276 



NATURE 



\yuly 18, 1889 



has the greatest conductivity taken as unity, and the num- 

 bers so obtained are compared with the relative affinities of 

 the same acids determined by one of the methods already 

 described, a very close parallelism is noticed between the 

 two series of numbers. By carefully studying the effect 

 of dilution on the conductivities of monobasic acids, 

 Ostwald has arrived at the conclusion that the dilutions 

 at which the molecular conductivities of monobasic acids 

 exhibit equal values bear a constant relation to each other. 

 For instance, the molecular conductivity of monochlor- 

 acetic acid at any dilution is equal to that of butyric acid 

 when the solution of the latter is 256 times more dilute 

 than that of the former acid. By tnolecular conductivity 

 of an acid is meant the conductivity of a solution of a 

 quantity of the acid proportional to its molecular weight. 

 If /x = molecular conductivity, and X = electrical con- 

 ductivity, as ordinarily defined, stated in mercury units, 

 then IX = io'«A, where n = number of litres to which the 

 molecular weight of the acid taken in grammes is diluted. 



The conductivities of the stronger monobasic acids, 

 such as nitric, hydrochloric, chloric, vary but little with 

 dilution ; the maximum values are reached in moderately 

 dilute solutions. The conductivities of the weaker acids, 

 such as phosphoric, acetic, butyric, however, vary much 

 with dilution, and increase very considerably as dilution 

 increases. The rate of increase varies ; as a rule, the 

 weaker the acid the greater is the increase for a specified 

 dilution. The maximum values are not the same for all 

 acids. Ostwald's investigations show that the affinity of 

 an acid is closely connected not so much with the maxi- 

 mum conductivity of a solution of that acid as with the 

 rate of increase of conductivity relatively to the maximum 

 conductivity. To determine the affinity of an acid, by the 

 electrical method, it is, therefore, necessary to determine 

 the molecular conductivity of an aqueous solution of that 

 acid at varying dilutions until the maximum conductivity 

 is reached. 



But it is very difficult, if not impossible, to determine 

 directly the maximum conductivity of a solution of a weak 

 acid, because when very much water is present the un- 

 avoidable impurities in the water affect the conductivity 

 more than the minute quantity of acid which is present. 

 Ostwald has found that the maximum conductivity of a 

 monobasic acid in solution can be calculated from deter- 

 minations of that of the sodium salt of the acid, and 

 moreover that the maximum conductivity of the sodium 

 salt can be calculated from the observed conductivities at 

 different dilutions. The method by which these results 

 are arrived at cannot be gone into here ; suffice it to say 

 that it is based on an extension and modification of the 

 generalisation made by Kohlrausch, to the effect that the 

 conductivity of an aqueous solution of a normal salt of a 

 strong monobasic acid is the sum of two constants, one of 

 which depends only on the nature of the acid, and the 

 other only on the nature of the base. 



The further application of the electrical method to find 

 the affinity-coefficients of acids rests to a large extent on 

 the extension made by Arrhenius to electrolysis of van 't 

 HofFs latv of osmotic pressure. The law asserts that 

 equal volumes of solutions of definite substances, at the 

 same temperature and osmotic pressure, contain equal 

 numbers of molecules, which numbers are the same 

 as would be contained in equal volumes of gases at the 

 same temperature and pressure. The law has been 

 verified in different directions ; it cannot, however, be 

 accepted as a final statement. One conclusion drawn 

 from the law of van 't Hoff, by thermodynamical reason- 

 ing, is that solutions of definite substances in the same 

 solvent which have the same freezing-point exert equal 

 osmotic pressures at their freezing-points ; and hence, 

 solutions which contain equal numbers of molecules in 

 equal volumes, and which therefore exert equal osmotic 

 pressures, have the same freezing-point. This deduction 

 is identical with the law of molecular lowering of freezing- 



point, empirically established by Raoult. This deduction, 

 if granted, enables the osmotic pressures of solutions to 

 be calculated from observations of the freezing-points of 

 these solutions ; the calculated pressures can then be 

 compared with those determined by direct experiment. 

 There are many apparent exceptions to the law of mole- 

 cular lowering of freezing-point, and to the law of van 't 

 Hoff. Arrhenius explains the exceptions by supposing 

 that the substances in question are partially dissociated in 

 aqueous solution, and that therefore a specified volume of 

 one of such solutions contains a greater number of mole- 

 cules than would be the case if dissociation had not 

 occurred. This explanation rests on the analogy between 

 the gaseous state and the state of substances in dilute 

 solution. As the pressure of the vapour obtained by heat- 

 ing ammonium chloride is greater than that calculated by 

 Avogadro's law on the assumption that the vapour con- 

 sists of molecules of NH4CI, but as the observed pressure 

 agrees with the calculated pressure when the vapour is 

 assumed to consist of equal numbers of molecules of 

 NHg and HCl, so the apparently abnormal osmotic 

 pressures of many solutions may be reconciled with the 

 law of Van 't Hoff by assuming that the compounds in 

 these solutions are more or less dissociated into simpler 

 molecules. Substances which are not (by hypothesis) 

 dissociated in aqueous solution are generally, if not 

 always, non-electrolytes. The exceptions to the law of 

 van 't Hoff occur chiefly, if not wholly, among electrolytes. 

 Ostwald, following Arrhenius, supposes such electrolytes, 

 to be more or less dissociated into their ions in aqueous 

 solutions. 



As this hypothesis of electrolytic dissociation rests on 

 the identity of the laws expressing gaseous dissociation 

 and dissociation in solution, it follows that generalisations 

 made regarding gaseous dissociation may be applied to 

 dissociations in solution. Suppose that a gaseous sub- 

 stance is dissociated into two gases ; let the pressure of 

 the undissociated portion be p, and the pressure of the 

 dissociated portion be pi ; then, at constant tempera- 

 ture, the relation of p to p^ is expressed by the equation 



■^ = c. Again, the pressure of a gas at any specified 



temperature is proportional to its mass, 11, and inversely 

 proportional to its volume, v : now, as the osmotic pres- 

 sure of an undissociated compound in solution, according 

 to the law of van 't Hoff, is equal to the pressure which the 

 same mass of that compound would exert if it existed as 

 a gas occupying the same volume as is occupied by 

 the solution, the osmotic pressure in the solution,^, may 



be put as proportional to ~ ; therefore, from the equa- 



V 



tion already given, — = C. 



Let \x^ = molecular conductivity of a binary electrolyte 

 at infinite dilution, and let /i,. = conductivity of v litres 

 containing one molecular weight in grammes of theelectro- 

 lyte ; then, the fraction \i-J\ji.^ expresses the molecular 

 conductivity at any stated dilution referred to the maxi- 

 mum conductivity, and on the hypothesis of electrolytic 

 dissociation the same fraction expresses the portion of 

 the electrolyte which is dissociated in terms of the whole 

 quantity of the electrolyte taken as unity. If this fraction 

 is expressed by /<?], and if u represents the undissociated 

 portion of the electrolyte, we have ic = \ - \>-i>l\i-a,- ^f 



now we put m = — ' , and substitute in the equation 



uvju^ = C, we have 



V = C. This equation states 



that r — V must have the same value for all dilutions 



of any one binary electrolyte ; a statement which is 

 amply confirmed by the researches of Ostwald. The 



