SOLUBILITY RELATIONS OF ISOMERIC ORGAXIC COMPOUNDS. I . IKTRODUCTIOK BY JOHN JOHNSTON
The starting point of the investigations, begun about five years ago, to be described in a series of papers under the general title as above, was the belief that one of the outstanding problems of chemistry is the mechanism of organic reactions, and that any reliable observations. which might aid in reconnoitering this field would be useful. In particular, we desired to learn more as to the factors which determine the position in the benzene ring of a second substituent group relative to that of the first substituent-the factors, namely, which favor the formation of the ortho, meta and para isomers; t,his case being chosen partly by reason of its large importance, partly because the substances are definite and easily available in a substantially pure state. Now if one will study the effect, say of temperature or concentration, upon the relative yield of the three isomers, one must have a means of determining how much of each is present in the reaction mixture; but the compounds, being isomeric, cannot usually be determined by a chemical method', and SO recourse must be had to some other mode of analysis. Of these, the most promising appeared to be that based upon measurements of mutual solubility, that is upon the freezing or equilibrium diagram of the three isomeric substances. This method is, of course, not new, it has been used by Holleman and even as a control in the industry; but the published results on this type of system are in effect little more than random scratches upon the surface of the field. Such determinations of mutual solubility have, of course, been made in large number, though not in any very systematic way2. For instance, they have been made a t only one or two temperatures, instead of covering adequately the range of the solubility curve; or the substances used have been those readily available, the result being that the observations commonly do not extend to all three isomers. Moreover, many of the data are less reliable than one would wish to have them, because the experiments were clearly not carried out, or interpreted, with sufficient precision, or because insufficient attention was paid to the purity of the samples of material. Nevertheless the data available, though they are in these respects unsatisfactory and incomplete, indicate that more systematic work should yield useful generalizations with respect to the solubility, and related properties, of organic compounds. We. were therefore encouraged to hope that, apart from the initial object of securing a method of analyzing mixtures of certain isomers, we might unA recent example of the use of a chemical method, applicable to certain types of case, may be found in the paper of Francis and Hill: J. Am. Chem. SOC.,46, 2498 (1924). The long Reries of papers by Kremann and collaborators, in the Monatshefte during the last fifteen years, have been concerned more with systems (e. g. of phenols and amines) 1n which compounds appear, A similar remark applies to the papers of Kendall and hls collaborators: J. Am. Chem. SOC.,43,691 (1921) et seq.
SOLUBILITIES O F ISOMERIC ORGANIC COMPOUNDS
883
cover some regularities of behavior which could be correlated with the chemical constitution of the substances. Indeed, organic systems offer a very promising field-as compared with inorganic systems-for learning something of the factors which determine solubility; for in them one can readily secure an almost continuous gradation of both solute and solvent by successive substitution of similar groups, a fine gradation of constitution and structure which is not possible in the characteristic inorganic systems. This remark applies t o many properties other than solubility, heat of fusion or specific heat; and there is a wide field, the systematic cultivation of which-though, a t the moment, somewhat laborious-is certain to yield information which will advance the whole science of chemistry. Some slight progress in this direction is being made. For instance in many systems of the ortho, meta and para isomers of a given composition, the solubility of any one component in mixture with either of the others, or with both, is in accordance with the law of the ideal solution, and is therefore at any point readily calculable from a small number of constants pertaining to the pure components. Indeed Narbutt’ showed that the mutual solutjons of ortho, meta, para nitrobromobenzene are nearly ideal; and Holleman, Hartogs and van der Linden2 observed the coincidence of melting curves of binary systems of the three nitroanilines and state that these are therefore “so-called ideal” melting curves. In order to learn in how far this is true for other similar systems, the available data were plotted, with the result that in most cases the solutions seemed to be substantially ideal. As to the proportion of this type of system to which this conclusion is applicable, we must be uncertain until the work has been extended to 5 far larger number of substances, and in particular to those which may be regarded as extreme examples; but the present evidence indicates that the assumption of ideal solubility would in any case of this kind be a safe first approximation. Another provisional conclusion is that pairs of ortho compounds (or of meta, or para) form solid solutions; whereas, as we have just seen, an ortho compound separates in the pure state, and forms no solid solution with the corresponding (i. e. containing the same two substituent groups) meta or para isomers. This is of practical importance in connection with the purification3 of such substances; and it indicates that the influence of the relative position of two substituents upon the crystal structure of the compound outweighs that of the chemical nature of the two. Nevertheless it is to be expected that if the two substituent groups are in one compound very different (e. g. much larger) from those in the other, incomplete solution would be the result; and it will be interesting to learn just how different the pairs of groups would have to be in order to cause the two crystalline compounds to be incompatible. The measurement of a solubility is in essence the determination of the concentration of the solution in equilibrium with the crystals of the substance ~
~~
Narbutt: Z. physik. Chem., 53, 697 (1905). Hollemann, Hartogs and von der Linden: Ber. 44, 704 (191I ) . In some cases we have found that a long series of fractional crystallizations was necessafy to ensure adequate purity of the material.
884
JOHN JOHNSTON
at a definite temperature. This is done in two main ways. The more usual way is to leave the excess of the crystals in contact with solvent (strictly speaking, with solution) a t a definite temperature until saturation has been attained; and then to determine by some appropriate method, the proportion of solute to solvent in the solution. This method is used in ascertaining the solubility curve of a salt or the freezing temperature of an aqueous solution, the latter being a point on the solubility curve of ice in the solution. I n cases where the method of analysis is cumbrous or inexact (as it is in many organic systems) the other way is followed; one ascertains the temperature a t which the first crystal of the solid separates from a slowly cooled solution of known composition, or sometimes, that a t which the last crystal disappears when the system is heated slowly. This may be done by direct visual observation; more commonly, however, it is deduced from the appearance of a break on the cooling (or heating) curve which brings out the mode of temperature change of the system under definite conditions of environment. The uncertainty of the method is not in the temperature measurement itself, but in the difficulty of ensuring that this temperature really corresponds to equilibrium in the solution of the gross composition taken; for if some of the solid has already crystallized at the temperature noted, the concentration of the solution will be correspondingly different. By the use of proper methods of experimentation and interpretation, these difficulties can however be surmounted, and results of adequate accuracy secured. I n the course of the earlier determinations of solubility in the binary systems of the nitroanilines and nitrochlorobenzenes, it was observed that the results were more closely in accordance with the law of the ideal solution, the more carefully the experiment had been interpreted. This led us, on the one hand, to consider anew the theoretical form of the cooling curve, on the basis of Newton’s law of cooling; on the other hand, to undertake the direct measurement of those properties of a substance (namely, its heat of melting, and secondarily, its specific heat as solid and as liquid) which determine the course of its solubility curve when the sclution is ideal. For it was found that the heat of melting, as derived from the slope of the solubility curve, in some cases agreed well with the calorimetric value recorded in the literature, whereas in other cases it did not; these discrepancies disappear when these heats were redetermined and therefore are due to inaccuracies in the published calorimetric data. The results of the two distinct lines of experiment are now in very satisfactory agreement; for instance, the heat of fusion (which is of the order of 3 700-6600 calories per mol) as derived from the initial slope of the solubility curve, differs from that directly determined in this laboratory, by only about 80 caloiies, which is about the error involved in reading this slopefroma graph on a fairly large scale. This concordancemay be stated in another way, namely, that the divergence between the solubility curve as calculated from the calorimetric data and that observed, amounts only to a few tenths of a degree. I t may be mentioned that the heat of fusion of many of these substances, as given in the literature, may be too small by as much as 1000 calories; this error is
SOLUBILITIES O F ISOMERIC ORGANIC COMPOUNDS
885
probably due to lack of purity of the material’, and to neglect ot the fact that the heat diffusivity is low and hence, unless small amounts only are used, all of the heat in the sample will not flow into the calorimeter in the ordinary period of such experiment. In the ideal solution there is no change in heat content or in volume when the components mix to form a solution; in other words, the components do not affect one another appreciably and the properties of the solution are linear functions of its composition. For instance, the partial vapor pressure, or the activity, of each component is, in accordance with Raoult’s law, proportional to its mol fraction; if this relation is combined with what is often referred to as the van’t Hoff reaction isochore, we get the equation d l n N A - AHA d T R T2 where In NA is the natural iogarithm of NA,the mol fraction in the solution of A the substance crystallizing, AHA is its molal heat of melting (hence, in the ideal case, its heat of solution also) and R is the constant of the ideal gas law. If we integrate this equation between T and TA,the melting temperature (on the absolute scale) of pure A, on the kasis that the change of AH,i with T is inappreciable, we get AHA AHA = -RT RTA (11) since NA is unity (and hence In NA is zero) at the melting temperature T A . When AH is expressed in calories, R = 1.9885; so we may write, converting to ordinary logarithms, l o g N ~ = - - - +AHA --- I AHA (IIIa) 4.579 T 4.579 T.4 This is of the form log r\’ = a / T b, or y = ax b, and therefore, under the conditions specified, the graph of log N against r/T is a straight line2, the slope of which is proportional to the heat of melting of the crystals in equilibrium with the solution. A special case of equation IIIa, applicable however only to dilute solution, is the familiar formula used in calculating molecular weight in solution from measurements of the change in freezing or boiling temperature of the solvent. Before proceeding, I wish to emphasize the advantage of expressing concentration of a solution in appropriate units-in terms of chemical units instead of arbitrary units such as grams or liters. The most convenient chemical unit of quantity of substance is the mol, defined most simply as the number of grams in the simplest molecular weight of the substance. For the present purpose the best mode of expressing concentration is by means of the
+-
+
+
The form of the heat-content curve of a solid a t temperatures near its melting-point is a criterion of the purity of the sample in some cases, e.g. when by reason of the admixture a partial melting sets in. Obviously the graph of T log N against T is also linear; the slope of this line is proportional to the entropy increase accompanying melting of the solute. This form is for certain purposes more convenient.
886
JOHN JOHNSTON
mol fraction N (or the molal percentage C = IOON);thus if we have nAmols of substance A and ng of substance B, the respective mol fractions are
The advantage of using this unit of concentration is especially marked ip the case of organic substances. For example, the curves representing in these terms the solubility a t various temperatures of a single solute in a series of solvents, form a sheaf converging to the melting temperature of the solute; whereas in terms of the usual arbitrary units, they may be scattered irregularly over the diagram. This regularity has the practical advantage that one ca8n deduce the solubility, with sufficient accuracy for most practical purposes, at any temperature if it has been measured a t a single temperature; and moreover, if the curves for a series of representative solvents are known, one can get a good approximation to the solubility in another solvent without having to make any new measurements. In deriving equation IIIa we assumed that the heat of fusion of A does not vary with temperature, which is equivalent to the assumption that the specific heat of liquid and solid A (C, and C, respectively) are identical. Taking this difference into account, we write AHA = AH’A CTT PT2 (where (Y and p are empirical constants derived from the calorimetric data), and obtain, in place of equation IIIa,
+
+
The second and third terms introduce corrections which are comparatively small and in many instances negligible; correspondingly the graph of log N against I / T is a slightly curved line instead of being rectilinear, as it would be if equation IIIa were strictly valid1. It has in fact been found that, in the specific type of system under discussion, the actual solubility curve follows equation 111 more closely, the more accurately the measurements have been made. Now the quantities which enter into this equation, for the solubility of A, refer only to the solute A and not a t all to the solvent; consequently the solubility curve of A is identical, in so far as it extends, for all cases in which the other component or components form an ideal solution with liquid A. For component B there is a precisely similar equation and line, which starts from its melting temperature T B a t a slope which depends upon its characteristic heat of melting AHB; and this 1 Equation I11 or IIIa was, apparently, first given by LeChatelier (Conipt. rend., 100, 50 (1885); it was discussed by Roozeboom (“Die Heterogenen Gleichgewichte” I1 - I , pp. 270-283 (1904)) who also gives prior literature references. It was used by Schriider (Z. physik. Chem. 11, 449 (1893) ) and by Narbutt (Ibid, 53, 697 (1905) ) on organic systems; by Mamotto (Nuovo Cimento, 13, 80 (1907); 15, 401, (1908) ) on metal systems. It has been discussed by van Laar in 1903 in a series of papers in Verslag Akad. Amsterdam, summarized and extended in Z. physik. Chem., 63,216 (1908); 64,2j7 (1908). Its usefulness has rerently been emphasized by the work of Washburn and Read (Proc. Nat. Acad. 1, 191 (1915)~Hildebrand et al. (in a peries of papers in J. Am. Chem. SOC.,from 1916 on, and in his recent monograph on Solubility), Kendall (J.Am. Chem. SOP.43,691 (1921) et seq.,) and others.
SOLUBILITIES OF ISOMERIC ORGANIC COMPOUNDS
887
line, likewise, is, under the specified conditions, independent of what A may be. With different pairs, the pairs of curves end at different temperatures, this end-point being the characteristic eutectic temperature below which the liquid phase is unstable. For a binary system this end-point is clearly at that value of T a t which NA NB = I , or, on the plot of equation 111, that a t which the sum of the antilogarithms of log NA and log NB is unity; and this value of T is readily found by trial. Consequently one can calculate both eutectic composition and temperature from the solubility curves of A and B;
+
1
100 N
LOG FIG.
I.
Plot of log I O O Nagainst ~ o o o / Tfor an ideal ternary system, showing the three binary, and the ternary, eutectic temperatures.
or, conversely, use the observed eutectic temperature-which is readily measured with accuracy-as a check upon the course of the two solubility curves and the assumption of ideality. If the ortho-compound (say) forms ideal solutions with both the meta and para separately, and the binary solutions of meta and para are likewise ideal, the behavior of the ternary solutions must also be ideal. In other words, the solubility curve of ortho in mixtures of para and meta together is the same as in either separately, and is therefore calculable as before. In the ternary system the eutectic corresponds to the condition NA -I- NB Nc = I , and is therefore readily derived from the three solubility curves. This is illustrated by Fig. I which represents a plot of log C (C = IOON)against ~ o o o / Tfor an ideal ternary qystem; each of the three lines is the solubility curve of one component,, starting at its melting temperature and ending at the ternary eutectic temperature, the several eutectic temperatures being derived as outlined above. In this ideal type of case, therefore, the complete ternary solubility diagram-as required for analysis of unknown mixtures of the three components -may be constructed from a small number of observations. Indeed in
+
888
JOHN JOHNSTON
principle one needs but six observations, three of which are the melting temperatures of the pure components; the other three are the heats of melting, or appropriate solubility measurements which in general are simpler to carry out. In practice one would usually determine the solubility of each component at more than one point, in part for the sake of accuracy, in part because one would wish to be assured that the system does in fact yield ideal solutions, With the aid of the completed equilibrium diagram, one can readily analyze any mixture of the three pure 0, m, p components. One observes the temperature of the cooling mixture a t which the first crystals separate, and then that at which the second component begins to appear; if this is doubtful or impracticable, one adds a known proportion of one component and observes anew the temperature at which the first crystals separate. By proceeding in this way, one can determine the composition of such mixtures with an accuracy of I or 2YG. If the material is always contaminated with a small proportion of water or a solvent (as it may well be if derived directly from a manufacturing operation), it suffices to make the original observations on material similarly contaminated, and to construct a modified diagram which can then be used directly, as outlined above. In view of the result that the corresponding ortho, meta and para isomers form ideal solutions with one another, it was of interest to determine the solubility curve of each in a series of typical solvents, in order to ascertain if there are any substantial differences, as between the three isomers, in the form of solubility curve in a given solvent. Such determinations, which appear not to have been made in any systematic way hitherto', enable one to judge as to the advantage of a given solvent for the purification by recrystallization of one isomer initially contaminated with one, or both, of the others. Moreover, one might hope, in view of the regularities previouqly adverted to, that the behavior of one system could, within limits, be applied,-transferred so as to speak,-to a number of the related systems, at least to the extent of acquainting one with the general course of the solubility curve, and in this way saving work. Starting from the point that we wished to be able to analyze certain mixtures of isomers, and proposing to use for this purpose the mutual solubility, we have been led to investigate a number of things which a t first sight have little bearing upon the original question; and these, in turn, have led to others not initially contemplated. For this reason largely, the evidence in support of the general statements made above will be presented in a series of separate papers, under one general title, dealing with the several lines of investigation. Yale l!niversity New Haven, Conn. 1Except for the work of Sedgwick and his collaborators who have measured the solubility, through a range of temperatures, of several sets of 0,m, p isomers in water and benzene, and in some cases in n-heptane, ethyl and butyl alcohol. (J. Chem. SOC. 119, 979, 1001, 1013 (1921); 121, 1844, 1853, 2256, 2263, 2586 (1922); 123, 2813, 2819 (1923), 125, 522 (1924).
