December 29, 1923] 



NA TURE 



937 



Here there are seven elements, but nine sub- 

 stances. One need not be a profound mathematician 

 in order to understand that according to the scheme 

 of a chemical reaction evolved b}'^ us, Treadwell's 

 example just given contains, in the equation of reaction, 

 substances the coefficients of which in certain limits 

 can be arbitrarily changed. Such substances are : 

 on one hand, H2SO4 and HjO, on the other SO,. 



Thus, if we express the number of elementids by 

 the letter L, the number of chemical substances 

 taking part in the reaction by the letter M, we shall 

 get for the simplest case of a chemical equation the 

 expression : 



M=L + i. 



We have looked through a number of chemical 

 works and have found no exceptions to this rule. 

 The seeming exceptions, carefully analysed, were 

 found to be only complications, substantiating the 

 rule announced. In the well-known " Analytical 

 Chemistry " of Prof. Treadwell (vol. i.) out of 1240 

 reactions, 688 follow directly the rule announced. 

 We shall show below that the seeming exceptions 

 ire only more complex cases. 



Let us consider a first possible complication : it is 

 evident that by addition of two or several chemical 

 equations, we obtain a new chemical equation, but 

 a more complex one ; to find in this case the applica- 

 bility of the simplest rule governing a simple chemical 

 reaction, a special analysis is required. 



Let us consider the case of double decomposition, 

 which from a chemical point of view consists of two 

 reactions : a reaction of combination and a reaction 

 of decomposition. This complication affects adversely 

 the immediate applicability of the rule announced. 

 In this case the number of elementids increases, but 

 the new elementids give algebraical equations result- 

 ing in the same solutions as those given by the number 

 of equations demanded by the, rule L=M-i, so 

 that to find the necessary coefficients it is sufficient 

 to take only the algebraical equations according to 

 our rule. To demonstrate this we will take an 

 example : 



;«riAgNO, H-^^H^S ^y^HNOa +y2Ag2S. 



Here there are the following equations : for Ag, 

 ^1=2^2. for NO3 (elementid), -r^ =^j, for H, 2.^2=^1. 

 These suffice already, for by taking ^2 =1. we obtain 

 ;Vj =2, x.^=\ and y-^ =2. It is possible to make an 

 equation for sulphur, x^ =^y\, but this equation gives 

 no new data and can only serve to control the pre- 

 ceding equations. 



Here is another example * of a complex reaction : 



8KC103-i-24HCl-8KCI + i2HjO-h9Cl2+6C10,. 



The corresponding simple reactions are : 



KC103+6Ha =KCl+3H20-f-3Cl2 

 5KC103-f6HCl =5KCl-f 3H20-f6C102. 



Adding together the last two equations and dividing 

 throughout by the factor 3 common to all the co- 

 efficients, we obtain a more simple expression than that 

 given above, for we get : 



2KCIO, +4HCI =2KC1 +2H,0 -t-Cl, +2CIO,. 



Here again the " new condition," regulating the 

 decomposition of chlorate of potassium, will be 

 expressed by the quantitative analytical data of the 

 percentages in the reaction products of chlorine and 

 chlorine dioxide. These last examples show already 

 that, as in the application of the familiar phase 

 rule, the appearance of each " new condition " in- 

 creases by one the number of substances. Designat- 



• Treadwell, " An.ilytical Chemistry," voL i 



ing the number of new conditions by n as in the phase 

 rule, we get for this case the expression : 



M„ = L-M+«. 



As in the familiar case in the application of the 

 phase rule, we can designate as non-variant chemical 

 reactions those following the simple rule M=L-Ki, 

 as, of course, the formulae for these reactions do 

 not admit of a variation of coefficients. A chemical 

 reaction obeying the rule M„ =L-(-i +w has n degrees 

 of freedom. Thus the reaction above investigated 

 of the action of sulphuric acid on K3Co(CN)s, if 

 written according to Treadwell, will have one degree 

 of freedom (inter-relation of the number of molecules 

 HoO and SO3), i.e. for this case «— i and thus 

 Mi=L-f2. Accordingly in Treadwell's equation, we 

 have Ml =9 and L =7. 



The reactions of hydrogen peroxide when hydrogen 

 peroxide acts as a reducing agent show this : 



ATiAgjO -j-;f2H202 ^y^f) ^-Jz^^ +y3Ag. 



In this case L=3 {i.e. Ag, H, and O), M =5, i.e. 

 Ag„0, HoO,, HoO, O2, and Ag. It would seem that 

 this is an exception to the rule ; but actually there 

 is no exception, as the last equation is subject to a 

 new condition : the quantity of hydrogen peroxide 

 and the quantity of silver oxide are determined by 

 the fact that the molecule of oxygen is formed by 

 one atom of oxygen taken from the hydrogen 

 peroxide and one atom of the silver oxide. Algebraic- 

 ally this condition can be expressed by putting 

 x-^ =x^. The solution is then quite definite. 



Lastly, let us investigate the case of reactions 

 often met with in organic chemistry, where a small 

 number of elements forms a great many substances. 

 We will take the decomposition by water of the alloy 

 of iron and carbon at high temperature and pressure : 



3FepC, -|-4«.H20 =^Fe804 -f.V2C„H2„+2 +>'3C„H2„ 



-Fy4C„H2„2+ . . . 



An immediate application of the rule M=L-f-i 

 can be made only in the case of the formation of 

 one hydrocarbon (case of double decomposition), as 

 in the decomposition of the carbide of aluminium. To 

 the other case the rule M„ =L 4-i +n must be applied, 

 as each new hydrocarbon must be characterised by 

 quantitative analytical data showing its percentage 

 in the reaction products in order to be able to write 

 a stoichiometrically correct chemical equation. 



The expression M„=L + i+n and the simpler one 

 M =L-t-i form the basis for deducing the algebraical 

 equations necessary for the determination of the 

 equation coefficients of a given chemical reaction. 

 The general number of algebraical equations will be 

 equal to « 4- L, where L is the number of equations 

 corresponding to the number of elementids, and n 

 is the number of equations which must be deduced 

 to meet n special conditions. 



All the rules given in this paper can be formulated 

 also by a single expression : 



Mn^A + i-l-«, 



where A is simply the number of elements taking 

 part in a given chemical reaction. 



Wl. Kistiakowsky. 

 Petrograd, June 1923. 



NO. 2826, VOL. I 12] 



Mechanism of the Hydrogen Chlorine 

 Combination. 



The object of the present note is to describe some 

 work in progress here on an attempt to test directly 

 the Nernst theory [Zeit. Electrochem., 24, 335, 1918) 



2 C 2 



