TRANSACTIONS OF SECTION B. 4.93 
vint of any non-associating organic compound which contains at least one 
—CH,—C group, and that of its next higher homologue (at any rate up to tem- 
peratures of about 300° C.), may be calculated with an error rarely exceeding 1°5 
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ToousyT 
seems also to be applicable to any ester which contains at least five atoms of 
carbon in the variable alkyl or acyl group (the mean error for 40 values of A 
is +0°-93), and with smaller error when the number of carbon atoms is still 
larger ;! it is probably also applicable to the higher fatty acids, cyanides, ketones, 
and nitro-compounds. 
and generally under 1°, by means of the formula A= The formula 
Comparison of Molecular Volumes. 
The fundamental idea on which both Kopp and Schréder based their methods 
of calculating the molecular volumes of organic compounds from the atomic 
volumes of the component elements was the constancy of the increase in molecular 
volume for each addition of CH,. With regard to this point the question was 
greatly discussed whether the comparison should be made at the same temperature, 
say 0°C., or at the boiling-points of the compounds under the same pressure. 
Later, when Van der Waals brought forward his conception of corresponding 
states, it was thought probable that the comparison should be made at cor- 
responding or equal reduced temperatures ; that is to say, at temperatures which 
bear the same ratio to the critical temperatures. If the generalisations of Van 
der Waals were strictly true, the boiling-points under corresponding pressures 
would be corresponding temperatures, but that is not usually the case. The com- 
arison may, therefore, be made either at equal reduced temperatures or at the 
foititig points under equal reduced pressures ; or, lastly, it may he made at the 
critical points themselves, and, thanks to the law of Cailletet and Mathias, the 
critical volumes can be ascertained with a great degree of accuracy. 
In order to find whether the difference in molecular volume for each addition 
of CH, is really constant it is best to examine such perfectly normal substances 
as the paraffins, and the data for four consecutive members of the series—n-pen- 
tane, n-hexane, n-heptane, and -octane—are fortunately available. 
In the table below the molecular volumes and the differences, A, for an 
addition of CH, are given under the following conditions ; 9— 
A. At O°C, 
B. At the respective boiling-points under | atm. pressure. 
C. At equal reduced temperatures (0°6396). 
D. At the respective boiling-points under equal reduced pressures (0-022 11). 
E. At the respective critical points. 
| A B C D | E 
Paraffin —| Nise —= - 
M.Vol| A |M.Vol| A M.Vol| A M.Vol) A M.Vol| a 
| | 
n-Pentane 111°33 | ‘117°80 | 116-13 116-13 309-3 | 
15-44 22-13 | 20°09 | 21-06 568 | 
n-Hexane |126°77 139°93 136:22 137:19 (3661 
15°69 22-63 20°18 21-49 | 60-2 
n-Heptane 142-46 162°56 156-40 158°68 426°3 | 
15-88 23°70 20°54 21:83 | 62°6 
n-Octane (158-34 186:26 176-94 180°51 488-9 | 
‘ Thus the observed B.P. of »-hexyl formate is 153°-6, and the value of A 
calculated from the formula is 22°8, giving 176°-4 as the B.P. of the next higher 
homologue, This agrees very well with the observed B.P. of n-heptyl formate, 
176°-7, but not with that of n-hexyl acetate, 169°-2. Again, the observed B.P. 
of methyl caproate (hexoate) is 149°6, and the calculated value of A is 23°-0, 
giving 172°6 as the B.P. of the next homologue. The observed B.P. of methyl 
cenanthylate (heptoate) is 172°-1, but that of ethyl caproate is only 166°-6. 
* The atomic weights [C=11:97, H=1] employed in the original papers are 
retained, 
