112 LE BAS: RELATION BETWEEN VOLUMES OF ATOMS OF XI.-A Relation betzoeerL the Volumes of the Atoms o f certain Organic Compounds at the Melting Poirit and their Valencies. Intequretatioiz by Means o f the Ba rl o w - Pop e T h e 03- y. By GERVAISE LE BAS, B.Sc. IN October, 1905, the author discovered that the volumes of the atoms in certain members of the paraffin hydrocarbon series and their derivatives taken near their melting points and also in many solid compounds, both organic and inorganic, mere very nearly integral multiples of the volume of combined hydrogen. In many cases these integral multiples coincide with the fundamental valencies of the atoms in question. This result, independently of its intrinsically interesting character, is a t the present time especially significant in consequence of the ideas put forth by Barlow and Pope in their recent important paper on the correlation of molecular structure and crystal- line form (Trans., 1906,99,1675).By regarding crystalline structures as closely-packed assemblages built up from the spheres of influence of the constituent elements, these authors have arrived a t the conclusion that, the fundamental valency of an element is proportional within narrow limits to the volunies of the atomic spheres of influence, It follows from this that a particular inolecular complex may beCERTAIN ORGANIC COMPOUNDS AT THE MELTING POlNT. 113 regarded as one in which the component atoms appropriate to them- selves portions of space proportional in volume to their valency, but, as, indeed, Earlow and Pope point out, the absolute volume, as the atomic sphere of influence of an element, is liable to differ from compound t o compound.It would seem, however, to follow, if no other determining factors than those promised by Barlow and Pope are operative, that the indicated relationship butween the valency and the volume of the atomic sphere of influence should be traceable throughout a whole series of homologous substances such as the normal paraffins. No obvious reason exists why the atomic sphere of influence of carbon or hydrogen should change appreciably in pasing from one member to another of such a series, especially if the terms chosen lie SO high in the series as to have nearly the same percentage composition. This aspect of the new theory finds support from an examination of molecular volumes, taken under the specified conditions. Tho data are derived from papers published by Krdff t on the normal paraEns (Ber., 1882, 15, 1716) and on the alcohols (Bey., 1883, 16, 1714).The values quoted in the following table are for liquid hydro- carbons at the melting point ; these temperatures are, as shown in the fifth column of the table, approximately equal fractions of the boiling points on the absolute scale, and hence may be considered ~ L S approximately equal fractions of the critical temperatures. The molecular volumes may thus be regarded as determined under corresponding conditions, that is, under conditions such that the repulsive forces in all cases have just overcome the attractive forces which hold them in their places in the crystalline structure.Xcctuvated Normal Hydrocarbons, CnKZql. + 2. Mol. Vol. Diff. Ty x S= Calc. FV. Undecane, C1,H, ......... 68 Dodecane, C,,H,6 ......... 74 Tetradecane, C,4H30 ...... 86 Pentadecane, C16H32 ...... 92 Octadecane, C,,H,, ...... 110 Tridecanc, C,,H,, ......... 80 Hexadecane, C,&[,, ...... 98 Heptadecane, Cl'lH36, ... 104 Nonadecane, C1,H4, ...... 116 Eicosane, C,,H,,. ........... 122 Heneicosane, CZiH44 ...... 128 Docosane, C,H,, ........ 134 Tricosane, C23H48 ......... 140 Tetracosane, C24H50 ...... 146 Heytacosane, C,H, ...... 164 Hentriacontane, C31Hs4.. . 188 Dotriacontane, C,,H,, , . , 194 Pentatriacontane, C,,H7,. 212 Mean values ........ VOL. XCI. = v. 201 '4 219.9 237'3 255.4 273'2 291'2 309-0 326.9 344'7 362.5 380.3 398.3 416'2 434.1 487'4 558.4 576'2 629.5 ....for CH,, 18-5 17.4 18.1 17.8 18.0 17.8 17.9 17.8 17.8 17'8 18'0 17.9 17.9 53 *3 71 *O 17'8 53.3 17.83 M. p,/B. p. 0.527 0.536 0'524 0530 0.520 0.519 0'513 0.512 0'506 Y/ w. 2'962 2.971 2.966 2,970 2.970 2.971 2'971 2.972 2.971 2.971 2-971 2.972 2.971 2.973 2.972 2.970 2.970 2'969 2.970 mol. vol. 201 -96 219.78 237 -60 255.42 273.24 291.06 308.88 326-70 344.52 362'34 380.18 398-00 415-80 433.62 487.08 558.36 576.18 629.64 II14 RELhTlON BETWEEN VOLUMES OF A4rI'OMS -4ND THEIll V>iLEX;CIES I n the table, TV is the valency number and the quotient W is the molecular volume divided by the valency number, thus representing the volume appropriated by one unit of valency in the respective hydro- carbon.The mean value of the latter, namely, S=2.970, is con- veniently described as the unit stere. It is apparent at once, from the constancy of the individual values OF 8, that the concept above referred to, and which is of fundamental importance in Barlom and Pope's theory, can be extended to the statement that in the series of normal paraffins regarded under corresponding conditions specified the spheres of atomic influence of carbon and hydrogen preserve almost the same relative magnitudes throughout the series. The extent to which this conclusion is true is measured by the closeness of the correspondence between the obaer ved molecular volumes (column 3) and the values, calculated as the products of the valency volume and the mean value of the unit stere, in the last column.The table shows that the mean increment of the molecular volume for the homologous increment CH, is 17.S3, a value which, when divided by the valency volume W=6, for methylene gives 2,972 for the value of the unit stere, a number almost identical with the mean value of S obtained from column 6. A more direct way of calculating the value of the unit or univalent stere for hydrogen is by means of equations of the following kind : 2X= 2P of C,,H2, - Vof C,,H,, ~ 5 . 7 . 25' = (V of C,,H,, + Vof C16H3J - V of C,,H,, = 6. S s 2.85. X = 3. The average value of X obtained in this way confirms that previously The volume of carbon is also found directly as follows : The conclusion is thus deduced that the molecular volume Y(at the melting point) of a normal solid paraffin of the molecular composition C1LH211+2 is given by the formula V = ( 6 1 ~ + 2 ) s = 6nX + 2X, where X= 2.970. Considerations similar to the above may be applied to homologous series of derivatives of the normal paraffins, as, for instance, the primary alcohols. The following table gives the observed molecular volumes of several of these compounds examined by Krafft (Zoc.cit.). found, namely, 2.970. Vof C = 17.83 - 5.94 = 11.89 = 4 x 2,972 = 427.OP'l'ICAL IYFLUENCE OF CONTIGUITY O F UNSATURATED GHOU 1's. 115 Nornzal AZcohoZs, C,,H,,,*OH. ?V. v. Yf w. 1 V X s. Noiiylcarhinol, C,,H2;0H ............... 64 189.3 2.943 190.08 Undecglcarbinol, C,,H,,'OH ............ 76 223.9 2.946 225.72 Tridecylcarl,iiiol, C,,H,,'OH ............ 88 259.8 2.953 261 '36 Pzntadecylcarbinol, C,,H,'OH ......... 100 296.0 2.960 297.00 Hcptadecylcarbinol, C,,H,:.'OH ......... 112 332.3 2970 332.64 As against the slight divergence of T/TVfrom the normal on the part of some of these alcohols, it has been found by a study of the ketones and fatty acids, in which latter series the hydroxyl group appears, that a satisfactory constancy is maintained. Thus, under the stated conditions, the molecular volumes of the primary alcohols C,,H,,+lOH derived from the normal paraffins are expressed by the equation V = (6% + 4 ) s = 6988 + 48. In a subsequent paper, the method of interpretation here described mill be applied to other homologous series and also to unsaturated substances. It is also the intention of the author to show that the regularities observed by Schroder in his study of solid compounds have underlying them relations similar to those given in this paper. So far as the carbon compounds are concerned,it may be stated that Schroder's value for the stere is 5.95, or double the value which is here assigned to S, the unit stere. MUXICIPAL SCHOOL OF TECHNOLOGY, MAKCIIESTER.