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MORTIMER
of calcium hydroxide explains the copious generation of hydrogen in the case of calcium chloride solutions and might also explain why i t has been found impossible, for example by Smith and Bennett,ll t o prepare by electrolysis in aqueous solution an amalgam with over 0.09% of calcium. I n the case of zinc chloride, since any zinc hydroxide that might be formed on the surface would dissolve in the excess of hydroxyl ions as sodium zincate or the zincate ion, ZnOz, no catalytic decomposition of the amalgam takes place. The fact that in the presence of zinc chloride the gelatin solutions gave no such trouble, is interesting because of the conclusions of Isgarischew12from experiments on the electrolysis of zinc sulfate in the presence of gelatin that adsorption compounds are formed between the zinc ion and the gelatin and that this adsorption is greatest a t 0.025% concentration of gelatin.
Summary 1. The accuracy of the sodium amalgam electrode for determining sodium-ion concentration in aqueous solution has been investigated. 2. The effect of various concentrations of ammonium, potassium, calcium a n d zinc chlorides and gelatin on the potential of 0.1 n' sodium chloride solution has also been studied. The author desires to thank Professor E. K. Marshall for courtesies extended during this work. BALTIMORE, MARYLAND [CONTRIBUTIOS FROM THE
DEPARTMENT OF CHEMISTRY, UNIVERSITY 1
ILLINOIS WESLEYAN
MELTING POINT, LATENT HEAT OF FUSION AND SOLUBILITY BY F. SPENCER ~IORTIMBR Received January 30, 1922
Introduction Commercial laboratories as well as educational laboratories which are working with organic compounds are constantly confronted with questions having t o do with solubility and choice of solvent for use in purifications. In the great majority of cases the desired information is not available from the published data. I n such cases it is necessary either to determine the solubility experimentally or to resort to some method of calculation. The more successful of the various methods used for calculating solubility generally employ an equation involving Raoult's freezing-point law together with the second law of thermodynamics. Perhaps the simplest and most useful of these expressions is log A'= 5 +I 4.58 T Smith and Bennett, THISJOURNAL, 32, 622 (1910). lrIsgarischew, Kolloidchem. Beihefte, 14, 25 (1921). I1
MELTING POINT, LATENT HEAT O F FCSIOs, ETc.
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In this expression N represents the mole fraction ol the solute. (By solute is meant that component which first crystallizes in the pure state upon cooling the system.) L is the molecular latent heat of fusion, ‘1’ is the absolute temperature of the melting point of the system and 1 is an integration constant. In general i t may be said that these equations have been successful only for the so-called “ideal” mixture. By ideal mixture is meant t.hosc binary systems the components of which may be considered to have the same thermodynamic environment when both are in the liquid state and both, are a t the same temperature. Two of the criteria for such a system are that there shall be neither any heat effect nor any volume change when the two liquid components are mixed. The complete absence of any secondary molecular effects such as association and compound formation is implied in the definition. Therefore, if in any case the heat effect for the solution process of dissolving a solid in a liquid differs from the latent heal: of fusion of the solute a t the temperature in question, then this simple form of the solubility law does not express the true solubility. Hildebrand’ in a series of very able papers, has shown that the degree to which a given binary mixture of non-polar substances departs from the formula for ideal mixtures is closely related to the magnitude of the differences in internal pressures of the components. In the fourth pap” of t‘he series he has described a method for evaluating solubility data and has indicated how the solubility of many substances may be approximately calculated providing the solubility of the given substance has been determined in solvents having a similar internal pressure to that of the soh-ent in question. In evaluating solubility data Hildebrand plots the common logarithm of the mole fraction of solute against the reciprocal of the absolute temperature of the melting point of the system. The experimental solubility points when plotted in this manner should, if there are no secondary mo!,ecular effects, lie on a straight or only slightly curved line over fairly wid.e ranges of temperature. When the solubility curves of a given solute in ;t variety of solvents are plotted in this way there is obtained a series of l.ines, such as those shown below in Figs. 1to 4, which converge to a point a t the melting temperature of the solute where 1V = 1 . 0 (log lv = 0.0). According to the hypothesis put forward by Hildebrand the nearer the internal pressure of the liquefied solute is to that of the solvent in question the nearer will the experimental curve approach to the ideal solubility curve calculated from the latent heat of fusion of the solute. Therefort?, if two solvents should be found to have exactly the same internal pressures, then the molecular solubility of each solute should be thL same 1
Hildebrand, THISJOURSAL, 38, 1-45? I I R I A J ; 39, 2297 (1917); 41, 1067 (1919);
42, 2180 (1920).
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F. SPENCER MORTIRIER
for the two solvents. Hildebrand? has prepared a table of relative internal pressures from which, having a series of solubility curves for any solute, the solubility curve of any such solute may be approximately located for any other solvent the position of which in the table of relative internal pressures is known. 'The obvious disadvantages of this method of calculating solubilities are, first, the internal pressures are known for only a relatively small number of substances. Second, the method has not been applied to polar substances. Third, in any case the solubility must have been determined in a series of selected solvents before the solubility in other solvents can be determined. In the pages which follow we have described a method of calculating solubility which requires but a minimum of physical measurements. It will be shown that the proposed method applies approximately not only to systems of non-polar components but also to those systems containing polar substances, providing that the internal pressures of the components are not widely different and that there are no molecular complexes or solid solutions produced. It should be possible also to foretell which mixtures will give partially miscible liquid systems, and also something of the degree of miscibility of the two liquids.
Development of the Method From Equation 1 it is evident that the slope of the log N os, 1IT curves is related to the latent heat of fusion of the solute in the following manner Slope=S=
ALog N -L a ( l / T ) = 4.58
Equation 2 applies only to those binary mixtures in which the heat eBect of the solution process is equal to the latent heat of fusion of the solute. Now i t is a general rule, providing no secondary molecular effects are produced, that the negative heat effect accompanying the solution process is greater than the latent heat of fusion. I n all such cases the slope of the logarithmic curves must be greater than that of the ideal curve. This is well shown in each of the Figs. 1 to 4 below. The ideal slope for any solute is that slope which would be obtained with a solvent which gives a thermodynamically ideal mixture. I t is evident from Equation 2 that the value of the ideal slope may be calculated by dividing the latent heat of fusion of the solute (in small calories per mole) by the constant 4.55. If now the experimental values of the slopes of the log A; vs. 1 T curves for a given solute in a variety of solvents, be divided by the value of the ideal slope for that solute there is obtained a series of factors the magnitude of which is a measure of the non-ideality of the mixture.
* Hildebrand,
THISJOURNAL, 38, 1452 (1916); 41, 1087 (1019).
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