MOLECULES AND ATOMS 333 



them, then the depression o?, or fall (counting from 0) of the tempera- 

 ture of the formation of ice will be (according to Pickering) 



n = Q 0-010 0-025 0-100 0-250 1-000 

 d = 0-0103 0-0280 0-1115 0-2758 1-1412 

 which shows that for high degrees of dilution (up to 0-25 n) d ap- 

 proximately (estimating the possible errors of experiment at 0> 005) 

 =nl-10, because then d=0, 0-0110, 0-0275 2 0-1100, 0-2750, 1-1000, 

 and the difference between these 'figures and the results of experiment 

 for very dilute solutions is less than the possible errors of experiment 

 (for n 1 the difference is already greater) and therefore for dilute 

 solutions of sugar it may be said that n molecules of sugar in dis- 

 solving in 100 molecules of water give a depression of about l'l n. 

 Similar data for acetone (Chapter I., Note 49) give a depression of 

 l-006 n for n molecules of acetone per 100 molecules of water. And 

 in general, for indifferent substances (the majority of organic bodies) 

 the depression per 100H 2 is nearly n\'\ to nl'0 (ether, for instance, 

 gives the last number), and consequently in dissolving in 100 grms. oi: 

 water it is about 18'0 n to 19'0 n, taking this rule to apply to the 

 case of a small number of n (not over 0-2 n). If instead of water, 

 other liquid or fused solvents (for example, benzene, acetic acid, ace- 

 tone, nitrobenzene or molten naphthaline, metals, &c.) be taken and 

 in the proportion of 100 molecules of the solvent to n molecules 

 of a dissolved indifferent (neither acid nor saline) substance, then the 

 depression is found to be equal to from 0'62 n to 0'65 n and in 

 general Kn. If the molecular weight of the solvent = m, then 100 

 gram -molecules will weigh 100 m grms., and the depression will bo 

 approximately (taking 0-63 n) equal to m 0-63 n degrees for n molecules 

 of the substance dissolved in 100 grms. of the solvent, or in general the 

 depression for 100 grms. of a given solvent = kn where k is almost 

 a constant quantity (for water nearly 18, for acetone nearly 37, <tc.) for 

 all dilute solutions. Thus, having found a convenient solvent for A 

 given substance and prepared a definite (by weight) solution (i.e. know- 

 tog how many grms. r of the solvent there are to q grms. of the 

 substance dissolved) arid having determined the depression d i.e. the 

 fall in temperature of freezing for the solvent it is possible to deter- 

 mine the molecular weight of the substance dissolved, because d = kn 

 where d is found by experiment and k is determined by tlie nature 

 of the solvent, and therefore n or the number. of molecules of the 



substance dissolved per 100 grms. of the solvent, Mj the molecular weight of the 

 dissolved substance (in the solution), and M the molecular weight of this substance 

 according to its composition and vapour density, then i = M .'M j. The experimental data 

 and theoretical considerations upon which these formulae are based will be found in texV 

 books of physical and theoretical chemistry. 



