CRYOSCOPIC MEASUREMENTS WITH NITROBENZENE. PART 111. 345

LIV.-Cryoscopic Measurements with Nitrobenzene. Purl I I I . Equilibrium in Nitrobenzene fhlutiom.

By FREDERICK STANLEY BROWN.

So far as the author is aware, no example of chemical equilibrium in solution which obeys the law of mass action has becn studied by the freezing-point method : most work in this direction has been done on strong electrolytes, which do not obey this law, and on associated substances, where this is doubtful. While woyking on asscciated substances, it was considered advisable to te5,t the experimental methods by the study of examples which undoub tedlp do obey the law of mass action : polynitro-aromatic compotlnds form, with aromatic hydrocarbons, molecular compounds which disso- ciate in solution in accordance with the law of inass action, ;as has been shown by solubility measurements (Behrend, 2. phylsilcal. Chem., 1894, 15, 183; Kuriloff, ibid. , 1897, 24, 697).

I n this paper, the dissociation of naphthalene picrate and of naphthalene-trinitrotoluene in nitrobenzene solution is investigated. Previous work (Brown and Bury, J., 1024, 125, 2219) has shown that naphthalene is a normal solute in nitrobenzene, and preliminary experiments have established the fact that trinitrotolume mid, somewhat surprisingly, picric acid are also normal.

E X P E R I M E N T -4 L.

The experimental methods have been fully described in previous papers (Roberts and Bury, J., 1923, 123, 2037 ; Brown and Bury, Zoc. ci t . ) . All work described in this paper has been ca,rried out in moist nitrobenzene in contact with the salt hydrate pair

N *

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316 BROWN : CRYOSCOPIC MEASUREMENTS WITH NITROBENZENE.

Na,SO,,O-10H20. It has been found advantageous to insert a tlhin copper disk as baffle plate in the inner tube, about half an inch above the surface of the liquid, to prevent splashing, which may cause an appreciable error in the calculated concentration of the remaining solution at the end of a long series.

The compounds were prepared by crystallising equimolecular proportions of the pure components from alcohol, followed by slow drying in a vacuum over calcium chloride. Quick drying in a warm atmosphere results in loss of naphthalene. Naphthalene picrate was obtained in golden-yellow needles, m. p. 149.5'. Naphthalene- trinitrotoluene separated as very pale yellow needles, melting per- sistently at 96.4", which is a little lower than the value 97-98' given by Hepp (Annnlen, 1882, 215, 378).

Results. A + B, if n represents the

total mols. of compound added, and a the fraction dissociated, there are at equilibrium (1 - a)n mols. of undissociated compound and a n of each of the two components, the total mols. of solute being (1 + a)n . By substituting this last value in Brown and Bury's equation (4), one obtains the expression

where n, represents mols. of solvent, At, is the observed depression, C and A!, are the factors to compensate for the water in solution, and k has the value 55-81.

111 an equilibrium of the type AB

At = 4 + At, = k[(l + (4% + Qn,l/[(l + a)n + (C + 1)%1,

This leads to

(X = ~ ~ / n [ { A t / ( k - At)) - C ] - 1 . . . - (1) If the concentrations in the mass action equation K = [A][B]/[AB] are again expressed aa mol. fractions, we arrive at a value for the equilibrium constant in measurable quantities :-

The results are shown in the accompanying tables, each of which contains the collected data of three independent series. The first column gives the number of grams of compound per 100 grams of solvent (w), At, is the observed depression, a(obs.) and K arc calculated from equations (1) and (2). The values of a (calc.) have been obtained from equation (2), assuming the mean value of K . Taking into account the possible error of 0*003' in the deter- mination of At,, the agreement between the observed and calcu- lated values of a, and the constancy of K , are satisfactory.

The Free Energy of Formation of Naphthalene Picrate. Naphthalene picrate reaches its solubility limit a t a depression

(Aft') of 2*380°, corresponding to an actual temperature of 2.966".

K = a2n/[l - a][(1 + a ) n + (C + l)n,] . . . (2)

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PART 111. EQ LJILIBRIL31 IX KITBOBENZENE SOLUTIOK. 347

TABLE I. ~ol~zte-Na,~hthalene-trinitrotoluene (Molecnlar weight = 355.2).

w. Atu. a (obs.). a (calc.). K . 1.0547 0.399" 0.9'33 0.993 0.524 2.4362 0.907 0.980 0.9s-k 0.394 2.7309 1,014 0.978 0.982 0.408 4-2 138 1.5'45 0.972 0.07 L 0.485 5.L427 1.863 0.960 0.965 0.392 6.1878 2.227 0.960 0.959 0.467 6.4683 2.319 0.957 0-957 0.455 7-243 1 2.578 0.952 0.950 0.454 7.3 5 94 2.620 0.933 0.952 0.471 8.5054 2.995 0.9'47 0.947 0.468 8.6726 8.057 0.931 0.945 0.525 9.4009 3.290 O.l)-k(j 0.942 0.504

10.645 :*cis1 0.937 0.935 0.506 11.766 4.010 0.927 0.929 0.439

Mean 0.464

TABLE 11. Solute-Naphthalene picrate (RIolecular weight = 357.3).

v

U' . 2.0664 2.1831 3,3670 4.2689 4.6508 5-3871 6.0586 0.3179 6.7241

At,,. 0.766" 0.806 1.225 1.532 1-662 1.908 2.127 2.210 2-33 9

a (obs.). 0.977 0.970 0.956 0,942 0.941 0.929 0.925 0.916 0.908

a (calc.). 0.971 0.969 0.955 0.945 0.940 0.932 0.925 0.923 0-918

Mean

I - . 0.286 0.23 1 0.234 0.217 0.232 0.215 0-228 0.208 0.20 1 0.228

We are thus in a position to calculate its free energy of formation by means of the usual van 't Hoff isotherm :-

A = RTlnN, x hT2/N3 - RTlnK,

where N,, AT2, and AT3 represent initial concentrations of components and campound respectively, expressed in the same units, i. e., rnol. fractions, that were used in determining K , the equilibrium constant. We are concerned with the formation of the solid compound from tlic solid components. The initial concentrations will therefore be those concentrations at which the solids are in equilibrium with the saturated solution, i . e . , their solubilities.

At the solubility limit the picrate is still considerably dissociated, but the solubility, N,, of the undissociated compound can be obtained direct from the freezing-point readings by plotting the logarithm of i t s mol. fraction, (1 - a)u/[(l + a)n + (C + 1)n9], against the observed depression and iaaking a small extrapolation to 2.380". This leads t o a value of ATp = 0.00187.

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348 PRYDE, HIRST, AND HUMPHREYS : CONSTITUTIONAL STUDIES

The limits of solubility of the components are not reached in the range of experiments, but their " ideal " solubilities a t the same temperature (3" approx.) may be calculated in mol. fractions by the method of Hildebrand (" Solubility," American Chemical Society Monograph, 1924, p. 37), a justifiable proceeding in view of the fact that it has been shown that they form ideal solutions. Assuming for picric acid a molecular latent heat of fusion of 4160 cals. (Morti- mer, J. Amer. Chem. Xoc., 1922, 44, 1416), and a melting point of 122", Nz becomes 0.1021. No specific heat data are available, and neglect of these must make the result slightly low. Using the complete thermal data as given by Hildebrand (op. c i t . ) , the calcu- lated value of N , is 0-1857.

By substituting the above values for iV in the van 't Hoff isotherm, and taking K = 0.228 as a mean, the free energy of formation of naphthalene picrate a t 3" is 2083 cals. per mol. This is in close agreement with values given by Bronsted (2. physikal. Chern., 1912, 78, 284) of 2050 cals. at 20.1", from E.M.F. measurements, and of 2150 and 2190 cals. at 0 and 20°, respectively, from solubility data.

I am indebted to the Department of Scientific and Industrial Research for a maintenance grant, and to M i . C. R. Bury for having suggested this work and for advice during its progress.

EDWARD DAVIES CHEMICAL LABORATORIES, UNIVERSITY COLLEGE OF WALES,

ABERYSTWYTH. IReceived. December 15th, 1924.1

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