-1ogx
to represent the solubility curves of over five hundred systems b r hbulating values of a and b determined experimentally from curves in which -log X and 1/T were used as coordinates. Under these conditions Equation 4 is that of a straight line having a slope of 0.05223 a and an intercept b. If astraight line did not result, if there was compound formation, or if the data were insufficient, a tabular form of recording was used. Mortimer states that a is the heat of fusion of the "solute" in joules per grammole if the solution is "ideal". To make use of Mortimer's data, the values of a and b and the absolute temperature T are substituted in the log equation, 1
=
-X
26,640
- 2.176
is solved for X = 1 or -log X = 0, we obtain a value of T = 639.4' K. or 366.3" C. for the melting point, whereas the value given is 216.5' C. By adjusting values of a and b it would be possible to obtain a log curve of the above form which would include the solubility fort,he experimental range of 150 to 55" c. and also the melting: point 216.50 c. This equation n,ould then give a point lying on the anthracene curve which would be valid for solubilities in t h e range 150 to 550 C , and would also be fairlyaccurate up to the melting point. sincethis tvas not the task attempted in the present investigation, such points have been omitted.
Present address, Taylor Refining Company, Corpus Christi, Texas.
93
94
INDUSTRIAL AND ENGINEERING CHEMISTRY
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n.
Vol. 36, No. 1
INDUSTRIAL AND ENGINEERING CHEMISTRY
January, 1944
TABLE I. Solute (Solid Phase) Benzene
Ethylene dibromide
Acetic acid
Solvent (Liquid Phase) 1. Phenol 2. Nitrobenzene 3. o-Bromonitrobenzene m-Bromonitrobenzene p-Bromonitrobenzene Diphenylamine 4. Benzoyl chloride m-Dinitrobenzene 2,4-Dinitrotoluene 2,6-Dinitrotoluene 3,4-Dinitrotoluene 5. Nitrobenzyl chloride Pyridine 6. Bromoform o-Chloronitrobenzene m-Chloronitrobenzene p-Chloronitrobenzene 7. p-Bromotoluene Diphenyl Ethylene dibromide 8. Ethylene dichloride Naphthalene Paraldehyde Toluene p-Xylene 9. Camphene
c.
-10.0to -40.0 t o -20.0 to -20.0 to -5.3 to 0.25 to -10.0 t o
1. Dimethyl oxalate 2. Benzoic acid Dimethyl succinate 3. Phenol 4. a-Chloroacetic acid
8.4 9.5 -7.0 -15.0 -4.0
SYSTEMS
Eutectic Temp., ’ C. -5.3 -24.6 -8.7 -3.1 3.7 -6.8 -26.5 -0.8 -0.7 0.2 -5.0 -3.3 -41.0 -26.0 -10.6 -5.7 -4.0 -18.5 -5.8 -27.6 -53.0 -3.5 -27.0 -99.8 -22.2 -45.0
9.7 9.7 9.7 9.7 9.7 9.7 9.7
-20.0 -27.6 -5.3 0.25 -12.4
to to to to to
16.7 16.7 16.7 16.7 16.7
8.4 9.5 -7.0 -15.0 -4.0
20.0 t o 10.0 t o 5.0 to 25.0 to 25.0 to
40.6 40.5 40.5 42.4 42.4
-5.3 -15.0 -16.5 16.5 11.8
22.0 t o 41.0
22.0
29.0 33.5 31.5 36.3
29.0 33.5 31.5 36.3 14.0 84.0 15.0
APPEARING IN FI.GURE 1 Solute (Solid Phase) Na hthalene &ontinued)
p-Dibromobenzene
Acenaphthene
-20.0
...
Phenanthrene
aldehydk
1. 2. 3. 4. 5. 6.
Naqhthalene p-Nitrophenol rn-Sitrophenol @-Naphthylamine a-Naphthylamine Picric acid pToluidine
p-Nitrotoluene
a-Chloroacetic acid
0
1. Paraldehyde 2. Toluene 3. -Xylene 4. genzene Diphenylamine Naphthalene 5. p-Bromotoluene
Phenol
o-Nitrophenol
Temp. Range,
to to to to 20.0 t o 34.0 t o 15.0 to 3 5 . 0 to 26.5 t o 3 0 . 0 to 29.7 to 1 5 . 0 to 15.0 to
1. o-Cresol m-Cresol
45.0 44.0 44.0 44.5 44.5 45.5 44.5 52.0 51.4 51.4 51.4 51.4 51.4
1. Benzoic acid 2. Hexane 3. a-h-aDhthol 4. n-Toiuidine 5. Acetone 6. Ethyl ether 7. Ethyl acetate
Aniline Nitrobenzene Ethyl ether Carbon tetrachloride m-Chloronitrobenzene 5. Benzene Carbon disulfide Toluene 6. Bromobenzene 7. o-Dibromobenzene
1. .~ Aontnne -. I. Acetone ....~~. 2. Aniline 3. Carbon tetrachloride 4. Pyridine 5. Carbon disulfide o-Dinitrobenzene 6. Nitrobenzene Toluene 7. Indene 8. Chlorobenzene pDinitrobenzene 9. Fluorene 10. Chloroiorrn 11. Iodoacenaphthene 12. Chloroacenaphthene
...
-4i:o
...
30.5 14.5 29.0 55.0 32.3
20.0to 20.0 to 10.0 to 20.0 to 34.0 to 1 0 . 0 to 0.0to 1 0 . 0 to 5.0to 20.0 to
89.0 89.0 87.0 89.0 88.3 87.0 87.0 89.0 87.0 86.7
10.0 t o 10.0 to 10.0 to 20.0 to 10.0 t o 71.5 to 10.0 to 1 0 . 0 to 30.0 t o 10.0 t o 81.5 to 67.5 to 50.0 to 50.0 to 56.6 t o
95.0 95.0 95.0 95.0 95.0 92.5 95.0 95.0 95.0 95.0 92.5 95.0 95.0 92.5 92.5
...
8. 9.
29.7 -16.3 -2.8
Benzoic aoid
Anthracene
... ... ... ... ... ... 65.7
46.7 91.2 95.4 115.0 82.0
1. Kaphthalene 2. @-Naphthylamine a-Nitronaphthalene
100.0 t o 197.0 80.0 t o 179.0 27.3 t o 179.0
32.3 56.0 27.3
... ... ...
-3.0 -3.5 64.9 36.7 29.0
...
37.6 66.6.
Bend Piperonal Acetic acid Acetophenone a-Chloroacetic acid o-Chlorobensoic acid rn-Chlorobensoic acid p-Chlorobenzoic acid 11. Cinriamio acid
61 .O 31.9
... ...
si:i
67.5
95.0 t o 121.5 1 0 . 0 t o 40.0 70.0 t o 121.0 1 0 . 0 t o 80.0 95.0 t o 121.4 50.0 t o 121.4 4 0 . 0 t o 121.4 10.0 to 121.4 60.0 to 121.5 91.2 to 121.7 95.4 t o 121.7 115.0 to 121.7 82.0 t o 121.5
4. 5. 6. 7. 8. 9. 10.
70.0
...
... ... ...
1.
3.
Camphor
62.0
7i:i
... ... ...
Bknzene Toluene Xylene Nitrobenzene Chlorobenzene Indene o-Dinitrobenzene Acenaphthene
2.
... ... 53.3 ...
... ... ... ...
55.0 74.0 54.0 90.0
55.4 44.9
33.6 -11.45 26.5
...
0.3
... ... ... ... ... ... ... ...
15.8
1i:i
... ... ... ... 34.0 ... ... ...
... ...
Acetone Benzene Toluene Chlorobenzene Pyridine Kitrobenzene 7. Chloroform 8. Tetrachloroethane
7.6
12. Kitrobenzene Benzene Phthalic anhydride 13. e-liitronaohthalene o-Nitrophenot
Temp. Rang?, Eutectic C. Temp., C . 39.4 0 25
1. 2 3. 4. 5. 6.
6. 7.
47.3 46.5 56.8 47.6 26.0 30.5 -4.0
Kaphthalene
1. 2. 3. 4.
5.
16.5
1. Benzene 2. o-Dinitrobenzene n-Dinitrobenzene Fluorene 3. Picric acid 4. 2,6-Dinitrotoluene 5. o-Nitrotoluene p-Nitrotoluene
Solvent (Liquid Phase) 14. Di henyl Etiylene dibromide 15. Chlorobenzene Ethylene dichloride Pyridine 16. Chloroform D jphenylamine Diphenylmethane p-Nitrotoluene 17. Fluorene 18. Camphor
Fluorene
29.0 26.5
26.7 46.7
2,4-Dinitrotoluene
95
Carbazole
1. 2. 3. 4. 5. 6. 7. 8.
Pyrogallol Resorcinol Catechol p-Nitrophenol ,%Naphthol m-Xitrophenol a-Naphthol o-Xitrophenol
83.0
...
70.0
...
77.2 27.3 9.5
...
150.0 193.5 110.0 98.0 5.0 146.0 101.0
to to to to to to to
212.5 216.5 213.0 213.0 175.0 212.5 213.0
106.0 193.5 110.0 98.0
126.0 160.0 102.0 106.7 135.0 92.0 90.0 43.5
to to to to to to to to
236.0 236.0 236.0 236.0 285.5 236.1 235.6 236.0
126.0,
146 0 101.0~
loi:6 106,7 115.0 92.0 90.0 43.5
96
INDUSTRIAL AND ENGrNEEfifNG CHEMISTRY
If the melting points for a solute as given by different authors all had the same validity, then a best straight line drawn from -log X = 0 through the series of points to the temperature axis would give the most probable melting point. However, since much of the solubility data is rather old, the better procedure would seem to be t o draw the straight line from -log X = 0 t o the most accurate melting point of the solute known today. If a very accurate solubility determination i s made a t one temperature (say 20" C.) and a straight line is drawn from 20" C. t o the determined mole fraction, the point of intersection represents the equation for the solubility at any temperature, provided compound formation or immiscibility do not interfere. The dotted straight lines in Figure 1 come very close t o all of the points located as explained above, and terminate a t the temperature end close to the best values accepted today for the melting points of the respective solutes recorded on the lines. From what has been said above, it is clear that all points for a given solute located by the use of equations which include the identical melting points must lie exactly on the straight line terminating a t this temperature. Since this is not true of the data used, some points are not exactly on the lines, and no attempt has been made t o force them to the lines by recalculating values of a and b in the Mortimer equations, If, however, this point is kept in mind in future calculations of equations] all points will lie on the lines and errors in calculation will be readily recognized. To determine the solubility of a solute in a given solvent, i t is only necessary t o lay a straightedge from the temperature through the point and read mole per cent on the right-hand line. New solubility curves for "ideal" (in the sense used by Mortimer) i~olutionsmay be approximated by determining the solubility at
Vol. 36, No. 1
a single temperature and recording a point at the intersection of this line with the line pointed t o the melting point of the solute. By holding one end of the straightedge a t a given temperature] it is obvious that the solubility of a given solute, expressed in mole per cent, increases with the serial number of the solvent. This serial number is not the same for a given solvent in the various series. Figure 2 shows the relation between the familiar eutectic s o h bility curves and the present method of representation. At the left a family of curves originates at the melting point of benzoic acid which is present as a single pure constituent, A . The addition of component B lowers the freezing point of benzoic acid along the various members of the family of curves to the respective eutectic temperatures. From here on, component B , indicated on the curve, is the solid phase, the curve ending at the melting point of pure B. It is the family of curves at the left of the eutectic points which constitutes a series of points along a straight line in Figure 1. This family in Figure 2 includes only a part of the series given in Figure 1 and in Table I under benzoic acid as solute. The numbers are the same as those in the table. The sequence of curves 1 a, 3 a, 5 a, etc., of Figure 2 also shows that the mole per cent solubility of benzoic acid increases, a t a given temperature, with the serial number. LITERATURE CITED
Germann, E'. E. E., and Knight, 0. S., IND.ENO.CHEIM., 26, 467-70 (1934). Le Chatelier, H., Compt. rend., 100, 50-2, 441-4 (1885); 118, 638-41 (1894). Mortimer, F.S.,International Critical Tables, Vol. IV, pp. 17281,New York, McGrttw-Hill Book Co., 1928. Schroder, I., 2. physilc Chem.,11, 449-65 (1893).
