274 



NATURE 



{July 1 8, 1889 



position wholly in the direction of the stronger attraction. 

 Hence, according to Bergmann, substances may be ar- 

 ranged in the order of their affinities towards some 

 standard substanc*. If A, B, and C are each capable 

 of reacting chemically with D, and if the affinities of the 

 three substances are in the order A, B, C, this means 

 that addition of A to the compound BD, or to the com- 

 pound CD, will cause the production of the new compound 

 AD, and the liberation of B, or C. 



BerthoUet, like Bergmann, regarded chemical affinity 

 as an attraction between minute particles; but he asserted 

 that affinity is conditioned by the physical properties of 

 the attracting bodies, and also, and very specially, by the 

 relative masses of these bodies. A relatively small at- 

 traction may overcome a greater, if the mass of one of 

 the attracting bodies is largely increased relatively to 

 that of the other. Berthollet's view is expressed by him- 

 self in the words, " Toute substance qui tend k entrer 

 en combinaison, agit en raison de son affinitd et de sa 

 quantite." 



These two conceptions still divide the allegiance of 

 chemists. Berthelot's law of maximian work is the 

 modern form of the Bergmannic doctrine. Guldbergand. 

 Waages law of mass-action puts Berthollet's statement 

 into exact form, and includes in its expression the con- 

 ception of equivalency — a conception which has been 

 developed since the days of BerthoUet. 



A great deal of work on chemical affinity has been carried 

 on within the last few years. Ostwald has recently pub- 

 lished a memoir of first-class importance. The present 

 seems a good opportunity for endeavouring to give a 

 sketch of the position of the subject. 



The enunciation of Guldberg and Waage's law of mass- 

 action, and of the principle of the coexistence of reactiotts, 

 marksthebeginningof thedistinctlymodern era of the study 

 of affinity. The law of mass-action, first clearly put forth 

 by the Norwegian naturahsts in 1867, states that chemical 

 action is proportional to the product of the active masses 

 of the substances which take part in the reactiojt. The 

 active mass of any member of a chemical system is de- 

 fined to be the mass of that substance, stated in chemical 

 equivalents, in unit volume of the system. Thus, if in a 

 solution of hydrochloric acid, sulphuric acid, and caustic 

 soda, the substances are present in the ratio 



2HCI : H2SO4 : 2NaOH, 



the active masses of the three substances are 1,1, and i 

 respectively, H2SO4 being taken as one equivalent of sul- 

 phuric acid. 1'he investigations of Guldberg and Waage, 

 and others, more especially of Ostwald, have shown that, 

 if more than one member of a system is undergoing che- 

 mical change, each change proceeds as if it were inde- 

 pendent of the other, and each substance obeys the law 

 of mass-action. This statement is called by Ostwald 

 the principle of the co-existence of reactions. 



But the amount of chemical change which occurs when 

 substances react is conditioned not only by the active 

 masses of the substances, but also by their chemical nature, 

 their states of aggregation, the temperature, and other 

 variables. In their first memoir, Guldberg and Waage 

 grouped these variables together under the name coefficient 

 of affinity. 



Let two s'.ibstances, P and Q, react in solution to pro- 

 duce P' and Q', and let P' and (^' by their reaction re-form 

 P and Q ; let the active masses of P and O be repre- 

 sented by/ and q, and the active masses of P' and Q' by 

 p' and q' ; further, let the coefficient of affinity for the 

 reaction between P and Q be represented by k, and the 

 coefficient of affinity for the reaction between P' and Q' 

 by k' ; then the amount of decomposition of P and C) 

 which occurs will be proportional to the product kpq ; 

 and the amount of decomposition of P' and Q' will be 

 proportional to the product kp'q'. When the equation 

 kpq = Kp'q is fulfilled, the system will be in equilibrium. 



The ratio k'lk is found by throwing the equation into 

 the form — 



(P - x) (Q - x) = li'ik (P' + X) (Q' -(- x) ; 



where P, Q, P', and O' represent the masses, stated in 

 equivalents, of the four bodies initially present, and -i- 

 represents the number of equivalents of P and O which 

 disappear, and also the number of equivalents of P' and 

 O' which are formed, when equilibrium results. Experi- 

 mental measurements of P, O, P', and C2', and x are 

 required ; from these the ratio k'jk is calculated, and, 

 from this, values are found for x for different initial 

 values of P, O, P', and O'. 



In their earlier treatment of the equation of equilibrium, 

 given above, Guldberg and Waage spoke of the force 

 which brings about the formation of P' and O' being 

 held in equilibrium by the force which brings about the 

 re-formation of P and Q. The word force was used with 

 a somewhat vague meaning, and certainly not with the 

 meaning given to it in dynamics. Following the example 

 of van 't Hoff, in their later memoirs the Norwegian 

 naturalists regard chemical equilibrium as resulting 

 when the velocity of the direct change — i.e. in the above 

 case the change of P and O to P' and Q'— became equal 

 to the velocity of the reverse change, i.e. in the above 

 case the change of P' and O' to P and Q. The equation 

 of equilibrium arrived at by applying this conception is 

 identical with that already given. By velocity of the 

 change is to be understood the ratio of material chemically 

 changed to time used in the change. Ostwald's analysis 

 of the criterion of equilibrium, viz. that the velocities of 

 the direct and reverse changes are equal when equilibrium 

 results, is somewhat as follows. Let two bodies, A and B, 

 be changed to A' and B' ; Jet the active masses of the four 

 bodies, stated in equivalents, be/, q,p', q' ; let x be the 

 number of equivalents of A and B changed to A' and B', 

 and the number of equivalents of A' and B' changed 

 to A and B, at any moment ; and let ^ be the value attained 

 by X when equilibrium results ; then 



velocity of direct change = (/ - -r){q - x)c\ and velocity 

 of reverse change = (/' - x){q' - x)c' ; and the velocity 

 of the total change = (/ - x){q - x)c - (/ -^ x){q^ -\- x)c . 



Then .r = ^, and the velocity of the total change = o, 

 i.e. equilibrium results, when 



(/ - Vkq - \y = (/ + !)(/ + iY. 



This is the same equation as that given by Guldberg 

 and Waage. But in this equation c c represents the ratio 

 of the velocity-coefficients of the two parts of the change, 

 whereas the ratio kjU was called the ratio of the affinity- 

 coefficients. 



The simplest case in which to apply the above form of 

 the equation of equilibrium is when A and B are caused 

 to react in equivalent quantities without addition of A' 

 or B' ; in this case p = q = i, and/' = q' = o, and the 

 equation has the form 



hence 



(I - ifc =|V: 



By determining ^, i.e. the number of equivalents of A and 

 B changed, and i - |, i.e. the number of equivalents of 

 A and B remaining unchanged, when equilibrium results, 

 the ratio of the velocity-coefficients is found. This 

 equation has been applied to varied classes of changes. 

 Thomsen's measurements, by thermal methods, of the 

 distribution of a base between two acids when one of the 

 acids interacts with the salt of the base with the other 

 acid, confirm the equation. Ostwald's measurements, 

 by volumetric methods, of the same reaction which 

 Thomsen examined by thermal methods, also confirm 



