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Art. XLIX.—*The Latent Heats of Fusion of the Elements and Compounds*.

Communicated by Professor Easterfield.

[*Read before the Wellington Philosophical Society, 11th February, 1902*.]

#### Abstract.

Crompton states that A*w*/Tv = K, where A is atomic weight, *w* latent heat of fusion, T melting point on absolute scale, and *v* the valency of the element. Now, the valency of an element is known to vary, and as the results were not very concordant the author, from theoretical grounds, replaced this by the relation A*w*/T ^{3}√A/d where *d* is density and ^{3}√A/d repre-sents the space between the atoms. Just as the atomic heat of the elements is only constant for elements with atomic weights over about 40, so is this relation only true under the same conditions. In the case of the fourteen elements with atomic weights over 40 the value varies between 1 and 1 3, with the exception of the three, gallium, lead, and bismuth. But applying this rule to the compounds, and changing the atomic weight into molecular weight, still more concordant results are obtained. Out of thirteen inorganic compounds, with the exception of two the results vary from 19 to 23, being mostly near the mean 2.1. There is also good agreement among the organic bodies examined, the mean being about 2.4. The author intends to calculate more results, and to present fuller tables to the Society.

Various attempts have been made to arrive at a definite

law connecting the latent heats of fusion with the atomic weights and other physical constants. Berthelot (1895), after proving that in the case of the latent heads of vaporization MW/T′= constant (where M is the molecular weight, W the latent heat of vaporization, and T′ the boiling-point on the absolute scale), supposed a similar law to be true in the case of the latent heats of fusion.

Holland Crompton, in a paper entitled “Latent Heat of Fusion,”^{*} endeavoured to show that the equation A*w*/T*v*=a constant for the elements, A being the atomic weight, *w* the latent heat of fusion, and *v* the valency. The difficulty first encountered in this relation is due to the fact that the valency of an element varies with its mode of combination and with different physical conditions.

Shortly afterwards Deerr^{†} concluded that the relationship A*w*/T is constant only for certain groups of “similar” elements.

In 1897 Crompton published another paper,^{‡} in which he attempted to disprove the hypothesis of electrolytic dissociation. He arrives at the result *dw*/T= constant for mono-molecular liquids, where *d* is the density of the liquid. In the same paper the results are given for the elements, the densities in many cases being taken in the solid state. As shown below, the numbers are exceedingly divergent.

De Forcrand^{§} showed that M(W+*w*)/T′ is approximately constant: M is the molecular weight of the substance in the state of a gas at its boiling-point T′, and W and *w* are the latent heats of vaporization and fusion respectively. But W is generally about ten times as great as *w*; and, as MW/T′=a constant is true (Trouton's law), the value of *w* will make little difference in the result. Further, if the equation M(W+*w*)/T′ be divided by the constant MW/T′, it follows that W/*w*= a constant. Using Traube's numbers for the latent heats of vaporization of the following elements, which gave very satisfactory numbers for Trouton's constant, the values of W/*w* are—Mercury, 26; zinc, 14; cadmium, 15; bromine, 3; iodine, 3.2; bismuth, 17 Since these numbers should be equal if De Forcrand's relationship is a physical law, his generalisation may be dismissed without further consideration.

Now, let it be assumed for the present that A*w*/T = 8.8 (this value is only empirical. but its magnitude will not affect the following argument). On dividing the values of A thus obtained by the real atomic weights, the result is a series

[Footnote] * Journ. Chem. Soc, 1895, 67 315.

[Footnote] † Proc. Chem. Soc, 1895, and Chem. News, 1897.

[Footnote] ‡ Journ. Chem. Soc, 70, 925.

[Footnote] § “Comptes Rendus,” 1901, 132, 878.

of numbers which appear to be periodic functions of the atomic weights:—

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

Cu. | Zn. | Ga | Ge. | As. | Se. | Br. |

3.8 | 3.1 | 1.7 | 2.4 | |||

Ag. | Cd. | In. | Sn. | Sb | Te. | I. |

3.7 | 3.4 | 26 | 2.3 | |||

Au. | Hg | T1. | Pb. | Bi. | ||

3.8 | 3.6 | 3.6 | 4.4 | 1.9 |

It will be noticed that the values tend to increase from top to bottom and from right to left—*e.g*., zinc to mercury and iodine to silver. It would seem, therefore, that some periodic quantity must take the place of the *v* in Crompton's formula to make the relation true for all the elements.

It can be proved that TS/*w* = a constant, where S is the specific heat of the element, by using the relation TC = a constant, C being the coefficient of expansion. But Pictet proves TC ^{3}√A/*d* = K, the expression ^{3}√A/*d* representing the mean distance between the atoms if *d* is the density. Applying this, it follows that—

TS ^{3}√A/*d*/*w* = constant.

But AS = constant (Dulong and Petit);

∴ A*w*/T^{3}√A/d = constant.

In Table II. are given the values thus calculated for the elements with atomic weights above 40 whose latent heats are known. As in the case of Dulong and Petit's law, the relationship does not hold for the elements with low atomic weights. The values of *d* are taken at ordinary temperatures for the substances in the solid state, except in the case of bromine, the specific gravity of which in the solid state is unknown. Most of the constants required have been obtained from the papers of Crompton and Deerr, while the values for silver and copper are due to Heycock and Neville.^{*}

[Footnote] * Trans. Royal Soc., 1897, 189, 25.

[The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

Element. | Aw. |
T. | ^{3}√A/d |
Aw/T^{3}√A/d |

Mercury | 565 | 234 | 2.41 | 1.00 |

Zinc | 1839 | 688 | 212 | 1.28 |

Cadmium | 1531 | 593 | 2.35 | 1.10 |

Bismuth | 2602 | 540 | 2.77 | 1.75 |

Gallium | 1336 | 286 | 228 | 205 |

Palladium | 3873 | 1773 | 209 | 105 |

Gold | 3227 | 1335 | 2 15 | 1.12 |

Tin | 1573 | 503 | 255 | 1.22 |

Lead | 1212 | 600 | 2.61 | 076 |

Thallium^{*} |
1183 | 562 | 262 | 0.82 |

Bromine | 1295 | 266 | 297 (?) | 1 63 (?) |

Iodine | 1485 | 387 | 296 | 1.28 |

Copper | 3140 | 1355 | 1.91 | 122 |

Silver | 2920 | 1230 | 216 | 1.10 |

Platinum | 5295 | 2052 | 210 | 1.23 |

The greatest discrepancies are observed in the cases of bismuth and gallium, the only two metals which are known to expand on freezing.

By using the results of Heycock and Neville for the freezing-points of alloys the value for lead becomes about 1. Their experiments confirm the values of zinc, cadmium, tin, and bismuth, the first three of which give concordant results for the constant. Using this value for lead, and excluding bismuth and gallium, the results vary from 1 to 1.3 for twelve elements with melting-points ranging from—40† to +1,800† C. The mean value is 1.16. In the table below the results are compared with those of Crompton:—

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Element. | A. | B. | C. | D. | E. |
---|---|---|---|---|---|

Mercury | 100 | −14 | 1.21 | −8 | 1.65 |

Zinc | 1.28 | +10 | 1.34 | +3 | 2.65 |

Cadmium | 1 10 | −5 | 129 | −1 | 1 84 |

Palladium | 105 | −10 | 109 | −16 | 2 83 |

Platinum | 1.23 | +4 | 1.29 | −1 | 2.33 |

Tin | 1.22 | +5 | 1.56 | +21 | 186 |

Silver | 1.10 | −5 | 237 | +80 | 2.08 |

Gold | 1 13 | −3 | 080 | −40 | 2.36 |

Copper | 1.22 | +5 | 1.16 | −10 | 3 26 |

Iodine | 128 | +10 | 1.27 | −2 | 1.48 |

Lead | 1.00 | −14 | 097 | −25 | 1 00 |

Thallium | 1 02 | −12 | 2 62 | +1 00 | 1.52 |

[Footnote] *Since the paper was communicated to the Society the latent heat of fusion of thallium has been directly determined by the author. The value thus found (mean of ten observations) gives a value of 1.02 for the final expression. Thallium thus conforms to the general law.

A represnts A*w*/T^{3}√A/d.

B represents precentage difference from mean.

C represents Cropmton's 1895 relation, A*w*/T*v*.

D represents precentage difference from means.

E represents Crompton's 1897 relation, 10×wd/T.

Thus the relationship A*w*/T^{3}√A/d is much the most satis-factory, the mean deviation being ±8 per cent., a deviation of the same order as observed in the law of Dulong and Petit. But it must be borne in mind that the latent heat of fusion is one of the most difficult physical constants to determine, and that if the densities were taken at some corresponding temperatures, such as at the melting-points, the results would perhaps be even closer. There is a large number of wide deviations in Crompton's first relation, while in the case of bromine and iodine it was assumed that the valencies were 3, which assumption is decidedly open to criticism.

In the case of compounds, if A is replaced by M (mole-cular weight) the values for M*w*/T^{3}√M/d are also found to be constant. The following are the data for those substances whose density in the solid state I have been able to find. The values for lead-bromide and silver-chloride are from the results of Weber, who deduced them from electrical experiments. The latent heats of antimony chloride and bromide and the bromides of tin and arsenic have been calculated from their depression constants. The remaining numbers are taken from Crompton's paper.

Compond. | Mw. |
T. | ^{3}√M/d |
Mw/T^{3}√M/d |
10 × dw/T |
---|---|---|---|---|---|

Lead-chloride | 5810 | 758 | 3.64 | 2.10 | 1 60 |

Lead-bromide | 5100 | 763 | 3.80 | 1 76 | 1.23 |

Lead-iodide | 5300 | 648 | 4 17 | 1 98 | 1.10 |

Silver chloride | 4400 | 730 | 307 | 1.96 | 2.35 |

Antimony-chloride | 2920 | 345 | 4 19 | 2 01 | 124 |

Tin-bromide | 2910 | 303 | 5 11 | 1.90 | 0.73 |

Antimony-bromide | 3490 | 369 | 4 42 | 2.15 | 1 10 |

Arsenic-bromide | 2740 | 295 | 4.39 | 2.11 | 1.14 |

Water | 1439 | 273 | 2.70 | 1.96 | 2.93 |

Iodine-chloride | 2297 | 289 | 3.70 | 2.14 | 1.02 |

Potassium-nitrate | 4949 | 606 | 3.65 | 2 24 | 1.69 |

Sodium-nitrate | 5520 | 578 | 3.40 | 2 81 | 2 46 |

With the exception of lead-bromide and sodium-nitrate, the numbers vary from 1.9 to 2.2, with the value 2.07 as mean.

Compond. | Mw. |
T. | ^{3}√M/d |
Mw/T^{3}√M/d |
10 × dw/T |
---|---|---|---|---|---|

Acetic acid | 2661 | 277 | 3 84 | 2 50 | 1.61 |

Phenylacetic acid | 4293 | 348 | 4.80 | 2.56 | 1.00 |

Azibenzene | 5187 | 342 | 5.31 | 2.85 | 0 87 |

Benzoic acid | 4607 | 396 | 4.56 | 2.55 | 1.08 |

Orthonitrophenol | 3725 | 316 | 460 | 256 | 1 10 |

P. dichlorobenzene | 4395 | 325 | 4 90 | 2.76 | 1.15 |

P. dibromobenzene | 4862 | 358 | 5.04 | 2.70 | 1.06 |

Diphenyl | 4391 | 343 | 5.36 | 2.39 | 0.83 |

Naphthalene | 4559 | 353 | 4.81 | 2 67 | 0.99 |

Resorcinol | 4906 | 383 | 4 41 | 2.90 | 1.37 |

Patatoluidine | 4177 | 312 | 4.67 | 2.87 | 1 21 |

Parabromphenol | 3961 | 337 | 342 | 462 | 4.73 |

Phenanthrene | 4450 | 369 | 5.50 | 2.19 | 0 71 |

Thymol | 4130 | 321 | 5.36 | 2 41 | 0.81 |

Nitropaphthalene | 4383 | 329 | 5.06 | 2 64 | 0.97 |

Anethoil | 4070 | 294 | 5 30 | 2.61 | 0 94 |

Nitrobenzene | 2743 | 264 | 4.45 | 2 35 | 1 02 |

Acetophenone | 35.0 | 293 | 4.86 | 2 53 | 1.02 |

Benzophenone^{*} |
4320 | 321 | 5.38 | 2.50 | 0 90 |

Chloracetic acid* | 3850 | 334 | 4.04 | 2 90 | 1.71 |

Acetoxime* | 3022 | 333 | 4 22 | 2 15 | 1.12 |

With the exceptions of acetoxime and phenanthrene, the numbers vary from 2.35 to 2 9. The mean value 2.57 is distinctly greater than the value obtained for the inorganic compounds. Whether this difference is due to the large number of atoms in the compounds of carbon or whether it is one of those peculiar properties of this element remains to be seen. The value of the constant is about twice as great as that obtained for the elements themselves.

I have neglected to compare Crompton's 1895 relation Mw/TEV with the others, because until chemists can agree as to what is really meant by the sum of the valencies (EV) in a compound the results thus obtained will be of no value. In the last column of Table IV. is placed his second relation ship, 10 x *w*d/T. Regarding this, he says that when the result is about unity the liquids are non-associated, and when greater the liquid is proportionately associated It may be remarked that about 25 per cent. of the values are considerably “below” unity.

[Footnote] * Specific gravity in the solid state determined by the author.

By combining the equation M*w*/T^{3}√M/d with the well-known law of Van t'Hoff, D = 02T^{3}/*w*, the result is D = KMMT^{3}√M/d, where D is the molecular depression of the solvent and K a constant. Hence the molecular depression of any body can now be calculated without a knowledge of the latent heat of fusion.

Trouton's law states that—

MW/T^{1} = K^{1}.

But M*w*/T^{3}√M/d = K;

*w*/W = M*w*/T^{3}√M/d/T^{1}

That is, the latent heat of fusion is to the latent heat of vaporization as the freezing-point multiplied by the cube root of the specific volume is to the boiling-point. This, of course, is only true when Trouton's law is true–that is, when the molecular condition of the body is unchanged in passing from the liquid to the gaseous state.