SOLUBILITIES AND COOLING CURVES O F THE MONONITROPHENOLS" BY I,. I,. CARRICK
The first systematic theoretical work of note on solubility was done by van't Hoff ; l who originally derived a solubility equation from the analogy between solutions and gases. He compared solubility to evaporation and saturation t o maximum vapor pressure. Then starting with the fundamental thermodynamic equation rl dT AVdP = -. . . . . . . . . . . . . . . . . . . . . . . . .
1
he derived the solubility equation
in which Q is defined as the heat absorbed in dissolving one mole of the solute in a saturated solution, the other terms having their usual meaning. Van Laar2 has derived a somewhat similar equation connecting heat of solution and solubility in the case of electrolytes. The examples which he cites show close agreement between observed and calculated values. An equation showing another relation between solubility and heat of solution has been deduced from Planck's thermodynamic equation by Dahms. Correct results were obtained in the two examples cited. Wilderman4 and Colson6 have also formulated equations showing relations between solubility and heat of solution, which like many others only record an interesting coincidence and are not capable of universal application. *Thesis submitted to the Graduate School of Indiana University in partial fulfillment of the requirements for the degree of Doctor of Philosophy. 1 van't Hoff Lectures, vol. 1, p. 35. 2 Zeit. phys. Chem., 35, 11-17 (1900). 3 Wied. Ann., 64, 507-518 (1898). cZeit. phys. Chem., 42, 481-486 (1903). 8 Comptes rendus, 162, 753-56 (1916); 161, 586-89; 787-90 (1915).
Solubilities and Cooling Curves
629
Solubilities calculated from conductivity measurements are in good agreement with the experimental values but the method has no general application, as it can only be used with advantage where the solute is sparingly soluble and is completely ionized in solution. It cannot be used a t all for nonelectrolytes. Spencer1 and Bodlander2 have attempted to calculate the solubility of salts from electrode potentials. Good results were obtained by Spencer for T1103. Bodlander's method gave results which varied greatly but were of the same magnitude. In many cases it was necessary to assume complexity of ions, or to make corrections for liquefaction and vapor pressure. In general there are special details to be . observed, which entail a prior knowledge of a substance's solubility. Should the component be non-ionized the method is inapplicable. Kyato3 found a relation between indices of refraction and solubility and formulated an equation for calculating solubility which was later modified by Getman and W i l ~ o n . ~ The results of both formulae are only approximate, the largest error occurring in dilute solutions. In the equation of T ~ r e rand , ~ Hardman and Partington6 the solubility of a substance in any particular solvent is expressed as a function of the temperature. Hardman and Partington secured good results for the few solvents tested, but this would be true for a limited number of examples with almost any equation connecting temperature and solubility, which contains three constants depending on the nature of the solution. Dolezalek7 has assumed that the partial pressures of the constituents of an ideal mixture should be proportional Zeit. phys. Chem., 80, 70-78. Ibid., 27, 55 (1898): 8 Mem. Coll. Sci. Eng., 1, 265, 290-303 (1907). 4 Am. Chem. Jour., 41, 344-348 (1909). Jour. Chem. SOC.,97, 1778-88 (1910). Ibid., 99, 1769775 (1911). 7 Zeit. phys. Chem., 64, 727 (1908); 71, 191 (1910). 1
a
L.L.Carrick
630
to the molecular concentration of each, and that the total pressure is the sum of the two linear partial pressures, the total pressure being then represented by a straight line. Out of 160 examples only 70 agreed with the theory while 90 were exceptions. Starting from Gibbs” function, Miller2 has deduced a formula for the calculation of solubility, but he gives no examples of the application of his equation. A formula analogous to that of Ramsay and YoungS for the calculation of a complete vapor pressure curve from a knowledge of the vapor pressure of a substance a t two temperatures and a complete vapor pressure curve for another substance is proposed by P i n d l a ~ . ~He proposes the equation R = R’ C(t’ - t ) . . . . . . . . . . . . . . . . . . . 3 in which R and R’ are the ratios of the absolute temperatures a t which the substances have the same solubilities. C is a constant with a small positive or negative value and is different for each solubility curve; t’ and t are the two temperatures a t which one of the substances has the two values of the solubility in question. The calculated results from this equation are quite good as long as the curves are regular. J. H. Hildebrandj has approached the subject of solubility from the standpoint that Raoult’s law is more applicable to solutions than van’t Hoff’s equation, as most investigators heretofore have held. With this in mind he has derived the expression
+
4 in which N is the solubility in mole fractions, L the molecular heat of fusion of the solute, T, the melting point on the the ’ absolute temperature absolute scale of the pure solute and ’I Trans. Conn. Acad. iii (1876-1878). Jour. Phys. Chem., 1, 633-642, 1896-97. 3 Phil. Mag., (V) 21, 33, 1886. Proc. Roy. SOC.,69, 471-78 (1902). 6 Jour. Am. Chem. SOC.,38, 1452-73 (1916); 39, 2297-2301 1067-80 (1919). 1
(1917); 41,
Solubilities aizd Coolifig Curves
63 1
a t which the solubility is desired. Hildebrand states that positive variations are to be expected when the internal pressure of the solute and solvent are not the same, and when the solute and solvent are polar, that is they tend to form compounds with each other. Since no account is taken of the variation of the heat of fusion with the temperature the solubility curve constructed by plotting solubility in mole fractions as abscissas and temperature as ordinates is approximately a straight line. Schroder,l Le Chatelie? and van Laar3 have derived the eauation LRT2 dT d logex = ....................... 5 which when integrated gives the equation logex =
- L (To- T) . . . . . . . . . . . .. 6
in which x is the mole fraction of the solvent, R the gas constant, L the latent heat of fusion of the pure solvent, To the absolute temperature of fusion of the pure solvent and T the absolute temperature a t which the solvent melts in the presence of the second component. Baud and Gay4have derived the same expression starting from the Clapeyron equation 1,dT = AT(V - U)dP . . . . . . . . . . . . . . . .. 7 Washburnj has also deduced this same equation by combining the equation of Boldingh logex RT ........................ 8 7r = - ---
vo
representing the relation between osmotic pressure and concentration of the solution, with the equation connecting osmotic pressure and freezing point Zeit. phys. Chem., 11, 449 (1893). Comptes rendus, 118, 638 (1894). a Proc. Akad. Wet. Amsterdam, 5, 424; 6, 21 (1903). Comptes rendus, 150, 1687(1910). 6 “Principles of Physical Chemistry,” p. 172. 1
2
632
L. L. Carrick d?r L dT = - V T . . . . . . . . . . . . . . . . . . . . . .
9
so as to eliminate dn, the osmotic pressure. If we express the solubility of the solvent in terms of the mole fraction of a saturated solution it is claimed that the solvent, when associated with any solute to form an ideal solution, is entirely independent of the nature of the solute. This is on the assumption that there is no dissociation or association. Substances which are either, do not fall under the category of ideal solutions and consequently the equation does not express the relationship between them. Under the above assumption solubility is a function of the temperature only. Both Washburn, and Baud and Gay have tested Equation 6 for binary mixtures which are ideal solutions, and found that it gives excellent results compared with the experimental values. This equation as been verified by the writer in the case of mixtures of the mono-nitrophenols.
Experimental Purification of h4aterials.-Acetone : C. P. acetone after standing in contact with quick-lime for two days, with frequent shaking, was distilled. The fraction passing a t 56.3 deg. C was retained and fractionated over anhydrous copper sulphate. Only the fraction passing a t 56.3 deg. C (corrected) was collected and set aside for use. When tested for impurities1 no test for residue, acids, aldehydes, water, substances oxidizable by permanganate was obtained. It was miscible with an equal volume of water yielding a clear solution. Benzene: C. P. benzene was twice distilled over anhydrous copper suplhate. A four-bulb fractionating column was used. Only the fraction passing a t 80.36 deg. C (corrected) was retained. The presence of water, carbon disulphide and thiophene was not detected.
* Outline of the tests used for impurities will be found in “Chemical Reagents, Their Purity and Tests” by E. Merck.
Solubilities and Cooling Curves
633
Ethyl alcohol: This was purified by allowing to stand two days in contact with quick-lime, with frequent agitation. The supernatant liquid was decanted and distilled over fresh quick-lime. The fraction passing at 78.4 deg. was collected. To insure dehydration and the removal of impurites with lower boiling points it was again distilled. A fractionating column and anhydrous copper sulphate were employed, and again only the fraction retained that distilled sharply at 78.4 deg. C (corrected). It gave no test for residue, fusel oil, molasses, alcohol, aldehydes, acetone or organic matter. Ethyl ether: U. S. P. ethyl ether was shaken with distilled water four times to remove any traces of alcohol and twice distilled over fused calcium chloride. Each time it was distilled, only the fraction boiling at 35 deg. C was retained. It was distilled a third time with the aid of a fractionating column and anhydrous copper sulphate, the fraction passing sharply at 35 deg. C (corrected) was collected for use. No residue, aldehyde, water or acetone was detected. Ortho- and para-nitrophenol : The para-nitrophenol was crystallized several times from water. The final product melted at 114 deg. C (corrected), the accepted melting point. The ortho-nitrophenol was first steam distilled and then crystallizedfrom alcohol. It melted at 44 deg. C. Meta-nitrophenol:l The meta-nitrophenol was prepared from meta-nitroaniline by diazotizing with potassium nitrite and boiling the diazonium compound until the evolution of nitrogen ceased. On extraction with ether i t was found that any tar resulting from the diazotization was also taken u p by the ether. The ether was distilled off, and the tar and meta-nitrophenol were separated by heating with (1: 1) dilute sulphuric acid. The tar floated on the surface of the dilute acid and the meta-nitrophenol crystallized out. The metanitrophenol was recrystallized from water until a product melting a t 93 deg. C (corrected) was obtained, which remained unaltered on further crystallization. The meta-nitrophenol was prepared in the laboratory of the North Dakota Agricultural College.
634
L. L. Carrick
Method of Determining Solubility.-A method similar to. the one herein described, but differing in some particulars, was used by N. V. Sidgwick' for the solubility determinations of the mono-nitrophenols in water. The method which the writer has used will be described in some detail, as it seems to be one which may be used to advantage in the determination of the solubility of solid substances whose equilibrium in solution is quickly attained. Some of the material whose solubility is desired, is weighed into a 50 t o 7 5 cc ground-glass-stoppered erlenmeyer flask of known weight. The amount of solute should be sufficient to saturate the solvent at 0 deg. C, when the solvent fills the flask about two-thirds full. A little solvent is added t o the solute in the flask, the exact amount being determined after the saturation point has been determined by weighing the flask and contents. Only enough solvent should be added t o produce a saturated solution of the substance near the boiling point of the solvent. After the addition of the solvent, the flask, with stopper removed, is immersed to within an inch of the top in a two liter beaker filled with distilled water. The water in the beaker is agitated mechanically and the flask is agitated continuously to hasten equilibrium between solute and solvent. The bath is heated with an electric hot plate provided with a variable resistance. The temperature is determined by a recalibrated thermometer suspended in the bath to the same depth as the solution in the flask. The temperature of the bath is gradually raised until the last crystals have gone into solution, this temperature being noted. The flask is removed and both the flask and bath cooled slightly below the saturation point. Then the flask is replaced in the bath and the temperature raised very slowly, the approximate temperature being already known. Just before the last crystals have gone into solution the glass stopper is inserted. The point at which the last crystal dissolves is read accurately, this point being the saturation temperature. The flask is now removed, cooled to room temperature, dried and weighed. The difference between this weight and the weight of the 1
Jour. Chem SOC., 107, 1202-1213 (1915).
.
Solubilities afid Cooling Curves
635
flask after the addition of the solute is the amount of solvent required to form a saturated solution with the given amount of solute at the temperature at which the last crystal went into solution. To find the next point on the curve, it is only necessary to add a little more solvent and repeat the above operation for saturation temperature. This time only one weighing is required to determine the amount of solvent used, while the amount of solute is the same as for the preceding point. By this method it is quite often possible to determine an entire saturation curve in the time usually required, by other methods, to locate one point. The solubility is determined under atmospheric pressure. The solvent which escapes before saturation does not vitiate the results. The solute, however, must be nonvolatile at the working temperature. Errors due to analytical methods and manipulation are avoided. It must be borne in mind as pointed out above, that the method is of value only when equilibrium between solvent and solute is quickly attained. This was the method used in determining the solubility of each of the mono-nitrophenols in acetone, benzene, ethyl alcohol, and ethyl ether. The results are tabulated in Tables I, 11, 111, and IV.
TABLE I Solubility in acetone of Ortho-nitroDheno1 I
I-
iMeta-nitroahen01
I
Para-nitro~henol
* O d,
&-
gzg
H $3
36.5 30.3 26.1 20.1 16.1 11.5 6.0 +0.2 -
236.67 566.29 398.97 258.96 211.37 166.48 131.42 102.44 -
92.56 84.98 79.97 70.50 67.88 62.48 56.79 50.60
84.0 305.88 92.88 97.0 74.5 905.20 90.05 85.6 63.0 533.20 84.21 75.2 55.2 422.81 80.87 61.7 43.0 301.32 75.08 50.4 34.5 255.22 71.85 41.2 25.0 223.43 69.08 33.2 10.1 190.91 65.63 24.6 169.35 62.95 18.1 10.1 0.0
192.5092.30 791.3188.78 546.8184.54 408.86 80.16 327.9276.63 284.10 73.97 262.74 72.43 229.8069.66 221.2368.87 204.4767.15 188.2866.99
L. L.Carrick
636
TABLE I1 Solubility in benzene of Ortho-nitro phenol
Meta-nitrophenol
1
Para-nitrophenol
2$ 8,8 8
E-2 0.E $
40.1 34.6 30.1 26.9 20.1 14.1 6.0 0.0
-
-
-
873.57 561.59 365.41 246.49 148.30 103.84 68.11 45.89
69.72 84.88 78.51 72.7C 59.72 50.94 40.51 31.4E
-
-
-
-
- Ortho-nitroDheno1
87.8: 85.0 81.5 74.0 66.0 57.5 48.0 38.0 22.0 6.0
-
852.51 571.09 375.51 120.43 45.94 20.98 9.86 4.99 1.83 .63
-
89.55 104.2 071.96 84.98 96.5 400.02 79.05 91.0 124.54 54.63 85.4 61.71 31.48 78.5 25.18 15.99 17.37 7 3 . 5 9.18 65.5 8.79 4.75 59.4 5.35 1.79 41.3 2.83 .62 32.1 1.67 20.1 .96 8.0 .65
11.54 io. 00 16.05 8.09 '0.11 3.78 8.08 5.08 2.75 1.63 .95 .64
TABLEI11 Solubility in ethyl alcohol of ___.
I
Meta-nitrophenol
Para-nitrophenol
41.3 1038.44 91.22 85.0 1105.25 91.7: 89.81016.75 91.05 37.3 545.48 86.68 77.2 851.47 89.4! 81.1 800.35 88.89 34.3 200.09 66.67 65.5 554.25 84.7- 71.2 545.00 84.50 30.2 69.58 41.03 57.5 422.62 80.8: 62.7 415.55 80.60 23.1 34.31 25.54 50.7 345.27 77.51 52.7 319.52 78.16 17.3 22.08 18.09 45.5 301.54 75.2( 45.2 278.94 73.61 12.4 17.71 15.04 3 0 . 5 221.24 69.0: 38.6 244.89 71.01 6.7 13.00 11.50 23.4 183.77 64.72 26.1 193.78 65.96 0.0 10.16 9.22 11.0 143.55 58.91 18.5 161.13 61.70 - +1 .o 116.91 53.8: 10.0 133.84 57.23 - - 0 . 0 115.75 53.65 *Solubility determined in a sealed tube.
Solubilities and Cooling Curves
637
TABLE IV Solubility in ethyl ether .of Ortho-nitrophenol
Meta-nitrophenol
1
Para-nitro phenol
I 'c
O
,0
d 1"
8; g
H 37.5 33.2 27.8 21.9 15.8 10.5 5.5 1.0
915.85 480.61 249.45 138.79 81.07 59.41 44.81 37.76
-
-
-
-
90.23 82.79 71.38 58.12 44.75 37.27 30.95 27.41
-
83.0 75.0 68.0 59.0 48.5 39.5 23.5 12.2 8.2
+0.2
-
-
065.84 508.89 355.06 269.22 212.75 178.74 143.67 127.24 118.20 105.92
-
91.44 83.5E 78.09 72.92 68.02 63.8s 58.96 55.9s 54.17 51.44 -
W'C
001.50 586.58 380.29 249.39 202.07 167.66 149.29 139.23 133.02 131.18 122.95
90.92 85.51 79.23 71.38 66.89 62.64 59.89 58.20 57.07 58.74 55.06 llZj.56 53.61 109.99 52.38
101.9' 97.1* 87.8" 70.5 59.9 46.8 38.1 31.7 28.7 24.1 18.0 10.1 1.0
The results of Tables I, 11, 111, and IV are depicted graphically in Figs. 1, 2, 3, and 4.
-
/OO C R A M S SOL V E N T 0
120
240
360
400
600
120
840
960
1080
Fig. 1 Solubility of the Mono-nitrophenols in Acetone
Although the literature contains many references concerning the solubility of the mono-nitrophenols in the four solvents used, there seems to be but one quantitative reference. Bogojawlenskil has recorded the solubility of these isomers * Solubility determined in a sealed tube. I
Schrift. Dorpat. Naturforsch-Ges., 15, 216-29 (1907).
,638
L. L.Carrick
in benzene and that of the ortho- and para-nitrophenol in water, On comparing his results for the solvent water with those of Sidgwick,l I find that there exists the same divergence as between the results obtained by me for benzene and those of Bogojawlenski. . From Fig. 2 i t will be seen that benzene is a good extraction solvent to use in extracting ortho-nitrophenol from either or both of its two isomers. Thus at 40 deg. C 100 grams of benzene will dissolve 850 grams of the ortho-nitrophenol while i t will dissolve less than 10 grams of either of
Fig. 2 Solubility of the Mono-nitrophenols in Benzene
Fig. 3 Solubility of the Mono-nitrophenols in Ethyl Alcohol 1
Jour. Chem. SOC.,107, 1202-1213 (1915).
Solubilities and Cooling Curves
639
the other two isomers. Fig. 3 shows that ethyl alcohol should be a good solvent for the purification of the orthonitrophenol by crystallization. The solubilities of the mononitrophenols in acetone and ethyl ether lie too close together for any practical application. None of these solvents are suitable for the separation of the meta- and para- forms.
100 GRAMS SOLVENT
Fig. 4 Solubility of the Mono-nitrophenols in Ethyl Ether
Carnelley and Thompson1 have formulated the following rules to enable one to predict the solubility of organic isomers : (1) For any series of isomeric organic compounds the order of solubility is the same as the order of fusibility, i. e., themdst fusible compound is likewise the most soluble. (2) For any series of isomeric compounds the order of solubility is the same no matter what may be the nature of the solvent. (3) The ration of the solubility of any two isomers in any given solvent is very nearly constant and is therefore independent of the nature of the solvent. The first rule holds for the solubility of these isomers in benzene, but it does not hold for any one of the other three solvents. In fact the order of solubility of the three isomers does not remain the same for different temperatures in the same solvent. Thus with acetone as solvent the order of solubility at 5 deg. C is ortho-, meta- and para-, the parabeing the most soluble and the ortho- the least soluble, while * J o u r Chem. SOC., 53, 782-805
(1883).
640
e
L.L.Carrick
a t 20 deg. C the ortho- is the most soluble and a t 50 deg. C the para- is the least soluble. Thus the order a t the higher temperatures is completely the reverse of the order a t the lower temperatures. The second rule does not hold. We have four solvents and there are three different orders of solubility, except near the point where the ortho- is miscible in all proportions with a small amount of solvent. The third rule is not even an approximation for the solubilities herein recorded, for in three of the four figures the solubility curve for the ortho- crosses the curve for the other two- substances which would preclude any possibility of there being a nearly constant ratio between the solubility of the ortho- and that of either of the other two substances. Thus for the solubility of the isomeric mono-nitrophenols in the four solvents used the generalizations of Carnelley and Thompson are of no value in predicting their solubilities. The writer has attempted to calculate the solubility of these solutes in the different solvents, by the various equations referred to in the introduction, but in no case was there more than approximate agreement. The equations of Findlay and Hildebrand were found by the writer to give the best results. The solubilities calculated by Equation 4 in acetone and the observed values for the ortho-, meta- and para-nitrophenols in actone are given in Table V. In Table VI appears only the calculated values for the ortho- and para-nitrophenols as the meta-nitrophenol curve was used as a curve of reference. The data incorporated in Table V is depicted graphically in Figures 5 , 6 and 7, together with the observed curves for each solute in the other three solvents employed. The graphic representation of the data in Table VI is shown in Figure 8. In applying Equation 3 the writer selected the metacurve as a curve of reference as it bears a closer relation to both the para- and ortho- curves than either the para- or the orthocurve does to the other two isomeric curves. By reference to Figures 1, 2, 3, and 4 it is manifest that the solubility curves of the isomeric mono-nitrophenols in acetone are as uniform throughout their entire length as any other solvent investigated.
Solubililies and Cooling Curves
641
TABLE V Comparison of solubility in acetone as observed and calculated by Equation 4 Ortho-nitrophenol Solubility in mole fractions
c
O
10
d 2".
gaa ,+23
Obs.
36.5 30.3 26.1 20.1 16.1 11.5 6.0 +0.2
.835 .702 .624 .519 .471 ,410 .353 .300
-
-
-
-
Meta-nitrophenol
.866 84.0 .767 74.5 .702 63.0 .618 55.2 ,565 43.0 .508 34.5 .447 25.0 .388 10.1 - to.2
-
Solubility in mole fractions
Solubility in mole fractions
Obs.
Calc.
Obs.
.845 ,791 ,691 .638 .557 .516 .481 .444 ,415
.864 .735 .597 ,514 .400 .333 .267 .191 .140
-
Calc.
-
Para-nitrophenol
-
-
-
97.0 85.6 75.2 61.7 50.4 41.2 33.2 24.6 18.1 10.1
.869 .767 .695 .629 .577 .543 .522 .489 .482 .460 0.0 .437
Calc.
,790
. 666
.565 .449 .365 .305 .258 .215 .185 .155 .117
TABLE VI Comparison of solubility in acetone as observed and calculated by Equation 3 I
I
Ortho-nitro phenol C = -0.00268 Temperaturtnof
Para-nitrophenol C = 0.000472
y in
L
B $5 0 6 0.0 5.0 10.0 16.0 20.0 30.0 40.0 44.0 50.0 60.0 70.0
o$
12.2 12.1 .415 13.3 13.2 .432 14.5 14.2 ,443 - 15.8 .463 16.8 16.6 ,475 19.1 19.1 .507 21.1 22.0 .552
.410 .427 .435 .453 .468 .507 .567
23.1 24.5 24.8 25.2 26.5 31.2
.640 .668
-
-
-
.592 . 608 .725
-
-
0.0 10.1 20.0 30.0 41.2 50.0 60.0 70.0 80.0 90.0
-
-5.2
-
17.6 28.4
-
51.1 63.0 74.8 86.4
-
I
Be
-
-
2.3 11.1 26.4 42.0 54.1 67.0 80.0 92.3
,442 .460 .500 ,550 .597 .654 ,727 .817
-
-
-
-
6 32 e
-
-
.425 ,445 .493 .555 .608 ,678 .767 .893
-
L.L. Cnrrick
642
Hence, Equation 3 when applied to the calculation of the solubility of the mono-nitrophenols in acetone gives as good results as in any of the other solvents used. Even so the solubilities calculated by Equation 3 only approximate the observed values. The agreement given is much closer than it otherwise would be if I had not assumed the point of intersection as one temperature in the calculations. Results that agree fully as well could have been obtained if any point on the curve and the fusion temperature of the pure solute had been used. The relation is only approximate and unless you know the point of intersection of the curves, if there is one, it is still more approximate. 60 40
Fig. 5 Comparison of the Ideal Solubility Curve of o-Nitrophenol, calculated by Equation 4, with its Solubility Curves in Acetone, Benzene, Ethyl Alcohol, and Ethyl Ether
Fig. 6 Comparison of the Ideal Solubility Curve of m-Nitrophenol, calculated by Equation 4, with its Solubility Curves in Acetone, Benzene, Ethyl Alcohol, and Ethyl Ether
x
Solubilities awd Coolivlg Curves
643
Fig. 7 Comparison of the Ideal Solubility Curve of p-Nitrophenol, calculated by Equation 4, with its Solubility Curve in Acetone, Benzene, Ethyl Alcohol, and Ethyl Ether 100
ao 60 40
20
0
.I
A
.s
.6
.7
.a
9
Fig. 8 Comparison of the Observed Solubility in Acetone of 0-, p-Nitrophenol with that calculated by Equation 3
The variation in the calculated solubilities, Table V, would be explained by Hildebrand on the basis that these substances do not form ideal solutions, therefore do not follow Raoult’s law. As pointed out by Hildebrandl when there is a great difference between the internal pressures of the solute and solvent or when the substances are polar, there will be a positive deviation of both components from Raoult’s law. In Table V I 1 is shown the relation between the internal pressures of these substances at 20 deg. C. 1
Jour. Am. Chem. SOC.,41, 1067-80 (1919).
L. L. Carrick
644
TABLE VI1 Internal pressures at 20°C Internal pressures calculated from :
$35 a 2
? >d
Ethyl ether1 Acetone Benzene1 Ethyl alcohol o-Nitrophenol m-Nitrophenol
17.134.6 23.556.3 28.980 .O 21.778.4 40.7214 45.0194@ 70mn p-Nitrophenol 52.4 -
346 246 # 373 240 # 8012 8012
103.8 3.64 73.3 5.85 88.8 6.48 57.6 5.61 .04.538.64 02.04 9.63
60.1 94.0 85.6 129.7 111.2
-
3.20 4.58 4.72 7.09 7.34 7.70
-
7.78
8012 101. 5311.23
The internal pressures have been arranged in ascending order in the last column of Table VII. The other two methods‘ of calculating the internal pressures do not give results that retain the same order. This may be due to incorrect assumptions either in the method of calculation or the data a t hand. None of the internal pressures are the same, but as we shall see from the latter part of this paper the mono-nitrophenols dissolve one in the other according to Raoult’s law, even though their internal pressures are not the same. We should expect, then, from internal pressure measurements that ethyl alcohol would be a good solvent to test Equation 4, but it does not give results that are any more comparable to the observed than does acetone. From Figures 5, 6, and 7 we see that the solubility curves of ortho-nitrophenol in the four solvents used come nearer Jour. Am. Chem. SOC.,41, 1067(1919). Jour. Chim. phys., 14, 3 (1916). Liebig’s Ann., 223, 263 (1884). The density was calculated in the undercooled condition from the relation given by Schiff thus: o-nitrophenol t o = 1,2945- 0.001385(t -45.2) 0.0000295(t -45.2) p-nitrophenol to= 1,2809 -0.00095(t 114) Only an approximate value. *Jour. Am. Chem. SOC.,39, 541-96 (1917). # “Recueil de Constants Physiques,” p. 244.
-
-
Solubilities and Cooling Curves
645
to conforming to the ideal solubility curve than do those of the meta or para- form. This is what we are led to expect for the internal pressure of the ortho- form and those of the solvents are closer together than in the case of these solvents and the meta- and para- forms, but we have no criterion to explain the marked deviation of ortho-nitrophenol in ethyl alcohol. It should according to internal pressure measurements agree closer than any of the other solvents. This might be attributed to dissociation, association or the formation of compounds between the solute and solvent. Even if one of these conditions does prevail it only explains the deviation of the observed and calculated curves, it does not explain why ortho-nitrophenol, which is almost normal in benzene1 and has a greater difference in internal pressure, lies closer t o the ideal curve, or for that matter why any of the other solvents lie between it and the ideal curve. Benzene when employed as a solvent for the isomeric mono-nitrophenols does not comply to Raoult’s law, even though it is not itself associated or dissociated. Auwersl gives the association factor for para- in benzene as 1.38 and that of ortho- as almost normal. This would explain the deviation of the para- form but leave the explanation of the ortho- unsettled. n’one of the methods of calculating solubility proposed to date are applicable to more than a small range of conditions and a small number of substances. In order to know which expression will apply we are compelled to determine experimentally the solubility.
Method of Determining the Melting Points of Binary Mixtures The sample has in each instance been heated to above the melting point and under slow cooling the freezing points have been determined. As the temperature a t which crystallization begins, may vary greatly, the true freezing point, due to undercooling, is not necessarily the temperature a t which Zeit. phys. Chem., 12, 689 (1893).
646
L.L. Cavrick
the first crystals appear. Cooling curves for each different mole fraction of solvent have been determined. I n all the cooling curves a decided arrest a t the maximum temperature of crystallization was noted, which continued for an interval of one to two minutes, followed by a rapid fall in temperature. This temperature was taken as the correct freezing point. If there had been no marked arrest, as there was in a limited number of cases, and the cooling curve had been gradual and regular i t would have been necessary to have taken the intersection of the cooling curve of the liquid and the cooling curve of the solvent, projected, as the correct freezing point. The readings were taken at half-minute intervals for the freezing point of the pure solvent. After the arrest due to the crystallization of the pure solvent the mixture was cooled until i t became rigid. In most instances, see Tables VIII, IX and X, a second arrest was observed. This was the separation of the eutectic mixture. Even though the observation of a second arrest was prevented by the mass becoming too rigid to stir, at a temperature above the eutectic temperature, a liquid phase could be seen between the crystals. The apparatus consisted of a test-tube containing the sample, a looped glass stirrer and a thermometer graduated to 0.1 deg. C. This thermometer as well as all others used was recalibrated. The test-tube was surrounded by a larger tube which was placed in a water bath, heated by the free flame of a bunsen burner. The bath was maintained at about 5 deg. C below the temperature of the cooling mixture. The water bath was agitated mechanically and the mixture stirred> by hand. This was especially necessary in determining the eutectic arrest. The mixture a t this stage usually became so thick a mechanical stirrer failed to produce proper mixing of the components. By this method the melting points of the three binary systems of the mono-nitrophenols were determined. The freezing point temperatures for the mixtures are given to the nearest 0.1 deg. C corrected for the immergent stem of the
Solubilities and Cooling Curves
.
647
thermometer. The composition of the mixture is given in mole fractions. Since the substances are isomers the mole and weight percent are the same and either may be found by multiplying the mole fraction by 100. The calculated values were calculated by Equation 6. In using this equation it is necessary to know the variation of Q with the temperature, Q being the latent heat of fusion. As the literature does not give the specific heats of the mononitrophenols in the solid and liquid state, except for solid o-nitrophenol, and since the specific heats of other organic compounds have been found to remain fairly constant, the writer has assumed that the change in specific heat with change in temperature is small and hence the variation of the latent heat of fusion of the mono-nitrophenols remains nearly constant. The total variation is usually small in comparison to the latent heat of fusion a t the melting point of the pure substance. It may be neglected without much error. Q is thus assumed to remain constant throughout the range of temperature employed. Brunerl gives the molecular heat of fusion of o-nitrophenol as 3725 cal. Substituting this value in Equation 6 and putting To = 317 deg. A., the melting point of pure o-nitrophenol, we have the equation
T = 2.571815-
logiox
. . . . . . . . . . . . . . . . . . . . 10
in which T is the resulting melting point after the addition of para- or meta-nitrophenol, and x is the mole fraction of the ortho- component. This is the equation employed in calculating the freezing points of the mixtures in Tables VI11 and IX, for the left branch, in which o-nitrophenol was considered as the solvent. The observed and calculated values for the binary system o-nitrophenol and para-nitrophenol are given in Table VIII. The results of Table VI11 are plotted in Figure 9. Ber. deutsch. chem. Ges., 27, 2106 (1894).
L. L. Carrick
648
Mole fraction of
83aJ
.800
.770 .750 .730 .667 .625 .588 .555 .500 .444 .375 .333 ,286 .231 ,161 .091 . 000
Solvent
Obs. I Calc. -
. 000
44 40.2 37.5 36.5 34.7
.091 ,167 .200 .230
. .25o .270 .333 .375 .412 ,445 .500 .556 .625
.667 .714 .769 .833
,909 1 .ooo
O C
--
c ta *-
1.ooo .go9 .833
Freezing point
34.7 35.9 44.5 51.4 56.7 61.3 67.5 73.6 80.3 84.1 89.0 94.0 99.7 06.0 14.0
-
39.1 34.5 32.5 30.6 31.8 35.4 45.7 53.1 57.1 -
68.0 75.3 81.6 85.8 90.2 95.2 100.8 106.9 -
1
I
Eutectic observed
-
Solid phase I
First arrest o-nitrophenol, second eutectic
34.7 34.5 34.7 34.5 34.5 34.5 34.2 34.4 34.5 34.4
Eutectic
First p-nitrophenol, second eutectic
-
-
I10 100 BO
P $60
40 20
Fig. 9 Cooling Curve of the Binary Mixture: 0-, p-Nitrophenol, calculated by Equation 6
The eutectic point is a t 34.5 deg. C corresponding (by extrapolation) to 27% of p-nitrophenol. The calculated and observed values agree very well, although from internal pressure measurements we would not expect such good agreement.
Solubilities and Coolilzg Curves
649
The results for the binary system 0-nitrophenol, m-nitrophenol are given in Table IX. In computing the calculated values the same equation was used as for Table VIII, for the left branch of the curve in which ortho- is the solvent, but Equation 12 was used for the right branch in which metawas the solvent. TABLE
Ix
The binary system : o-nitrophenol, m-nitrophenol Mole fractions of
. 000
,
.091 ' 167 .231 .286 .333 .375 .412
1.000 .go9 .833 ' .769
,231 .167
33.5 35.9
30.6 34.6
.091
39.1 44
39.1
. 667 .625
.588
.527 --"
.473 .445 .412 ,375 .334 .286
.625 .666 ,714 .769 .833 ,909 1.000
-
,500
I
-
.000
-
-
1
87.1 81.8 -1i.l 73.3
69.1 65.5 62.3 59.3 53.9 51.1 48.2 44.4 40.0 34.7 28.0
.714
.555
.588
Freezing point "C
93 88.8 83.9 79.2 75.4 72.3 68.6 65.1 62.7 57.1 54.2 50.2 46.8 40.4 35.2 31.6
.445 .e500
. at33
1
-
-
-
31.5 31.5
-
31.6
-
First arrest m-nitrophenol, second eutectic
31.5 31.7 31.5 31.5 31.5
-
31.5 31.5
-
Eutectic First arrest o-nitrophenol, second eutectic
The results of Table I X are plotted in Figure 10. The eutectic is at 31.5 deg. C corresponding (by extrapolation) to 70y0of o-nitrophenol. Here as in the previous figure the observed agrees very well with the calculated values.
L.L.Carrick
650
Fig. 10 Cooling Curve of the Binary Mixture: 0-, mNitrophenol, calculated by Equation 6
In Table X are given the results for the binary mixtures m-nitrophenol, p-nitrophenol. Since the literature does not give the value of Q in the case of p-nitrophenol, the writer has taken a point on the curve of Figure 9 and calculated the heat of fusion. Thus for p-nitrophenol, taking the point where x = 0.445 and T = 334.3 deg. A and substituting in Equation 6, putting To = 387 deg. A, we find Q
=
3950 cal. per mole.
Assuming this value for Q to remain constant and putting To = 387 deg. A in Equation 6, we find
T =
864.3 . . . . . . . . . . . . . . . . .11 2.2331 - loglox
which is the Equation I have employed in calculating the results in Table X for the branch of the curve in which parais the solvent. Since in Table VI11 we consider the p-nitrophenol the solvent as well as the o-nitrophenol, this equation was applied in the calculation of the results for Table VI11 in the right branch of the curve where para- is the solvent. The results of Table X are plotted in Figure 11. The eutectic is a t 61 deg. C corresponding (by extrapolation) to 45.5y0 p-nitrophenol. The calculated and observed values agree well. In Tables IX and X m-nitrophenol is considered as the solvent for one branch of the curve instead of the 0- and p-nitrophenols, respectively. The Q for the m-nitrophenol may be calculated form a point on the curve of Figure 11.
65 1
Solubilities and Cooling Curves nniE
x
The binary system: m-nitrophenol, p-nitrophenol
-Mole
Freezing point "C
fractions of
Obs.
7 1observed
,ale.
1-
1
Solid phase
I
1.000 .go9 .833 .769 .714
.667 ,625 .371
,527 ,500 ,455 ,400 ,334 ,250 .143 ,000
.000
93 87.1 82.6 77.1 74.1 70.4 67.1 62.4
.091 ,167 ,231 .286 .333 .375 ,429
61.6 66.3 70.5 77.8 82.7 91.6 01 . 6 14
.473 .500 ,545 ,600 ,666 . 750 ,857
1.000
87.1 81.8 77.1
-
69.1 65.5 60.7
-
60.3 60.1 60.3 60.6 61.0
First arrest m-nitrophenol, second eutectic
61.8 61 .0 68.1 G0.8 73 2 79 5 85.7 93.5 02.7 -
60.3
60.5 -
First arrest p-nitrophenol
Fig 11 Cooling Curve of the Binary Mixture: m-, pNitrophenol, calculated by Equation 6
Thus taking x = 0.714, T = 347.2 and putting deg. A, we find Q
=
4210 cal. per mole.
Assuming Q to remain constant and putting A in Equation 6, we have
T =
To = 366
921.1 2.517 - loglox
To c . . .12
* \ .
L. L.Carrick
652
This is the equation used in calculating the freezing points recorded in Tables IX and X where m-nitrophenol is considered the solvent. The method of determining the ternary melting points was the same as that employed for the binary systems, The extrapolated binary eutectic was considered as one component and the isomer not included in the binary eutectic as the other component of a binary system. Successive amounts of the third isomer were added to lower the melting point of the eutectic mixture until no further lowering was noted on the addition of another portion of the third isomer. The observed and calculated values for the three possible ternary systems are given in Tables XI, XII, and XIII. The various mole fractions of the ternary system in Table XI are made by adding to the binary eutectic ortho-, metanitrophenol, successive amounts of para-nitrophenol, Similarly, in Table XII, we have the binary eutectic ortho-, para-nitrophenol and meta-nitrophenol as the two components, also, in Table XIII, we have employed the binary eutectic para-, meta-nitrophenol for one component and the third isomer, ortho-nitrophenol, as the other component.
TABLE XI Mole fractions of uo
$$Z
p?3
4 ?.% 0
1.000 .979 .959 .940 .922 .904 .887 .854 .824 .796
Freezing point "C of eutectic
E p g
.r(
$,
. 000 .021 .041 ,060 ,078 .096 .113 .146 .176 .204
Observed
31 .6 28.8 27.9 27.1 26.3 25.7 25.4 24.4 23.0 21.8
Calculated
Solid phase
-
30.7 29.7 28.8 27.9 26.9 26.0 24.3 22.8 21.2
Binary eutectic 0-,m-nitrophenol
Ternary eutectic
653
Solubilities and Cooling Curves
TABLE XI1 The binary system : eutectic 0-, p-nitrophenol, m-nitrophenol Mole fractions of
6 $3
06 3$
3
8.3 8
v
'i
!++$
4%
I I
I
Freezing point "C of eutectic
I
Solid phase Observed
Calculated
--
"6
. 000
1 .000
.091 .167 .200 .230 .250
,909 .833 .so0 ,770 ,750 .
34.7 29.5 26.2 23.5 22.1 21.3
30
E9
22.2 21.1
1
Binaryeutectic 0-, p-nitrophenol Ternary eutectic --
.
Mole fractions of
1
Freezing point "C of eutectic Solid phase Observed
I.000
. 000
.939 ,896 .859 ,824 ,742 ,709 .632 .586 ,514 .472
.061 .lo4 .141 .176 .25s .291 .378 .414 .486 .528 .551
61. 57.2 54.3 51.9 49.3 44.8 41.0 37.5 33.7 28. 1 24.9 21.4
Calculated
57.1 54.6 52.4 50.2 45.3 42.8 37.4 33.9 28.0 24.3 22.1
~
.
.
_
Binary eutectic p-, a-nitrophenol
Ternary eutectic ,449 Calculation of the Ternary Eutectic Points Since at the eutectic temperature the solid that crystallizes out is pure.crystals of solute and solvent, that is, the mixture has a definite percent of pure solute and solvent, it seems logical to conclude that the heat of fusion of the eutectic is composed of two factors, (1) the mole fraction of the heat of fusion of one mole of the pure solute, and ( 2 ) the mole fraction of the heat of fusion of one mole of pure solvent. On this
_
L. L. Carrick
654
theory, let x and y be the components of the eutectic, Qx and Q, be the mole heats of fusion of thepure components, P, and P, the mole fractions of the pure components of Q e the heat of fusion of the eutectic mixture whose mole fractions are P, and P,. Then, the value of Q e is given by the expression Qe
=
Q,P,
+ QJPY . . . . . . . . . . . . . . . . . .13 .
Substituting the proper values in Equation 13, we have Qe = 3870 cal. as the heat of fusion of one mole of the binary eutectic whose mole fractions are 0.7 and 0.3, respectively, of ortho- and meta-nitrophenol. On putting this value, 3870 cal., for Q and T o = 304.6 deg. A, the melting point of the eutectic, in Equation 6, we find 14
which is the equation used to calculate the freezing points of the eutectic o-, m-nitrophenol as one component and the pnitrophenol as the other component of the ternary system ortho-, meta-, para-nitrophenol. These values are recorded in Table XI. Similarly for the binary eutectic in which the eutectic mixture of meta-, para-nitrophenol is taken as one component and ortho-nitrophenol as the other component, we have from Equation 13 that Qe = 4090 cal. as the heat of fusion of one mole of the eutectic whose mole fractions are 0.455 and 0.545 of para- and meta-nitrophenol, respectively. Substituting this value in Equation 6 for Q and putting To = 333.3 deg. A, the melting point of the eutectic, we find
T =
894.8 . . . . . . . . . . . . . . . .15 2.684 - loglox
This equation was used to calculate the values recorded in Table XIII. To calculate the lowering of the melting point of the binary eutectic temperature of o-, p-nitrophenol by the addition of successive amounts of m-nitrophenol, in which 0.73 and 0.27 are the mole fractions of the o- and p-nitrophenol, respectively, we have from Equation 13 that Qe = 3790 cal.
Solubilities atzd Cooliizg Curves
655
as the eutectic heat of fusion per mole, Putting Q = 3790 and To = 307.7 deg. A, the melting point of the pure binary eutectic, in Equation 6, we have 829.2
. T = 2.695 - loglox . . . . . . . . * . . . . . . 16 The values calculated by this equation are given in Table XII. The results of Tables XI, XI1 and XI11 are shown graphically in"Figures 12, 13 and 14, respectively.
Fig. 12 Cooling Curve of the Binary System: Eutectic 0-, mNitrophenol, p-Nitrophenol, calculated by Equation 6
Fig. 13 Cooling Curve of the Binary System: Eutectic 0-, p-Nitrophenol, m-Nitrophenol 60
50 ho
50 10
Fig. 14 Cooling Curve of the Binary System: Eutectic p-, m-Nitrophenol, o-Nitrophenol, calculated by Equation 6
The agreement between the observed and calculated values as seen by Figures 12, 13 and 14 are so close that the assumption we made, in computing the eutectic heat of fusion,
656
L. L. Carrick
is justified. This assumption could only be entertained at the beginning on the ground that these place isomers in binary mixtures form ideal solutions when one dissolves in the other. If there had been any dissociating, associating or forming of compounds between the solute and solvent the calculation of the mole heat of fusion would not have been so simple. This method affords an easy means of calculating the ternary eutectic curve in the case of ideal solutions of organic isomers from a knowledge of the binary eutectic composition and temperature. If we compare the equation of Hildebrand for calculating solubility with that derived by Washburn for the calculation of the freezing points of binary mixtures, we see that they are identical in form. The terms have the same significance, except in the solubility equation N denotes the mole fraction of the solute, while in the freezing point Equation 10, the analogous term, refers to the mole fractionof the component in excess and is called the mole fraction of the solvent. Both equations are based on the assumpton that the components of the solution in one case and the mixture in the other, are neither dissociated nor associated, and that the heat of fusion remains constant. Substances that are sufficiently alike chemically to form ideal solutions will follow these laws, that is to say solubility whenever the solution is ideal, is entirely independent of the nature of the solvent and is merely a function of the temperature. This equation may be used as a criterion to detect ideal solutions. In the case of the solubility of one mono-nitrophenol in the other it is evident that they are neither dissociated or associated as the observed and the calculated cooling curves agree excellently. On comparing the right branch of the cooling curves in Figures 9 and 11 it is seen that the observed and calculated curve of the one holds for the other. The same is true of the left branch of the curves in Figures 9 and 10, and also, theleft branch of the curves in Figure 11 and the right branch of the curves in Figure 10. These examples simply emphasize the fact that if there were no other factors governing solu-
Solubilities and Cooliizg Curves
657
bility, except temperature, when the cooling curve had once been determined, it would apply equally as well in the presence of all other substances. Each of the cooling curves has a point of inflection. The greatest divergence between the observed and calculated curves is a t this point. This may be due to some previous assumption as to the physical constants employed or chemical properties. The observed and calculated eutectic temperatures (extrapolated) agree within 0 deg. C to 4.5 deg. C and the compositions (extrapolated) only disagree by 0.03 of a mole fraction. This is quite gratifying but is what we should expect in the case of place isomers. The eutectic horizontal in no case was traced to the pure components. Although the mixture became so stiff i t could not be stirred, still liquid could be seen in the intercrystalline spaces. Without doubt if the crystallized solvent could be filtered off the eutectic horizontal could be traced to the pure components. The freezing point of the eutectic mixture agrees well with the eutectic arrest in the freezing point of the various mixtures. These cooling curves afford an excellent means of determining the purity of any one of the mono-nitrophenols when the impurity is either one of the other isomers. By simply determining the melting point and then referring to the proper cooling curve one can read off directly the mole fraction of the solvent corresponding to this temperature. In Table XIV is shown the composition of the observed ternary eutectic mixtures as approached from the three binary eutectic mixtures. TABLE XIV Ternary eutectic composition Observed eutecti: temp., C 0-, m-nitrophenol 0-, p-nitrophenol
m-, p-nitrophenol Average
.557 .546 .551 .xi1
.239 .250 .249 .246
.204 ,204 .200 * 203
21.8 21.3 21.4 21.5
Calculated eutectic temp., "C
~-
21.2 21.1 22.1 21.46
L. L. Carrick
658
It seems that the composition is nearly the same no matter from which binary eutectic the ternary is approached. These values should be the same, but error was introduced in extrapolating the binary eutectic composition. The mean of the observed and calculated eutectic temperatures agrees almost perfectly. The variation of the components from their mean is in no case over 0.007 mole and in the case of the para-component is not over 0.003 mole. From the three binary systems a space model illustrated in elevation and in projection on the base has been drawn. See Figure 15. The divisions representing the composition are in mole fractions. There is but one ternary eutectic point. The solid phase ortho-, meta- and paranitrophenol are in equilibrium with the liquid a t a temperature of 21.5 deg. C. PARA IOU%
m ~ n i oo o ~ Fig. 15
0-,
m-, p-Nitrophenol
Summary 1. It is shown that none of the methods proposed are suitable to predict the solubility of the three isomeric mono-nitrophenols in the common organic solvents acetone, benzene, ethyl alcohol, and ethyl ether. 2. The cooling curves for the different binary and ternary systems of the mono-nitrophenols have been determined experimentally and
Solubilities and Cooling Curves
659
found to compare favorably with the calculated form. 3. The law used to calculate the cooling curves for the binary mixtures is shown t o be equally suited for calculating the cooling curves of the ternary mixtures. 4. The mono-nitrophenols in the presence of each other behave as ideal solutions. 5. Benzene is a good solvent to extract ortho-nitrophenol from aqueous solutions of the mono-nitrophenols.
Acknowledgment In conclusion the writer wishes to express his thanks to Prof. 0. W. Brown, under whose direction this work was carried out, for his suggestions and criticism, and also, Mr. C. 0. Henke for his aid in preparing this paper for publication. Laboratory of Physical Chemistry Indiana University Bloomington
