278 BRIQGIS THE THEORY OF DUPBEX AFPINITY. XX1X.-The Theory of Duplex Afinity. By SAMUEL HENRY CLIFFORD BRIGGS. IN a former paper (T. 1908 93 1564) it was shown how the old conception of duplex affinity cap be applied in devising con-stitutional f o m u l z for complex inorganic compounds. In a sub-sequent paper (ibid. 1917 111 253) the theory of duplex affinity was treated from the point of view of the electrical structure of matter. It was assume! that every element is able to exert both positive and negative affinity positive affinity being a tendency to lose electrons and negative affinity a tendency to attract electrons. A further distinction was made between primary and secondary affinity the secondary affinity being opposite in sign to the primary affinity and only coming into action after the primary affinity has been satisfied.By means of these assumptions it was possible to correlate a number of apparently disconnected pheno-mena including the structure and stability of complex compounds, the strength of acids and bases polymerisation etc. The present communication is concerned more particularly with secondary affinity and some conclusions have been reached which have made it possible to apply the theory of duplex affinity in several new directions. Secondary Negative A fltritg and Secondary Positive Affinity. As in the previous paper (T. 1917 111 253) Lodge’s view (Nature 1904 70 176) that’ the electrons in an atom are bound to the positive charge not by a sir,gle line of attraction or elastic thread but by a bundle of a very large number of lines of force, is adapted.For the sake of simplicity it is supposed that the atoms are spheres although this is not an essential feature of the general argument. The volumes of the atomic spheres are assumed to be directly proportional to the so-called atomic volumes of the elements. The term ((valency” is used in this paper in a strictly electro-chemical sense in accordance with Sir J. J. Thomson’s theory (Phil. Mag. 1914 [vi] 27 757). Consider the case uf two univalent atoms A and B which c m -bine to form a compound A B as the result of the transfer of an electron from A to B A having positive primary affinity and B havipg negative primary affinity. Owing t o the attraction of B for the electron a number of lines of force which united th BRICKS THE $HEORY OF DUPLEX AFFINITY.279 electron to the positive nucleus of the atom A are broken. Call this number u. Then in the atom B u lines of force joining electrons in the atom B (previous to its combination with A ) t o its positive nucleus will be loosened as a result of the passage of the electron from A to B. Suppose now that the compound A B undergoes electrolytic dissociation in solution into the ions rl and B f . The positive nucleus of the cation A' will be able to bind u lines of force from electrons in other atoms that is to say, the cation A' will have negative affinity and in this way the secondary negative afiity of the element A arisa. The electrons in the anion B' on the other hand will have u. lines of force loosened and therefore be able to attach themselves to the positive nuclei of other atoms.Consequently the anion B f has positive affinity which is the secondary positive affinity of the element 13. Attention must now be directed to a fundamental difference between secondary negative affinity and secondary positive affinity. According to the modern views on the electrical struc-ture of matter the positive nucleus is situated a t the centre of the atom and its spatial dimensions are extremely minute compared with the volume of the atom as a whole. As we have seen above, however secondary negative affinity arises from the power of the iiucleus to attract lines of force (or electrons). Since the nucleus is a t the centre and is so exceedingly'small it follows so far as the effect on other atoms is concerned that secondary negative affinity may be regarded as an attractive force distributed equally over the surface of the atomic sphere.Secondary positive affinity on the other hand emanates from the outer electrons (valency electrons or mobile corpuscles) in the atom. The secondary positive affinity cannot therefore be regarded as being equally distributed over the atomic sphere but must be confined to certain individual electrons or rings of electrons. In other words secondary negative affinity conforms to Werner's theory of affinity (" Neuere Anschauungen auf dem Gebiete der anorganischen Chemie," 3rd ed. p. 83) whereas secondary positive affinity does not. This difference between secondary negative affinity and secondary positive affinity appears to be of consider-able importance in the building up of inorganic compounds as will be more clearly seen below.When the ions A' and B f combine to form the molecule AB, some of the looeened lines of force in B will be attached to the positive nucleus of A as shown by the "ionic formula" .-.-+A'-B'--+ (T. 1917 111 253). If the number of lines of force thus attached is denoted by v then in the compound AB the positive nucleus of A is still able to bind u-u lines of force 280 BRIGGS THE THEORY OF DUPLEX AFFINITY. whereas the electrons in B have still u-v lines of force loosened and capable of attachment to the nuclei of other at,oms. The number u-v theref ore represents the unsaturated secondary negative affinity of A and the unsatura.ted secondary positive affinity of B indicated by the dotted arrows in the “atomic (T.1917 111 253).* formula ” -..-+A-B.--t and in the “ ionic formula ” --.+A *-B’--Imfluence of A tonaic Volume. Sinco the secondary negative affinity is distributed equally over the surface of the atomic sphere it follows that when the atomic volume is large v will be correspondingly small and u-v propor-tionat’ely large (see p. 286). When the compound A B is dissolved in a dissociating medium such as water the molecules of the solvent combine with A and B by means of the unsaturated secondary affinity thereby bringing about dissociation into the ions A’ and B’ (compare T. 1908 93 1564). Therefore i f u-v is large A B will be a strong electrolyte. As shown above however, u-v is large when the atomic voluine of A is large and this is the reason why the salts of the alkali metals are the st’rongest electro-On the other hand although when the atomic volume of A is large the total unsaturated affinity is correspondingly large never-theless the intensity of the affinity per unitn area of the atomic sphere varies in8versely as the square of the radius and is there-fore large when the atomic volume of A is small.Consequently, the molecular compounds (nX. A)B formed by satisfying the free secondary negative affinity of A4 by the free secondary positive affinity of n molecules of a compound ikf (such as ammonia or water) (T. 1917 111 253) will be most clearly defined and stable lyte6. * Three types of combination are distinguished (1) Combination due t o primary affinity only as in the formula --+ A - B -+ the passage of the electron from A to B being indicated by the thick arrow pointing from A to B.(2) Combination due to secondary affinity only as seen in molecular corn-pounds such as 2H,N -+ CuCl the union of the electrons in the nitrogen atom to the positive nucleus of the copper atom being indicated by the thin arrow pointing from nitrogen t o copper. (3) Combination due to both primary and secondary affinity as in the non-polar compound A It should be noted that the formulze --t A 3 B -- and A Z? B represent the limiting cases of the strongest possible electrolyte and the truly non-polar compound respectively. Most compounds will come in between the two formula A compound of intermediate properties might therefore be Written --+ A B--t but it is often convenient to write it as a compound of charged ions rather than of atoms and in this way the “ionic formula” B.---+ A’ c B’ -+ derived BRIGIGS THE THEORY OF DUPLEX AFXINITY. 281 when the volume of A is small. As a matter of fact those elements which form the most stable complex compounds are all found in the depressions of the atomic volume curve (chromium, manganese iron cobalt nickel copper zinc ruthenium palladium, rhodium silver osmium platinum iridium and gold) (see also the work of Ephraim on the effect of the atomic volume of the central atom on the stability of metal-ammonia compounds Bw., 1912 45 1322). Conversely the same reasoning elucidates the somewhat contra-dictory phenomenon that many of the salts of the alkali metals which are readily soluble in water separate from solution in the anhydrous state.These salts dissolve readily because of the large value of u-21. They do not give stable hydrates because of the small intensity of the affinity per unit area of the atomic sphere which results from the large atomic volume of the alkali metals. Non-polar Compounds. If the two ions A' and B/ were to combine in such a way that the secondary affinities completely saturated each otlher then the electron would be pulled back into A and the atoms would be held in combination by means of two equal bundles of lines of force one passing from the nucleus of A to the electrons of B and t'he other from the nucleus of B to the electrons in A .That is t o say A B would be a non-polar compound as shown by the formula A = B. The conception of secondary negative affinity developed above (p. 279) leads to the following conclusions with regard to the con-ditions for the formation of non-polar compounds in those cases in which the valency of the element ,4 with primary positive affinity is fully saturated. The conclusions do not however apply when .-I is not exerting its full valency as the mobile corpuscles still remaining on A introduce complications. The compounds to be considered therefore are those represented by the formula AB, in which x varies from 1 to 8 when B is a univalent atom. When x = l the secondary negative affinity of A is only partly saturated as already explained (p.2803 because only a part of the spherical surface of A comes under the influence of B. I f x=2 and A is therefore united to two atoms of B a larger part of the spherical surface of A is affected and in general as s in-creases more and more of the spherical surface of A is brought under the influence of B. Hence as x increases the tendency of A B to undergo electsolytic dissociation decreases (see p. 280) 282 BRIGQS THE THEORY OF DUPLEX AB"ITY. The salts of the metals in the earlier groups of the periodic table are theref ore the strongest electrolytes and the electrolytic proper-ties become less marked in the compounds of tho metals with higher valency (when they are exerting their full valency). If however AB is to be a truly non-polar compound the secondary negative affinity of A which is distributed equally over the surface of the a t m i c sphere must be completely saturated, and the optimum condition for such complete saturation will be reached when the atoms of B are symmetrically distributed in space around the spherical surface of A .Since the maximum valency is S the number of cases of sym-metrical distribution is strictly limited. If B is univalent x may be 4 6 or 8 when the atoms of B will be distributed around the spherical surface of A a t the corners of a regular tetrahedron a regular octahedron and a cube respectively. If B is bivdent the only possible case is x=4 when the B atoms are situated a t the corners of a regular tetrahedron. We should therefore expect to find the non-polar propertdes most strongly marked in compounds having the fomulz AB, AB, and AB when B is univalent and AB when B is bivalent.Since the forces between the molecules of non-polar compounds are small (Thornson Zoc. cit. p. 760) such compounds in addition to their inability to undergo electrolytic dissociation will also be comparatively volatile and more o r less inert. There are several striking instances of compounds with these characteristics in the four classes of substances under discussion. I n the group AB we have the,typically non-polar compounds, methane and carbon tetrachloride. The formula AB is represented by the gaseous sulphur hexa-fluoride SF, which is almost as inert as nitrogen (Moissan and Lebeau Compt. rend. 1900 130 865 954; Berthelot Ann. Chim.Phys. 1900 [vii] 21 205) and by the gaseous tungsten hexa-fluoride (Ruff and Eisner Ber. 1905 38 742) WB,. Only one compound of the formula AB has hitherto been pre-pared. This is osmium octafluoride (Ruff and Tschirsch Ber., 1913 46 929) which boils below 50° and is a highly stable although reactive substance. The class AB, in which B is bivalent includes the remarkable tetroxides of ruthenium and osmium RuOI and OsO,. These com-pounds both boil a t about looo and are so completely saturated that they are incapable of combination with alkali hydroxides. Indeed osmium tetroxide can be distilled off from its solution to which an alkali has been added (compare Ostwald " The Principles of Inorganic Chemistry," p. 757) BRIUQS THE THEORY OB DUPLEX AFFINITY. 283 Although symmetry of structure is thus often associated with, and conduces to non-polarity it does not follow that a 1 sym-metrical compounds will be without polarity as other factors such as the relative atomic volumes of A and B will also exert an influence.Conversely when A is not exerting its full valency non-polar combination is possible in subst4ances which are not spatially sym-metrical. Thus according to Thomson (loc. cit.) carbon monoxide and nitrous oxide are non-polar compounds. Other examples given by Thomson bring out the relationship between symmetry and non-polarity in another way. Although both carbon tetrachloride CCl, and methane CH4 are truly non-polar nevert'heless clilorof orm CHCI, and methyl chloride CH3C1, are polar compounds. Werner's Co-ordination Nzi,mbers md the Co-ordination Formula.Suppose the cation A' combines with molecules of a com-pound M pwsessing free secondary positive affinity such as dmmonia or water to give the complex ion (rtM . A ) * . Here also the conditions for maximum saturation of the secondary negative affinity of A will involve spatial symmetry in precisely the same way as was seen to apply in the formation of non-pdar compounds. The maximum value of n should therefore be either 4 6 or 8, according to the relative volumes of the atom A and the molecule M ; but the maximum value of n is the maximum co-ordination number of the element A and Werner (Isc. cit, p. 52) has shown that this is either 4 6 or 8. It would appear also that the geo-metrical relationship existing between the volumes of the central atom A and the molecule M is of more importance than the intensity of the affinity in determining the value of the co-ordina-tion number.We find f o r example that barium with a com-paratively large atomic volume has the maximum co-ordination number 8 as seen in the compound (Ba8NH3)C1, whereas cobalt, with a much smaller atomic volume has the maximum ceordina-tion number 6 in the compound (Co6NH,)C13 in spite of the fact that cobaltic salts have a much greater tendency to combine with ammonia than is shown by barium salts. Similarly boron with a very small atomic volume has the maximum co-ordination number 4 in the compound (BF4)H. Attention must now be directed to the limiting case in which the secondary negative affinity of A is cornpZeteZy saturated by the free positive affinity of M giving the complex ion ( n M .A ) * . In what way will the anion H' combine with this complex cation t 284 BRIGUS THE THEORY OF DUPLEX AFE'INTTY. give the molecule (mM . A ) B ? suppose that ill is a molecule of ammonia. (T. 1908 93 1564; 1917 111 253) ammonia was written I n discussing this question we may In the former papers =H = [I This formula was derived from the facts (1) that the hydrogeii atoms do not undergo electrolytic dissociation in solution in water, and therefore have both primary and secondary affinity saturaLeed, and (2) that the nitrogen atom has free secondary positive affinity, d s shown by the ease with which ammonia molecules can combine with the free secondary negat.ive affinity of metals in their salts to give metal-ammonia compounds.From the reasoning developed above however (p. 280) it is clear that this formula for ammonia, although correct so far as it goes is not quite complete because if the nitrogen atom still has u-2 lines of force loosened as expressed by the dotted arrow then each hydrogen atom must be able to +-- NZZH , bind *?I! lines of force to its nucleus. In other words each 3 hydrogen atom has still a litkle free secondary negative affinity. Since however the free secondary positive affinity in the ammonia molecule is confined to one atom only (the nitrogen atom) it masks the free secondary negative affinity which is distributed over the three hydrogen atoms. I n the general case of a compound A,B,, in which A and B have free secondary affinity if nz is greater than n the molecule A,B will react as if it had the free secondary affinity of B only.This characteristic will be the more strongly marked &he greater the difference between m and n and it will be all the more intensified the greater the volume of A (the atom with primary positive affinity) and vice versB. Thus we find that ammonia water and potassium chloride react as if they had free secondary positive affinity only in forming complex compounds, whereas cupric chloride ferric chloride etc. behave liike substances with free secondary negative affinity. The complete formula for ammonia should therefore be written in which each hydrogen atom hss a little free secondary negative affinity.Returning now to t.he combination of the complex (izM.A)' with t.he anion B' t o give the salt (mM.A)B we may take the concrete case in which the complex is (CO~NH,)"' and the anion is Cl' and assume that the secondary negative afiinity of the cobalt atom is completely saturated by the free secondary posit'ive affinity of the nit.rogen in the six molecules of ammonia BRIGGS THE THEORY OF DUPLEX AFFINITY. 285 The only possible way in which the chloride ions can unite with the complex to give the salt (C06NH3)C13 is by the saturation of the free secondary negative affinity of the eighteen hydrogen atoms by the positive affinity of ths chlorine ions. This gives Werner's co-ordination formula (Co6NII3)CI3 exactly in which according to Werner's phraseology the chlorine atoms are united to the outer sphere of the complex.It should be carefully noted however that the co-ordination formula only applies to the limitiizg case in which the secondary negative affinity of A is completely saturated by ?LM in the com-plex (%Ma A ) ' . If this saturation is not complete then the posi-tive nucleus of A will exert an attraction on the electro'ns in B, as shown by the "ionic formula " 7zM-A'-B'--+ (T. 1917 111, 260). A familiar example is seen in aquopentammine cobaltic chloride (Co H,03 a, which changes spontaneously into chloro-pentammine cobaltic chloride (Co c S)Cl,. Unless the cobalt atom exerts a direct attraction on the chlorine atoms as shown by the formula 5NH,-Co"'-CI,"'.-.~ H,O- it is impossible t o understand EiNH 5NH ) this spontaneous change.Application of t h c Tlieoiy of Buplex A f i l l i t y t o Oxygen Compounds. In the former papers (Zoc. c i t . ) most of the examples considered were halogen compounds. The development of the theory of secondary negative affinity in the present communication has made it possible to study oxygen compounds from the point of view of duplex affinity in such a way as to bring out some general relation-ships which are not touched on by other theories of affinity and valency . Take the case of a metal M which folrms a series of oxides, MO MO, MO, MO,. I n the oxide 1510 in which the oxygen atom has received two electrons from the atom M only part of the atomic sphere of M will come under the influence of the oxygen atcorn.Hence the secondary affinity of both atoms will be partly unsaturated and the formula will be ..-.&o*-+ * * Instead of denoting the passage of two electroizs by two thick arrows M 0 it is more convenient to write one arrow only with a small figure above to express the number of electrons which it represents for example, M - 0. 286 BRIQQS THE THEORY OF DUPLEX AFBINITY. When & I 0 is oxidised to give MO, a greater part of the spherical surface of M will come under the influence of the oxygen atoms, and the saturatian of the secondary affinity will be more complete than i n the first oxide MO. This will apfily still more in MO,, and most of all in MO, in which the oxygen atoms are distributed symmetrically in space around M. I n MO we therefore have the possibility of complete saturation of the secondary affinity with t,he production of a non-polar compound.The oxides OSO and RuO, referred to above (p. ZSZ) appear to approximate closely to this condition. The four oxides should therefore be written (assuming that MO is non-polar): 2 4 6 R .-+Mta ...-+ --+ MtO,--+ --+afz()3- -+ Mcr-0,. It may perhaps be better to write the non-polar oxide M S O , rather than MtO, as the electrons will not have left the M atom in this case. It should be carefully noted that since the secondary affinity of M is increased by each addition of an oxygen atom the satura-tion of the secondary affinity of the first oxygen atom becomes more complete as oxidation proceeds because the secondary affinity of M being distributed equally over the surface of the atomic sphere the intensity of the affinity present on that part of the spherical surface which comes under the influence of the first oxygen atom will increase with increase in the number of oxygen atoms combined.The free secondary affinity of the first oxygen atom will therefore decrease with increasing oxidation of M until in the final non-polar stage the secondary affinity of the first oxygen atom will be completely saturated. The same reasoning applies of course to all the other oxygen atoms as well. The Hydration of Oxides.-When potassium oxide and water are brought together tlhere are two ways in which combination may occur. The strongly marked free secondary positive affinity of the oxygen atom in the potassium oxide may attract the hydrogen atoms of the water which have slight unsaturated secondary negative affinity or the unsaturated secondary negative affinity of the potassium may combine with the slight free secondary positive affinity of the oxygen atom in the water molecule.We may therefore obtain a .-- +K,O-H ,O. .. f or -- +H,O-K,O -...+ or perhaps a ring st,ructure K,+O o-H2. I n potassium u-v is large, owing to the large atomio volume of potassium (see p. 280) and therefore the unsaturated secondary affinities of the potassiu BRIGGS THE THEORY OF DUPLEX AFFINITY. 287 atoms and the oxygen atoms are large. I n water on the other hand u-v is small (as seen from the very slight extent to which it is dissociated into hydrogen and hydroxyl ions); hence the un-saturated secondary affinities of the hydrogen atoms and the oxygen atom are small.I n each of the three folrmulae for K,O,H,Q we consequently have the two potassium atoms electrically equal the two hydrogen atoms electrically equivalent but the two oxygen atoms very different from each other. The tendency will be for bhe.affinities t o be redistributed in such a way as to make the two oxygen atoms also electrically equal and we therefore have the change K,O,H,O *- 2KOH. Similar considerations will apply to ~~ the hydration of other oxides. Bases and Acids.-When an oxide is hydrated the product may be either a base or an acid according t o l the manner in which it undergoes electrolytic dissociation i n solution. I f MOH were a base of the strongest possible type the formula would be written as (I) and i f it were the strongestl possible type of acid as (11) (T.1917 1111 253). It has already been shown (p. 286) khat increase in the number of oxygen atoms implies a more complete saturation of the secondary affinity of all the oxygen atoms already present in the oxide (anhydrous or hydrated). As the secondary affinity of the oxygen atom of the hydroxyl group becomes more completely saturated by the secondary affinity of M there is less affinity left to saturate the secondary affinity of the hydrogen of the hydroxyl group and the free secondary a4inity of the hydrogen therefore increases. Consequently the tendency of the hydrogen atom to be electrolytically dissociated becomes greater and the structure of the hydroxyl group changes from -0-H (basic) to Z0-H- (acidic) with increase in the number of oxygen atoms united to the element M .We therefore have the following general rule : W h e n a series of oxides of t h e same elemend M a r e hydrated, t h e hydrate of t h e highest oxide i s t h e strongest acid ( o r weakest base). I n other words in a series &LOH the greater the value of x the stronger the acidic properties (or the weaker the basic properties). Y j. 0 288 BRIGGS THE THEORY OF DUPLEX AFFINITY. This rule appears to hold good throughout the periodic table. It is exemplified most clearly in the compounds of the elements in the sixth seventh and eighth groups these being the elements which exhibit the most numerous stages of oxidation.Thus ferrous oxide is basic ferric oxide less basic (as shown by the greater ease with which ferric salts are hydrolysed) and iron tri-oxide is acidic. The oxides of chromium form a similar series from the basic chromous and chromic oxides to the acidic chromium tri-oxide. Manganous oxide is basic manganic oxide less basic and manganese dioxide no,t definitely basic or acidic whereas man-ganese trioxide is acidic and dimanganic heptoxide strongly acidic. The oxides of chlorine give rise to a series of acids increasing in strength from the very weak hypochlorous acid HOC1 to the strong chloric and perchloric acids HOC10 and HOCIO,. Among nitrogen compounds hyponitrous acid is very weak nitrous acid is stronger and nitric acid is one of the strongest acids known.The fact that ruthenium and osmium tetroxides are not acidic, although diruthenium heptoxide is strongly acidic is only an apparent exception t o the rule. Owing to their highly saturated character as has already been shown (p. 282) these compounds are incapable o f combination with water and cannot therefore give rise to hydrated oxides. They therefore do not come within the scope of the rule which applies t o hydrated oxides only. The Hydrogen Ion and the Catalytic Activity of Acids. From the point of view of the theory of duplex affinity the hydrogen atom is particularly interesting. According to the views of van den Broek and others (Ann. Reports 1913 18 271) the hydrogen atom is *built up of a positdve nucleus and one electron (compare Allen T. 1918 113 390).Consequently the hydrogen ion H’ must consist of a positive nucleus only. The secondary negative affinity of the hydrogen ion must theref me be considered to be concentrated in a “ point” uf nuclear dimensions rather than distributed over the surface of a (comparatively) very large sphere. The conclusions which have been arrived a t i n the above discussion from the consideration of the atomic sphere will therefore not neces-sarily apply to hydrogen. Thus it is not essential for the produc-tion of non-polar compounds that the hydrogen atom should be surrounded by negative atoms as in the cases of sulphur and osmium for example (see p. 282) methane being a typical non-polar compound. The identity of the hydrogen ion with the positive nucleus of the hydrogen atom may perhaps ultimately furnish a rational ex BRIGGS THE THEORY OF DUPLEX AFFINITY.289 planation of the catalytic activity of acids somewhat on the follow-ing lines. Take a molecule AZ-B with a tendency to dissociate according to the equation ABe2ZA-t-B. A hydrogen ion (nucleus) if brought into contact with such a molecule will attract to itself some of the lines of force joining the electrons in A to the positive nucleus of B or the electrons in B t o the positive nucleus of A , --+AZB+ -giving \ J H 4 The bond uniting ,4 to B will therefore become weaker and the tendency of AB to dissociate will be increased. It is consequently tm be expected that the hydrogen ion will accelerate a chemical change which is already taking place or even induce a change which would not otherwise occur.Theoretically speaking other positive ions should act in a similar manner ; but since the secondary negative affinity of all other element5 is distributed over the surface of a comparatively very large sphere instead of being concentrated in a “point” of nuclear dimension the catalytic activity of other cations will be exceedingly small compared with that of hydrogen ions. According to the theory of acids developed in the former paper (T. 1917 111 253) i f we neglect unsaturated affinity the general formula for acids may be written H Z X . I f x is the value of the saturated primary affinities and y the value of the saturated secondary affinities in the formula H S X y may vary from y=x (the weakest possible acid) to y = 0 (the strongest possible acid).If we now write the formulae to sho’w the unsaturated affinities, the strongest possible acid has the forniula (I) and the weakest possible acid the formula (11). -.-*H-X- H Z X (1.) (11.) The formula (I) is the case where v (see p. 279) is vanishingly small. Strictly speaking it is the formula of the dissociated acid (21 = 0). The unsaturated secondary negative affinity of the hydrogen atom in a molecule of the strongest possible acid (I) is hherefore equal to that of the hydrogen ion itself and as we pass down the series through acids of decreasing st*rength the un-saturated secondary negative affinity of the hydrogen atom becomes less until it vanishes as seen in formula (11). It therefore follows that the undissociated molecule of a very strong acid should also exert catalytic activity which catalytic activity should decreas 2 90 BRIGCGIS THE THEORY OF DUPLEX AFPINITY.with decreasing strength of the acid becoming zero in the weakest possible acid (11). It has been shown experimentally that the undissociat>ed molecule of an acid has catalytic activity the activity diminishing with decreasing strength of the acid (Goldschmidt and Thuesen Zeitsch. physikal. Chem. 1912 81 39 ; Dawson and Powis, T. 1913 103 2135; Dawson and Reiman ibid. 1915 107 1426; Snethlage Zeitsch. physikal!. C'hem. 1913 85 211) but according to Dawson and Powis the activity of the undissociated acid in some cases is much greater than that of the hydrogen ion. I n considering this question i t is necessary to take into account the effect of solvation.According to the theory of duplex affinity the chief cause of electrolytlic dissociation is the combination of solute and solvent ky means of unsatnrated secondary affinity (see p. 280). I n a solu-tion of an acid we therefore have the following equilibria: Undissociated molecule + solvent E-Z solvated molecule. Solvated molecule EZiZ solvated hydrogen ion + solvated anion. Solvated hydrogen ion Z5iG solvent + hydrogen ion. Solvated anion EZsolvent + anion. Hydrogen ion + anion T5G undissociated molecule of acid. Take now the extreme case in which the secondary negative affinity of the hydrogen ion is completely saturated by the secondary positive affinity of n. molecules of the solvent S (as i n a very basic liquid) to give the complex ion nS.TI*. The positive charge will now be distributed over the comparatively very large outer' sphere of the complex (compare p. 284) instead of being concentrated in the nucleus of the hydrogen ion and the catalytic activity of the complex will therefore be comparatively very small. Solvation will therefore reduce the catalytic activity of both hydrogen ion and undissociated molecule and the observe'd catalytic activity of the hydrogen ion and 'the undissociated molecule in any given experiment will not be proportional to t h e real catalytic activity of each when unsolvated but will depend on the degree of solva-tion of acid and hydrogen ion in accordance with the abovemen-t>ioned equilibria. Again if the solvation is slight the solvated ion and the solvated molecule may also have appreciable catalytic activity.These principles are in agreement with the experimental observa-tions on the relative catalytic activities 5 f acids in different media. Wat'er forms complexes much more readily than alcohol ; therefore in aqueous solution solvation should be greater than in alcoholic solution and the catalytic activity of acids should be less in water than in alcohol (compare Kistiakowski Zeitsch. physikal. Chem. BRIGCIS TEE THEORY Ol? DUPLEX AFFINITY. 291 1898 27 253 and especially Dawson T. 1911 99 1). Dawson has found that in alcoholic solutions the catalytic activity may be one hundred times as great as in water. Further the addition of water has been found to decrease the catalytic activity in alcoholic solutions and this has been shown to be due t o combination of the water with the hydrogen ions (Goldschmidt and Udby, Zeitsch.physikal. Chem. 1907 60 728; Lapworth T. 1915 107, 857). It would be of considerable interest from the point of view of this paper if experiments could be made on the catalytic activity of acids in some truly non-polar medium such as benzene or carbon tetrachloride. In such a medium solvation and ionisation would be reduced to a minimum because non-polar compounds are fully saturated and therefore unable to. combine with the solute. It has been shown for instance that benzene a t 1 8 O dissolves 2 per cent. of its weight of hydrogen chloride and that the solution is without electrical conductivity (Falk and Walker A mer. Chem . J . 1904 31 398). The catalytic activity in a truly non-polar medium would therefore be due t o the unsdvated molecule only, and in the case of a very strong acid would probably be very great compared with the activity of the undissociated molecule in aqueous o r alcoholic solution. F o r the sake of simplicity it has been assumed throughout this paper that the atoms are spheres. It must be emphasised in con-clusion however that the atomic sphere so often referred to is a purely geometrical conceptmion. We may suppose it la be a sphere described around the atom with the positive nucleus a t the centre, and the radius sufficient to include all the constituents of the atom (valency electrons etc.) within the sphere. The use of this con-ception is justified by the atomic volume relationships of the elements and by the fact that the atoms are not capable of inter-penetration when endowed with such smdl amounts of energy as correspond with the motions of thermal agitation of molecules (compare R . A. Millikan “The Electron,” pp. 139 191). [Received October 23rd 1918.