ROBERTSON: ATOMIC AND MOLECULAR HEATS OF FUSION. 1233 CXXV1.-A tornic and Molecular Heats of Fusion. By P. W. ROBERTSON. No satisfactory relationship has hitherto been found between the latent heat of fusion of substances and their atomic or molecular weights. Crompton (Trans., 1895, 67, 315) supposed the equation p/Tv= a constant to be true for the elements, where p is the atomic latent heat, T the melting point on the absolute scale, and 9 the valency. Apart from the fact that the experimental numbers give but poor agreement with the formula, exception must be taken to an expression which involves such a variable Later, Deem (Proc., 1895, 11, 125, and Chem. News, 1897,76, 234) concluded that p / T is a constant only in the case of certain groups of similar elements. In 1897, Crompton arrived at the result that dw/T= a constant for unimolecular liquids, w being the latent heat and d the specific gravity of the liquid (Trans,, 1897, 71, 925).Concordant values were ob- tained in the case of a number of organic compounds which had been proved unimolecular by other methods. When the results were too high to agree with the above expression, Crompton concluded that the liquids were proportionately associated. The number varied from 0.1 to 0.4 with the elements, the results being calculated in many cases from the specific gravity in the solid state. De Forcrand ( C m p t , red,, 1901, 132, 878) ahowed that the rela- VOL. LXXXI, 4 N constant ” as valency.1234 ROBERTSON: ATOMIC AND MOLECULAR HEATS OF FUSION. tionship M( W -I- w)/P is approximately constant, where iK is the mole- cular weight of the substance in the state of a gas at the boiling point T’, W the latent heat of vaporisation, and w the latent heat of fusion.Owing to the large magnitude of Was compared with w, in general, the results have little dependence on the latent heat of fusion. Further, BW/Z” = constant (Trouton’s law). By combining this with De Forcrand’s formula, it follows that V/w= a constant. Using the values obtained by Traube for the latent heats of vaporisation of the following elements,. which give concordant results for Trouton’s formula, the values of W/w are approximately : Bromine = 3 Iodine = 3 Zinc = 14 Cadmium = 15 Mercury = 25 Bismuth = 16 According to De Forcrand’s formula, these numbers should be identical.When the values of Aw/Tare considered, i t is seen that with few exceptions they have a certain periodic character. It would seem therefore that some periodic quantity must replace the value of the in Crompton’s formula to make it true for all the elements. It can be proved that TS/w =a constant, where X is the specific heat of the element, by using the relation TC=s constant, C being the coefficient of expansion. But Pictet proves that 2°C vy= a constant, the expression vv representing the mean distance between the atoms if Y is the atomic volume. Applying this, it follows that = a constant (Dulodg and Petit) FXG/T/W = a constant .*. Aw/TqT -5: a constant but AX It will be found that this expression agrees more accurately with the results of experiment than any which has hitherto been proposed.In Table I (p. 1235) are given the value8 of this expression for those elements with atomic weights above 40 the latent heats of which are known. Most of the const,ants required have been taken from Cromp- ton’s papers ; the values for copper and silver are due to Heycock and Neville, and the latent heats of lead and thallium have been deter- mined by the author, The value for lead is thus seen to be somewhat below the normal, whilst those of bromine, bismuth, and gallium are too high. It is a remarkable fact that the two latter elements expand on freezing, which occurrence is of comparative rarity, The specific volumes, except in the case of bromine, are those of the elements in the solid state. If the latent heat of bromine has been correctly determined, it wouldROBERTSON: ATOMIC AND MOLECULAR EEATS OF PUSION.1235 Element, ~ ~~ Zinc ............ Cadmium ...... Mercury ...... Palladium.,. ... Platinum ...... Gold.. .......... Tin.. ............. Lead ............ Thallium ...... Iodine ......... Copper ......... Silver.. .......... Bromine . . , , , , Bismuth ...... Gallium.. ....... - AW. 1839 153i 565 3873 5295 3227 1573 1340 1470 1485 3140 2920 1295 2602 1336 - - T. 688 593 234 1773 2052 1335 503 598 562 387 1355 1230 266 540 286 - 7 3 - Y. TABLE I. 2'10 2 *35 2.41 2'02 2'10 2.15 2.55 2 '61 2'57 2-95 1 '93 2.16 2'99 ' 2.77 2-28 - Robertson, pIT3JE 1 '28 1'10 1 '00 1 *08 1 '23 1-11 1 '23 0.87 1 '02 1 '29 1 '20 1'10 (1.63) 1-75 2'05 I'ercen tage deviation rom mean. + 13 - 3 - 11 - 4 $ 9 - 2 + 9 - 23 I- 10 + 14 + 6 - 3 - - - Clromptoii 1895, PI TV.1-31 1 2 9 1'21 1-09 1'29 0'80 1 *56 1'12 2'62 1-27' 1-16 2'37 1 '62" 1'60 1 *56 2rom p ton 1897, 10 x dw]T. 2-65 1 '84 1-65 2-83 2 -33 2 '36 1.86 1-22 1 -52 1.48 3'25 2'30 1.34 2-32 3 *98 * The valency of the halogens is taken as 3. seem probable that this element, like bismuth and gallium, expands on freezing. On comparing these results with those obtained by Crompton, i t is readily seen that the most definite relationship of this type yet obtained is as follows :--For the elements with atomic weights above 40 which do not expand on freexing, the atomic heat of fusion divided by the meltingpoint on, the absolute scale into the cabe Toot of the atomic volume is a constunt. Excluding bromine, the mean percentage deviation is k 10, with 1.13 as the mean value of the constant.It is interesting to note that in Dulong and Petit's law the variation from the mean is about +, 7 per cent. Since Dulong and Petit's law cannot be said to apply to compounds, it would seem improbable that the expression M w / T v v would yield constant results with the molecular heat of fusion. As a matter of fact, however, certain definite relationships are obtained in the case of compounds also. Thus the binary inorganic compounds and certain groups of organic compounds yield numbers in close agreement with one another. But the latent heats of those organic compounds which contain a large number of atoms in the molecule show wide deviations from the law ; for example, the latent heat of stearic acid (56 atoms) is about twice that calculated from the formula.This difference might be attributed (a) to the high molecular weight, (b) to the larger 4 ~ 21236 ROBERTSON: ATOMIC AND MOLECULAR HEATS OF FUSION. number of atoms in the molecule. That it is not due to the high molecular weight is shown by the fact that tribromoaniline and tribromophenol give latent heats in accordanc with the predicted values. The most probable explanation of the irregular results obtained with compounds containing a large number of atoms in the molecule would appear to be that J F does not truly represent the mean distance between the molecules. The possibility thus presents itself that accurate latent heat determinations may serve as a means for the calculation of this constant : TABLE ~I.-~%ovganic Compounds.Compound. Water ....................... Iodine chloride ............ Antimony chloride ...... Antimony bromide ...... Arsenic bromide ......... Tin tetrabromide ......... Lead chloride ............... Lead bromide ............ Lea.d iodide ............... Silver chloride ............ Potassium nitrate,. ....... Sodium nitrate ........... 1439 2297 3020 3490 2740 2910 5810 4520 1 5300 4400 494 9 5516 T. 273 289 346 367 295 303 758 763 648 730 606 579 37. 2.70 3'70 4-19 4 -42 4 -39 5-09 3 '64 3.80 4-17 3-07 3-65 3 -36 1 *96 2'14 2-09 2.15 2.11 1 '89 2.10 1 -56 1-98 1-96 2 *24 2 81 2.93 1'52 1 -03 1-10 * 1'08 * 0-73 * 1'60 * 1-23 * 1-10 * 2-31 * 1-69 * 2-46 * * Densities taken in tke solid state, Good agreement is shown amongst the binary compounds with the single exception of lead bromide.From electrical experiments, Weber has found the latent heat to be somewhat greater than that given in the table, whilst his value for latent heat of lead chloride was in close agreement with that found directly. Taking his value for lead bromide, the value of the expression Mw/F Jvbecomes 1-76, The mean variation for these ten compounds, with molecular weights ranging from 18 to 438, is only +, 5 per cent. from the mean. I t is remarkable that water agrees with the other compounds although it expands on freezing.ROBERTSON: ATOMIC AND MOLECULAR HEATS OF FUSION . 1237 TABLE III .- Organic Compounds . 2344 4906 4127 Compound . 298 4.36 383 4.41 321 5-36 Formic acid ............Acetic acid ................ Chloroacetic acid ....... Benzoic acid ............. Phenylacetic acid ....... Phenylpropionic acid . Lauric acid ................ Steazic acid ............. Naphthalene .............. Phenanthrene ........... Diphenyl ................. Di yhen ylmethane ........ p-Chloroaniline ........... p.Dichlorobenzene ....... p-Dibromobenzene ..... p-Bromophenol .......... Tri bromophenol ........ Tribromoaniline ........ Nitrobenzene .............. m-Dinitro benzene ........ Nitronaphthalene ........ o-Nitrophenol ........... Phenol ..................... Resorcinol .................. Thymol ..................... I- -_ 2640 2661 3890 4607 4293 3720 8985 13520 4559 4450 4391 4661 Acids . 266 277 334 396 350 322 316 337 Hydrocarbons .353 373 343 300 3 -33 3.84 3-91 4-56 4.80 5-14 6 *13 6.93 4-81 5-45 5 '36 5-54 Halogen derivatives . 4742 4395 4862 3961 4301 4608 342 325 358 33 7 366 395 2743 4901 4383 3725 Nitro.deriuatives . 264 363 329 316 Phenols . 4'13 4'90 5-04 4'62 4 -96 5.14 4'45 4-81 5'06 4.60 IlwlT 37 2.98 2.50 2 '98 2.61 2 '56 2.25 4'64 5'79 2 *67 2-19 2 '39 2'80 2-93 2 *76 2 *70 2.55 2-37 2.27 2-34 2'81 2'64 2'56 1'80 2 *90 2-40 10 x dwJT . 2-71 1'61 1-71 1.08 1'00 0 . 87 1-24 1'19 0.99 0*71 0'83 0'90 1'30 1-15 1'06 1-09 0'93 0'86 1'02 1'21 0.97 1-10 0'89 1'37 d-81 _r1238 ROBERTSON: ATONIC AND MOLECULAR BEATS OF FUSION. TABLE 111.-Organic Compounds (continued). 3830 4177 3720 Compound. 324 312 316 Diphen ylamine ........... a-Naphthy lamine ......... p-Toluidine ..............3022 3631 5187 4285 4070 3874 Acetophenone ............ Benzophenone 333 322 342 308 294 350 Acetoxime .................. Urethane .................. Azobenzene ............... Azoxybenzene ............ Anethole.. ................... Thiosinamine ............ 4.72 4 67 4-96 Aromatic Ketones. 4361 3588 i z Jliscellcbneous. 4 -86 5'40 4.22 4.30 5'31 5.42 6 '30 4.56 lFw/ T 3E ___-- 2-51 2-87 2 '38 2.52 2.51 2.15 2'62 2.85 2-57 2-61 2'43 LO x dwl II'. 0-78 1'21 0'95 1 *05 0'90 1-12 1 '34 0.87 0 '88 0'94 1'14 It is at once apparent that the agreement in the case of the organic substances is not as close as that observed amongst the inorganic binary compounds. There are, indeed, several striking exceptions. Thus phenol shows a deviation of more than 25 per cent. from the mean. Of the 36 organic substances mentioned, more than 30 give numbers which do not vary to a greater extent than f ' 7 per cent.from the mean. To test the theoretical considerations enumerated above, the latent heats of several substances of more or less importance to the result have been determined. I n addition, it has been necessary to find the specific gravities of a number of organic compounds in the solid state. In the determination of the latent heat, the simplest apparatus was employed. The substance placed in a test-tube was heated to the required temperature in a hot-air bath, and when the thermometer in the tube and the one in the bath registered the same temperature, the test-tube and its contents were rapidly plunged into a large calorimeter fjtted up with the usual precautions.This operation was repeated at Jiffereat temperatures, Lq the casg of the FpefalsJ the solid piece wa/sROBERTSON : ATOMIC AND MOLECULAR HEATS OF FUSION. 12% caught by the stirrer as it fell from the fractured test-tube. In repeating the experiment, a tube of equal weight was employed. The loss of heat of the calorimeter by radiation was practically nil when the latent heats of the metals mere being found, as the final temperature was reached in so short a time. Owing t o the paor cony ductivity of the organic compounds, however, the time taken to acquire the final temperature was considerably longer, although even in this case the change due to radiation is hardly noticeable. In general, when two observations were made a t the same temperature, one was made with the water in the calorimeter slightly below the temperature of the air and the other a little above.The solid organic compound was heated t o about 20' below its melting point, and several observations made a t about this temperature. It was found inadvisable to work at a higher temperature with the solid, for the presence of impurity is apt to make the specific heat increase rapidly near the melting point. Groups of observations were then made at intervals of 10 and 30Oabove the melting point. TABLE 1V.- Water + Water Value of Calorimeter = 630 grawts. Substance. Thallium.. ...................... ,, ........................ ,) ........................ ,, ........................ ,, ........................ ) ) ........................,, ........................ ,, ........................ ,, ........................ ........................ Lea); ......................... ,, ......................... ), ........................... ,, ......................... ,, .......................... ,) .......................... ,, ........................... Tin ............................. ,, .............................. ,, ............................. ,, ............................. ,) ............................. ,, ............................. ), ............................ ,, ............................. Phenanthrene .............. .............. 9 ) 3 , 9 ) .............. .............. Weight. 36 36 36 36 36 49 49 49 49 49 45 45 45 45 45 45 45 43 43 43 43 43 43 43 43 16 16 16 16 Temperature.230 230 255 315 350 240 260 265 305 330 260 260 290 290 350 350 365 160 160 190 190 240 270 285 290 75 80 85 110 Final tempera tnre. 18.05 17'15 22'05 3 8'1 18.5 17-4 18.6 18'25 19'45 20 '4 18-15 18.05 20.55 18.3 21'1 20 '6 19'6 16'35 19'95 19'1 19.9 22-0 19'95 19.8 22'2 21-45 24.0 24'4 21'45 Bise. 0.75 0.80 0.85 15 1.7 1.1 1'15 192 1 -9 2 '0 0 '9 0.95 1'05 1-05 1.8 1 '8 1-9 0.75 0'75 0'9 0'9 2'1 2.3 2 '35 2-4 0.55 0.5 0 55 1-551240 ROBERTSON: ATOMTC AND MOLECULAR HEATS OF FUSION. TABLE 1V.- Water + Watec Value of Calorimetev = 630 grams (continued). Substance. Phenanthrene . . . . . . . . . ....., Phenylacetic acid . . . . . . . . . . . , Y Y .............. .....*..... I 9 Y 7 ) Y Y Y Y Y Y .... ....... < .... * ...... . .... ....... 1 . . . . . . a * . . . I m-Dinitrobenzene , . . . , . . . . . . . 1 9 S Y Y Y Y Y 9 ) . , . . . . , . . . . . . . . . . . . . . . . .. .......... . . . . . . . . . . . . . . . . . . . . . a , . Thiosinamine . . . . . , , , . . . . . . . . . . 9 ) Y 9 ........... ....... ................ .. ,................. Y9 PY # Y ... ..,............ ........... I.. ... Tribromophenol.. . . . . . . . . . . . . . . . . . . . . . . I . . . . . 9Y Y Y Y Y Y Y 9 ) .... ..... ,..... *.............. ............... ............... Tribromoaniline.. . . . . . . . . . . , . . Y t Y Y I $ Y 9 Y 9 ............... . . . . . . . . . . . , . I . ....... .*...... . . . . . . . . . . . . . . . ....... *. .... * Weight. 16 16 25-3 25.3 25-3 25.3 25.3 25 -3 25.3 20 20 20 20 20 20 20 .a 20'2 20'2 20 *2 20.2 20'2 16 16 16 16 16 16 16 16 16 16 16 16 Temperature, 115 130 60 60 80 80 90 95 115 70 70 100 100 110 120 60 60 98 98 125 125 60 60 100 100 120 120 85 85 130 130 150 150 Final temperature. 19.7 21 -8 22-35 17.95 22.2 21 '8 23.05 20 *2 20-8 20-55 23 -5 20 -1 23.2 83 -1 21'0 20.2 19-55 18.3 23'25 20'95 22-35 19.6 20.6 19.55 21.1 22.2 21 -05 14'75 16% 18.36 18.45 17.95 16'5 Rise.1.7 2'0 0.5 0.55 2-1 2'2 2 '4 2.6 3.15 0 *5 0.5 1 -7 1.75 1.8 1.95 0% 0-65 2-35 2.25 2.75 2.8 0.35 0.35 1-05 1.05 1 '2 1 '3 0.65 0.65 1.5 1.6 1 *8 1-85 Latent Heats. (See Tab& IV.) Thalliuna.-The metal was heated in an atmosphere of coal-gas. Two series of experiments were performed, using different amounts of material. In the first series, the latent heat was found to be 7.0, and in the second, 7.4; mean, 7.2.The melting point was assumed to be 290'. This value for the latent heat is widely different from that (5.12) obtained indirectly by Heycock and Neville (Trans., 1894, 65, 31). Their value, however, is calculated from the atomic falls of only three metals. Further, the material they used contained "at least 98 per cent. of thallium." Small quantities of impurities are known to have a noticeable effect on the latent heat j thus, 3.5 perROBERTSON: ATOMIC AND MOLECULAR HEATS OF FUSION. 1241 cent. of solid matter has been found to depress the latent heat of ice from 80 to 54 (Petterson). The thallium used by the author was shown to be almost pure by the following analyses : 0.2292 gave 0.3710 TlI. 0.2348 ,, 0.4678 Tl,PtCl,.T1= 99.74 per cent. Lead.-From these experiments, the latent heat is found to be 6.45, assuming the melting point to be 330'. The results obtained by previous observers are : (1) Rudberg, 5.858 ; (2) Person, 5-369. The atomic falls obtained by Heycock and Neville in the case of lead vary so much that it is hardly safe to draw conclusions from them as to the latent heat of the metal. Taking the mean of the atomic falls between 4 and 6.4, the 1a.tent heat would seem to be about 6.3. The purity of the metal (Merck) used by the author is shown by the following analysis : T1= 99.81 per cent. 0.3224 gave 0.4728 PbSO,. P b = 100.15 per cent, Tin.-The experimental numbers give the value of the latent heat as 14-05, which is in close agreement with Person's value 11.262.The melting point was taken as 230'. Phenanthrene,-After separation from the anthracene present, which raises its melting point, the substance melted sharply at loo', and the melting point was not altered by recrystallisation. The latent heat was found to be 25. This is a little higher than the number 23, calculated from the molecular depression 120, obtained by Garelli and Ferratini (Gccxxettcc, 1893, 23, i, 442). PhenyZacetic Acid.-The acid used had a melting point of 77' and gave the latent heat as 32. Bruner" (Ber., 1894, 27, 2102) found the value 25.4 with a sample of the acid melting at 74.9'. m-Dinitro6el.lxene.-The latent heat of this compound does not seem to have been previously determined. A sample melting a t 90" gave the latent heat as 29.0. .Thiosinarnine,-This compound is doubly interesting from the fact that it is the only one in the list containing sulphur, and that it contains an ethylene linking. The material used had a melting point of 77" and gave the latent heat as 33.4.TribromophenoZ.-This substance is especially interesting on account of the magnitude of its molecular weight. The material used melted at 93' and was found to have a latent heat of 13.4. TribmoaniZine.-Two different preparations both melted at 122'. The latent heat obtained was 14.4. This is a little higher than that of tribromophenol. * Several of the latent heats obtained by this observer are lower than those of other experimenters, and some give smaller values for the expression Mw/T 37 than would be expected by analogy with similar compounds.1242 ROBERTSON: ATOMIC AND MOLECULAR HEATS OF FUSION.Substance. 1 Melting point. These Iatent heat determinations are summarised in the following table : Latent heat. -- I - Thallium .................................... Lead Tin ........................................ Phenanthrene .............................. Phenylacetio acid ........................ m-Dinitrobenzene ........................ Thiosinamine ............................. Tribromophenol ........................... Tribromoaniline ........................... ......................................... (290") (330) 77 90 77 93 122 (4;;) I I 7 -2 6'45 14.05 25 32 29.0 33.4 13-4 14-4 Specijic Gravities. It is a little remarkable that the specific gravities of comparatively few solid organic compounds are known, The values obtained in the following table were determined by means of the specific gravity bottle, water or petroleum of low boiling point being employed to fill the vacant spacc.The values given are the mean of two closely concordant results : Compound. Diphen ylamine ......................... m-Dinitrobenzene ....................... Benzophenono ............................. a-Naphthylamine ....................... Azoxybeiizene ............................. Thiosinamine ............................. Uretliane .................................. Chloroacetic acid ....................... Acetox in1 e ................................ Tribromophenol ......................... Tribromoeniline .......................... Sp. gr. 20"/20". 1.160 1.821 1.172 1'171 - 1*248 1.219 1 *11 1-53 0 -97 2.55 2.35 Molecular volume of solid. 105.6 111.1 155.3 122.1 158.8 95 -1 80.2 59% 75 -3 121.9 136.2 Slzcmmary. (1) For the elements with atomic weights over 40 which do not ex- pand on freezing, the expression Mw/r ,/p gives numbers the deviation of which from the mean is but slightly greater than that observed in the case of Dulong and Petit's law, (2) For the binary inorganic compounds, the mean percentage devia- tion of the values of Mw/TVTis only k5. (3) In the case of the carbon compounds, great regularityis noticedREVISlON OF THE ATOMIC WEIGIIT OF LANTBANUM. 1-29? among those of similar constitution, Thus for the disubxtituted benzenes the variation is 5 per cent. Compounds with two benzene nuclei give equally satisfactory results. There still remain a number of points to be cleared up in connec- tion with the subject of latent heats of fusion. Careful determinations with pure material of the latent heats of all the members of one or more series of organic compounds should throw much light on the relationship between lsteut heat, molecular weight, and chemical constitution, I n conclusion, the author would acknowledge his indebtedness to Professor Easterfield, who has superiatended the above work and helped him with much practical advice, VICTOI~IA UNIVERSITY COLLEGE, WELLINGTON, NEW ZXALAND.