August i8, 1904] 



NATURE 



381 



included, the higher the boiling-point — the smaller, as a 

 rule, is the contraction on mixing with water. 



\"ery similar remarks apply to the heat changes which 

 occur on mixing liquids. It appears that in the case of 

 n-ery closely related substances these changes are exceed- 

 ingly small, or negligible, as is indicated by the very minute 

 change of temperature which has been observed, thus : 

 ethyl acetate and propionate, — o''o2 ; toluene and ethyl 

 benzene, -(-o°-o5 ; n-hexane and H-octane, -|-o°o6 ; methyl 

 and ethyl alcohol, — o°io; chlorobenzene and bromo- 

 ■benzene, o°oo. 



It might be expected that in the case of less closely 

 related substances contraction would be accompanied by 

 evolution of heat and expansion by absorption of heat, but 

 this is by no means invariably the case ; for example, on 

 mixing 40 gram-molecules of propyl alcohol with 60 gram- 

 molecules of water there is a contraction of 1-42 per cent., 

 Taut a fall of I'lj in temperature was observed. Taking 

 the alcohols as a group, it is found that, the higher the 

 toiling-point, the smaller is the heat evolution or the 

 g^reater the absorption on admixture with water. 



Properties of Mixtures. 

 The behaviour of two non-miscible liquids when heated 

 together is well known, and I need only refer to the fact 

 that the vapour pressure is equal to the sum of the vapour 

 pressures of the pure components at the same temperature ; 

 that the boiling-point is the temperature at which the sum 

 ■of the vapour pressures of the components is equal to the 

 pressure under which the liquid is being distilled, pro- 

 vided that evaporation is taking place freely and the vapour 

 Is not mixed with air ; and, lastly, that the composition of 

 the vapour is independent of that of the liquid (so long as 

 ■both components are present in sufficient quantitv) and is 



•expressed by the equation —7 ~ u r\ ' where xx and xb 



.are the relative weights of the two components in the 

 ■vapour, Pa and Pb their vapour pressures at the observed 

 boiling-point, and Da and Db their vapour densities. 

 _ The vapour pressure, boiling-point, and vapour composi- 

 ition, then, can be calculated for non-miscible liquids, and 

 it has been stated that such liquids have never any close 

 ichemical relationship, and are usually not related at all. 



On the other hand, it has been mentioned that when the 

 •chemical relationship is very close the liquids are invariably 

 miscible in all proportions, and that there is very little, if 

 any, volume or heat change oi) admixture. 



So, also, the vapour pressure and boiling-point of a 

 mixture of closely related liquids are easily ascertained 

 ■from those of the pure components, and the composition of 

 the vapour bears a simple relation to that of the liquid. 



The vapour pressure of the mixture is given, at any rate 

 with a very close approach to accuracy, by the equation 



p _ wPa + (ioo-w )Pb 

 100 



■where P, T'a, and Pb are the vapour pressures of the 

 mixture and of the components. A and B, at the observed 

 boiling-point, and m is the molecular percentage of A. 



\'an der Waals concluded from theoretical considerations 

 that this relation should be true when the critical pressures 

 are equal and the molecular attractions agree with the 

 formula proposed by Galitzine and by D. Berthelot, 

 ■ayo= •Jitj'Op where a;., represents the attraction of the 

 unlike molecules and a, and a, the respective attractions of 

 the like molecules. That is certainly the case with 

 ■chlorobenzene and bromobenzene, which, as already 

 mentioned, show no heat or volume change on admixture, 

 for the maximum difference between the observed and 

 calculated pressure in three experiments was less than o-i 

 per cent. 



But the relation is, at any rate, very nearly true for 

 closely related substances -when the critical pressures are 

 not equal, for in the case of methyl and ethyl alcohol the 

 difference between the observed and calculated pressure was 

 within the limits of experimental error, and with four 

 other pairs of closely related substances the greatest mean 

 difference (for three readings each) was only 0-6 per cent. 

 Tt is not, however, as .'^peyers suggested, true for all non- 



NO. I 8 16, VOL. 70] 



these limits by means of the formula 



associated substances, whether closely related or not; indeed, 

 chemical relationship seems to be much more important than 

 the state of molecular aggregation, for the relation is true 

 for methyl and ethyl alcohol, while it is altogether untrue 

 for benzene and hexane. 



The boiling-point of a mixture of closely related liqu'- 

 may be ascertained from the vapour pressures of the com- 

 ponents, but not so simply as in the case of non-miscible 

 liquids, because the boiling-point depends on the composi- 

 tion of the liquid. 



In order to calculate the boiling-points of all mixtures of 

 two closely related liquids under normal pressure we should 

 require to know the vapour pressure of each substance at 

 temperatures between their respective boiling-points under 

 that pressure. Thus, chloroform boils at isa^o, and 

 bromobenzene at is6°-i, and we must be able to ascertain 

 the vapour pressure of each substance between 132° and 

 1560. 



The percentage molecular composition of mixtures which 

 exert a vapour pressure of 760 mm. must then be calculated 

 at a series of temperatures — say every two degrees — between 



Pb-P . 

 ■00 • pj^_p^ 

 where, in this case, P = 76o. 



Lastly, the molecular percentages of A, so calculated, 

 must be mapped against the temperatures, and the curve 

 drawn through the points will give us the required rela- 

 tion between boiling-point and molecular composition under 

 normal pressure. In the case of six pairs of closelv related 

 liquids the greatest difference between the observed 

 temperature and that read from the curve constructed as 

 described was o°-27. 



For liquids which are not closely related the differences 

 are usually much greater, and particular mixtures of 

 constant (minimum or maximum) boiling-point are not 

 unfrequently met with, especially when the molecules of one 

 or both substances are associated in the liquid state. 



The formula for the composition of the vapour from a 

 mixed liquid suggested independently by Berthelot and bv 

 Wanklyn, '-^ = !)[,''^^^^, (where xa and ^b, Pa and Pb, Da 



XB WBrnUB 



and Db, have the same meaning as in the equation for 

 non-miscible liquids, and Wa and 'Wb are the relative 

 weights of the two components in the liquid mixture), was 

 shown by F. D. Brown to be incorrect, and he proposed 



the simpler formula, £* = ^_ ^, where ^ is a constant 

 xb Wb 



which does not differ greatly from 5^. The subject was 



Pb 

 mvestigated mathematically by Duhem and by Margules, 

 and experimentally and mathematically by Lehfeldt and by 

 Zawidski. The two last-named observers deduced workable 

 formulae from the fundamental equation of Duhem and 

 Margules. and it is noticeable that both Lehfeldt's and 

 Zawidski 's formulae, in their simplest form, become 

 identical with Brown's. Zawidski 's, however, assumes the 



form -^ = -6 . J^. This formula is certainly '■not, as a 



XB Pb Wb ■' 



rule, true for mixtures of liquids which are not closely 

 related ; but, on the other hand, in the very few cases 



■ , . -*^a Wa 



exammed the equation — = <■. ,,, appears to hold for those 



Xb Wb 



mixtures for which the equation 



p _ otPa -I- (100 - m)P^ 

 100 



is true ; that is to say, generally, for closely related liquids. 



The question, however, whether c = :^ is an open one ; but it 

 Pb 



is interesting to remark that if this equality holds it should 

 be possible in many cases to calculate the vapour pressure 

 at any temperature, the boiling-point under any pressure, 

 and the composition of the vapour, of any mixture of two 

 very closely related liquids, if the boiling-point of one of 

 them under any one pressure, and the vapour pressures of 

 the other within sufficiently wide limits of temperature, are 

 known. For the boiling-points on the absolute scale of the 

 two liquids at the same pressure bear a constant ratio to 



