ANNUAL REPORTSON THEPROGRESS OF CHEMISTRY.GENERAL AND PHYSICAL CHEMISTRY.No attempt is made to report progress in more than a few fields.The output of work on solutions of electrolytes warrants a con-tinuation of last year’s Report on this subject, and a section onreaction velocity in such solutions is added. References to opticalactivity and mutarotation seem desirable as a sequel to the 1924Report. Subjects not recently dealt with are entropy, chemicalconstants, and electrification a t surfaces.The Third Law of Themnodynamics and the Entropies ofSolids and Liquids.Perhaps the most fundamental of physico-chemical problems isthe relation between the maximum work and the correspondingtotal energy change of a chemical reaction. A knowledge of thisrelation in general would enable all kinds of chemical equilibriato be calculated from thermal data alone (heats of reaction atsuitable temperatures, and the heat capacities of substances fromabsolute zero up to the highest temperature for which the equi-librium is to be calculated).The relation may be stated mostsimply in terms of the entropy change in the reaction by meansof the equation AA - AU = - T . AS, or by the analogous equationAF - AH = - T . A#. Here, AU is the total-energy increase inthe reaction, AH = AU + P . AV the “ heat content ” increase(i.e., the heat absorbed in a reaction a t constant pressure), AAthe maximum work done on the system, and AF = AA + P . AVthe free-energy increase of the system. The problem thereforereduces to a consideration of the entropy changes in reactions.The concept of entropy as a quantity which can be definitelyevaluated is chiefly due to G.N. Lewis and G. E. Gibson, whomade the first systematic tabulation of the entropies of element8and compounds.1 The entropy of a solid a t a temperature T,referred to its entropy at absolute zero, is given by the integrall J . A m r . Chem. Soc,, 1917, 39, 2564; A., 1918, ii, 2912 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.AS? = (C,/T) I dT, where C, is its heat capacity; and theentropies of liquids and gases are obtained by summing similarexpressions for all the heat changes required to bring them fromthe solid crystalline state a t absolute zero to the given temperature.The entropy change in a chemical reaction involves, in additionto the entropies of the substances concerned (referred to absolutezero), a knowledge of the entropy change in the reaction a t absolutezero, since ASP = A#,, + XAST.The third law of thermo-dynamics as formulated by Nernst was equivalent t o the state-ment that the entropy change in all reactions of (' condensed ''systems (solids or liquids) is zero at the absolute zero of tempera-ture. In 1920, Lewis and Gibson showed that this could not betrue when supercooled liquids or solid solutions are involved, andthey proposed to restrict the law to crystalline bodies, stating itthus : I ' If the entropy of each element in the crystalline form betaken as zero a t absolute zero, the entropy of any pure crystal a tabsolute zero is zero, and the entropy of any other substance isgreater than zero." E.D. Eastman3 has since argued that thereis a complete series of gradations from a perfectly crystalline sub-stance to t,he haphazard arrangement in an amorphous solid, andthat complicated systems of a low order of symmetry may haveappreciable positive entropy. L. Pauling and R. C. Tolman, how-ever, deny this and, in a statistical investigation of the entropy ofsupercooled l i q ~ i d s , ~ conclude that the entropy of a perfect crystala t the absolute zero is not dependent on the complexity of theunit of crystal structure: The third law may be tested by com-paring the entropy change in a reaction as deduced from equilibriummeasurements [ASP = (AH - A F ) / T ] with the entropy change(ZAA';), calculated from the heat capacities.Lewis and Gibson,in their 1917 paper, showed that the available data, of somewhatlow accuracy, supported the law (in its more general form). In1920, G. E. Gibson, W. M. Latimer, and G. S. Parks found thatthe thermal entropies of formation of formic acid and urea werein good agreement with the values obtained from equilibriummeasurements. In 1922, Lewis, Gibson, and Latimer drew upa revised table of entropies and demonstrated, in a number ofcaaes, close agreement with the requirements of the law. T. J.Webb has obtained a further confirmation in the cases of hydrated1'J . Amer. C%m. SOC., 1920, 42, 1529; A . , 1920, ii, 585.Ibid., 1924, 48, 39; A , , 1924, ii, 143.Ibid., 1926, 47, 2148; A ., 1925, ii, 952.Ibid., 1920, 42, 1633; A., 1920, ii, 686.6 Ibid., 1922, 44, 1008; A , , 1922, ii, 471.J . Phyaical Chm., 1926, aS, 816; A . , 1926, ii, 867QENERAL AND PHYSICAL CHEMISTRY. 13cadmium chloride (CdCl,,26H2O) and cadmium iodide. H. L. J.Biickstrom 8 investigated the change aragonite + caleite for thesame purpose, but found a difference, which he ascribed to an errorin the specific-heat curve of calcite at low temperatures.Further work has been done to confirm the conclusion thatsupercooled liquids and solutions have greater entropy than thecorresponding pure crystals, The first test of the point by Gibson,Parks, and Latimer 9 with solutions of ethyl and propyl alcoholwas inconclusive. R. Wietzel 10 found that there is probably anentropy difference between amorphous and crystalline forms ofsilica a t absolute zero.G . E. Gibson and W. P. Giauque l1 showedthat supercooled liquid glycerol almost certainly has a greaterentropy than the crystalline form. Now F. Simon and F. Lange lahave reinvestigated these cases and find in the case of silica anentropy difference of 0-9 -J= 0.3 unit, and in the case of glycerol4.6 & 0.3 units, a t absolute zero.The third law, in the form given it by Lewis and Gibson, i6being used to determine the free energies of substances whichcannot be conveniently determined by equilibrium measurements.Thus G . S. Parks and K. K. Kelley 13 have determined the entropiesof the oxides of magnesium, calcium, aluminium, and (ferric) ironand of magnetite a t 25" by heat-capacity measurements and haveobtained therefrom values of the free energies.Similar measurementshave been made with zinc 0xide.l' The free energy so determinedis in good agreement with the values obtained by direct methods,for which data are in this case available. The free energies of thefollowing organic compounds have been determined by the samemethod : Methyl, ethyl, and n-butyl alcohols 1 5 ; isopropyl alcohol,acetone, ethylene glycol, acetic acid, and palmitic acid Is; tert..butyl alcohol, mannitol, erythritol, and n-butyric acid 17 ; n-propylalcohol, ethyl ether, and dulcitol.18The entropy of a solid substance could evidently be calculatedfrom its complete specific-heat equation.Whilst the specific-heatequations for solids a t low temperatures account well for the forma J . Atmr. C h m . SOC., 1925, 47, 2432; A., 1925, ii, 1162. ' I b i d . , 1920,42, 1542; A., 1920, ii, 586.la 2. anwg. Chem., 1921, 116, 7 1 ; A., 1921, ii, 504.l1 J . Amr. Chem. Soc., 1923, 46, 83; A., 1923, ii, 124.la 2. Physik, 1926, 38, 227; A., 1000.Is J . Physical Chem., 1926, 30, 47; A., 232.C. G. Maier, G. S. Parks, and C. T. Anderson, J. Arne?. Chcm. Soc., 1926,G . S. Parks, ibid., 1925, 47, 338; A4., 1025, ii, 491.G. 8. Parks and K. K. Kelley, !bid., p. 9089; A , , 1925, ii, 949.G. S. Parks and H. M. Huffrnan, ibid., p. 2788.48, 2564; A., 1210.l 7 G. M. Parks and C. T. Anderson, ibid., 1926, 48, 1506; A., 78414 ~ N U U REPORTS ON THE PROGRESS OP CHEMISTRY.of the curve, an exact calculation of entropy on the same basis isnot yet feasible.Attempts have been made to find empirical equations for thoentropies of solids a t a given temperature. According to Latimer,19the entropy of an atom in a solid is a function of its mass, M , andof the constraints by which it is held.At temperatures a t whichthe specific heats have reached the equipartition value the con-atraints are held to be the same, and Latimer found that theentropies of 16 salts a t 25" were given by the sum of terms, S298. =$R log M - 0.94, for all the atoms in the salt. This equationdoes not apply to the metals themselves. E. D. Eastman20 hasattempted to introduce it term depending on the constraints of theatoms and has found that the equationwhere V is the atomic volume and p the compressibility, givesapproximately the entropies of many metals.Recently R. M.BufEngton and W. M. Latimer 21 have made some accurate measure-ments of the coefficients of expansion of solids a t low temperatures.Their measurements confirm the relation of E. Gruneisen 22 that theratio of the specific heat to the volume coeEcient of expansion ofa substance is nearly independent of the temperature. They usethis ratio (CP/3a, where a is the linear coefficient of expansion) forexpressing the " constraints " of different substances and findthat the equationgives the experimental entropies of a number of metals. It alsoapplies to salts when M is replaced by the geometrical mean ofthe weights of the ions.Szgr = +R log M + R log p312/V + 42.1,Smg $R log H + H log V - +R log (CP/3ti)r= 180.+ 26.5The Entropies of Gmes and Dissolved Substances.Simple thermodynamical considerations lead to the followingequation for the entropy X of ti mol. of perfect monatomic gas, attemperature T and pressure p :0. Sackurz3 showed that the constant So is proportional solely toM3/2, where M is the molecular weight of the gas, and the equationbecomesS = ~ R l o g T - R R ~ g p + S o . . . . , (1)S = $22 log T - R log p + SR log M + [SJo . . . (2)I* J. Arne?. Chem. soc., 1921, 43, 818; A,, 1921, %, 380.20 Ibid., 1923, 45, 80; A . , 1923, ii, 124.* I Ibzd., 1926, 48, 2305; A., 1088.9 1 Ann. Physik, 1908, Gv], 28, 211; A., 1908, ii, 563.23 Ibid., 1911, [iv].36, 958; A . , 1912, ii, 145GENERAL AND PHYSICAL CHEMISTRY. 15where [S], is a universal constant. H. Tetrode, and later S a ~ k u r , ~ ~evaluated this constant from statistical considerations, obtainingthe expressionwhere k is the gas constant per molecule (= R / N ) , r is the electroniccharge and h is Planck’s quantum constant. G. N. Lewisz5 hasalso made a calculation of [S], on the basis of his theory of “ ultimaterational units.” The expression obtained (in the same notation) is[S], = R log { ( 2 ~ ) 3 ’ 2 k 6 ‘ 2 ~ 5 ’ 2 / h 3 } , . . . . (Ba)where c is the velocity of light. The values of these expressionsare - 2.30 (Tetrode) and - 2.63 (Lewis). Experimental valuesare not known with sufficient accuracy to permit a decision betweenthe two expressions, but theoretical considerations appear to favourthe Tetrode expression.z6R.C. Tolman 27 determined the entropies of a number of gasesindirectly from vapour-pressure data and, except in a few casesin which a large extrapolation had to be made, found good agree-ment with (2). Lewis, Gibson, and Latimer28 showed that infour cases for which direct thermal data were available (He, A, Cd,and Hg vapours), there was remarkable agreement between thetheoretical and experimental values. It may be noted, however,that the data were not sufficiently accurate to distinguish betweenthe two values of [S], above. More recently, W. H. Rodebushand A. L. DixonZ9 have determined the entropies of vapoursof zinc and lead by vapour-pressure measurements and findgood agreement with the theoretical values.Similar measure-ments with sodium vapour by Rodebush and T. de Vries30 showonly moderate agreement. Tolman has also shown3’ that if anatmosphere of electrons be considered as a monatomic gas, itsentropy, as nearly as it can be computed from various thermionicdata, agrees with the theoretical value.The molecules of polyatomic gases may possess rotational andvibrational energy which must be taken into account in calculatingtheir entropies. Tolman 32 made the assumption that the entropy24 Ann. Phyaik, 1912, 38, 434; 1913, 40, 67; A., 1913,iL 128. 0. Sterngave a kinetic deduction of the same equation, Physikal. Z., 1913, 14, 629.* $ Physical Rev., 1921, ii, 18, 121.p e Compare H.C. Hicks and A. C. a. Mitchell, J . Amer. Chem. Soc., 1920,17 Ibid., 1920, 42, 1185; A., 1920, ii, 468.Ibid., 1925, 47, 1036; A . , 1925, ii, 492.ao Ibid., p. 2488; A., 1925, ii, 1142.* I Ibid., 1921, 43, 1692; A., 1922, ii, 18.Ibid., 1920, 42, 1185; A., 1920, ii, 468.48, 1520; A., 784.** Loc. cit., ref. (6).LOC. cit., raf. (27)16 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.of any gas is the sum of the entropy of a perfect monatomic gasunder the same conditions and the entropies of its rotational andvibrational energies. These are given by ~2'Cr,d log T, where C, =C,, - 4R is the difference between the actual heat capacity of thegas and the value for a monatomic gas. Only in one case, that ofhydrogen, of which the heat capacity drops to the value for amonatomic gas above its boiling point, can this equation be appliedto experimental data.Attempts have been made to evaluate this integral by theoreticalcalculations of the rotational and vibrational energies.In theca0e of a diatomic gas, it appears that only rotational energyneed be considered. H. C. Urey has to evaluatethe rotational energy of such gases by the uEie of an expressionof F. Reiche34 which gives the rotational energy of a moleculein a state characterised by two quantum numbers n,, n2 ast = P(n, + n2)/8x12, where I is the moment of inertia of themolecule. The relative numbers of molecules in different quantumstates are given by statistical equations ; I is obtained from themaxima A,, h2 of the band spectrum by the classical equationI = k T [ h , h , / x c ( ~ , - A,)],. Similar methods are applied to sym-metrical polyatomic gases, e.g., methane. R.C. Tolman andR. M. Badger extended this method,35 and recently H. C. Hicksand A. C. G. Mitchells6 have made a careful study of hydrogenchloride from the same point of view. Using '' half quantum "numbers to specify the possible rotational states of the moleculethey find the value of j C r d log T between 0" K. and 298" K. to be6.75. The value of the total entropy obtained by adding this tothe corresponding entropy for a monatomic gas agrees well withthe experimental figure.Another method of dealing with rotational energies is by theuse of an equation37 deduced by 0.Sackur, H. Tetrode, andothers :Good agreement was found in this case.S = SR log T + +R log M + R log V + S+R log I , , , , + S, . (3)$8 J . Amer. Chem. SOC., 1923, 46, 1446; A , , 1923, ii, 633.Ann. Phyaik, 1919, [iv], 58, 667.J . Amw. Chem. Soc., 1923, 46, 2277; A . , 1923, ii, 830.34 J . AWT. Chem. SOC., 1926, 48, 1620; A., 784.'7 0. Sackur, Ann. Physik, 1913, [iv], 40, 87; A . , 1913, ii, 128; H. Tetrode,ibid., 1912, [iv], 38, 441: L. Schames, PhyhkuZ. Z., 1920, 21, 38; A . , 1920,ii, 172; R. C. Tolman, J . Amer. Chem. Soc., 1921, 45, 866; A., 1921, ii, 381;P. Ehrenfest and V. Trkal, PTOC. K . Akad. Wetemch. Amsterdam, 1920, 23,162; A., 1920, ii, 738; Ann. Phyaik, 1921, 66, 609.Compare R. C.Tolrnan, Phy8iCd Rev., 1923, ii, 22, 470.LOC.cit., ref. (26)GENERAL AND PHYSICAL CHEMISTRY. 17where I,, I,, I , are the moments of inertia. This equation cannotbe employed directly, owing t o lack of information about momentsof inertia. Urey expressed- his results in terms of this equation,substituting the moments of inertia obtained by the methoddescribed above. Latimer and Eastman 38 have given variousempirical equations for the entropies of diatomic gases.A further important advance in this field has been made byW. M. Latimer and R. M. B~ffington,~~ who have calculated forthe f i s t time the entropies of inorganic ions in aqueous solution.Knowing the entropies of the solid salts and the heat-content andfree-energy changes on solution, it is possible to calculate theirentropies in solution.The entropies are obtained for a “hypo-thetical molar concentration,” i.e., they are obtained from dataat very small concentrations and converted to the correspondingvalues at unit (molar) concentration on the assumption that thesolution remains ideal. Although expressed as entropies in a(hypothetical) molar solution, they refer therefore to the propertiesof ions a t great dilutions.It is only possible to obtain in this way the sum of the entropiesof the ions of the salts; but relative values for individual ions,referred to the entropy of the hydrogen ion as zero, are readilyobtained and are sufficient for most purposes. The authors furthercalculated the entropies of the ions in the gaseous state by theequation for perfect gases and thus obtained values for the entropiesof solution of gaseous ions.The values so obtained exhibit aremarkable parallelism with the energies of solution of the gaseousions.@ Further, when these entropies were plotted against theatomic radii of the ions as deduced from the crystal measurementsof W. H. and W. L. Bragg, a linear relationship was discovered forions of each charge. It is concluded that the entropy of solutionof gaseous ions is to a high degree a function solely of the size andcharge of the ion.The relative entropies of ions in aqueous solution can be appliedt o a great variety of thermodynamical problems. A number ofexamples are given in this paper, and in a further paper W. M.Latimer 41 has used the data to calculate the normal potential ofthe fluorine electrode.3 8 LOC.cit., refs. (19) and (20).so J. Amer. Chem. Soc., 1926,48, 2297 ; A., 1102. K. F. Herzfeld attemptedto calculate electrolytic normal potentials on the assumption that the entropiesof dissolved ions are the same as in the gaseous state at the same concen-tration (Ann. Physik, 1918, [iv], 56, 133; A., 1918, ii, 289). Later he reversedthe calculation and estimated from normal potentials and solubilities, the“ bound energy ” (= TJS) of ions relative t o the silver ion (2. Ekktrochem.,1922, 28, 460; A , , 1923, ii, 12).u 1%’. 31. Latimer, ibid., 1926, 48, 1234; A., 648. 41 Ibid., p. 286818 ANNUAL REPORTS ON THE PROQRESS OF CHEMISTRY.Chemical Constants.The so-called '' chemical constants," or integration constantsof the Clausius vapour-pressure relation, d log pjdT = AH/RTe,are intimately connected with the entropies of the correspondinggases.Since investigations in the two fields have been carriedon by different groups of workers practically independently, it isconvenieiit to deal with them separately, but the results in onefield have obvious bearings on the other.In the earlier attempts t o evaluate chemical constants by Nernstand his school, empirical equations for the variations of heatcapacities with temperature were employed which were wide ofthe truth a t low temperature^.^^ The true integration constantis obtained by giving AH its value AH = AHo + I".Cp. dT,where AC, is the difference between the heat capacities of gasand solid, whenceAH,, + /cAC~ dT .dT + i, RT2 RT log p = -and accurate heat-capacity data a t low temperatures are requiredto determine the integration constant i. For a perfect gas havingconstant heat capacity C, down to absolute zero, iR + C, =So - SgS, where S,, is the entropy constant of the gas [equation(l)] and Xos the entropy of the condensed phase a t absolute zero.According to the Nernst heat theorem, S,,s is zero 42a; hence, for amonatomic gas, the Sackur-Tetrode calculation [referred to theabove equation (2a)l leads to the value i = log ( ( Z m ) 3 ' 2 k S / 2 / h 3 } .Using gram-molecular weights and converting to common loga-rithms we obtain the chemical constant C = C, + log,, M , whereC, is a universal constant numerically equal to - 1.589.A.C. G. Egertona collected the available experimental datafor ten substances (based on measured vapour pressures except intwo cases) and obtained a weighted mean - 1.596 f 0.008, ingood agreement with the theoretical value. I?. Simon,M however,using values of C determined for 14 elements, found considerabledeviations which appeared to increase with increasing heat ofvaporisation. Notable divergences are exhibited by the elementssodium and potassium, as first observed by R. Ladenburg andR. Mink~wski.~~ Recent investigations have confirmed these68 Compare A. C . G . Egerton, Phil. Mag., 1920, [vi], 39, 1 ; A., 1920, ii, 84.4Zo According to Lewis and Gibson this must be limited t o crystalline solids,43 Proc.Physical SOC., 1925, 37, 75; A,, 1926, ii, 277.u 2. physikal. Ohem., 1924, 110, 572; A , , 1925, ii, 98; ibid., 1926, 123,4 5 2. Physib, 1921, 8, 137; A., 1932, ii, 191.see ref. (2).404; A., 1103. Compare K. Wohl, ibid., 1924, 110, 166; A., 1926, ii, 98OENBRAL AND PHYSICAL CHEMISTRY. 19discrepancies. F. Simon and W. Zeidler 46 have redetermined theheat capacities of these elements a t low temperatures and obtainvalues of C greater than the theoretical values by + 0.52 f 0.23(Nrt) and + 0.33 0.32 (K). W. Edmondson and E g e r t ~ n , ~ 'whiIst criticising certain of these calculations, have substantiallyconfirmed this result.I n the calculation of the Sackur-Tetrode expression, identical"quantum weight factors" are assigned to solid and vapourphases.If the identity of these factors is not assumed a moregeneral expression is obtained, viz., i = log {gg/g, . ( Z ~ r n ) ~ ' ~ k ~ ' ~ / h ~ ) where gg and gs are the weight factors for the gaseous and solidstates. The nature of the quantum weight factors has been dis-cussed by A. Einstein,48 0. Stern,49 W. Schottky,50 and R. H.F0wler.~1 If gg/g8 = 2, i will be greater than the Sackur-Tetrodevalue by log 2. I n the case of the alkali metals, according toSchottky there is spectroscopic evidence for g, = 2, and if g, = 1the experimental values are approximately accounted for.In the last equation, the term g, refers to the solid (or con-densed) phase. It implies a finite entropy of the condensed phaseSoa = R log g,. A. Eucken and F.Fried 52 have attempted todetermine whether solids have finite entropies a t absolute zeroby comparing the integration constants, ig, of the equilibrium-constant equation of a number of gaseous reactions, with Xi, thealgebraic sum of the vapour-pressure constants of the substancesconcerned. These two quantities are only identical if all valuesof Sos are zero. They find differences outside the experimentalerror in most cases. These would be covered by a zero entropy of& R log 2, but the data are not sufficiently precise for a quantitativeagreement to be made out. Fried 63 has made a further test ofthe same point by determining electromotively the free energyof reactions of the type MO + H, = M + H,O (M = Hg, Pb, or2Ag), and comparing it with calculated values involving the chemicalconstant of hydrogen.It is claimed that the results indicatefinite zero-entropies. It may be observed that it is not entirelyclear that these calculations are always referred to the solids ascondensed phases.Little progress has been made in accounting for the chemical46 2. physikal. Chem., 1926, 123, 383; A., 1103.4 7 Proc. Roy. SOC., 1927, [A], 113, 620, 633.4a Verh. deut. physikal. UM., 1914, 16, 820.4p Ann. Phyeik, 1916, [iv], 49, 823; A., 1916, ii, 379.6 1 Phil. Mag., 1923, [vi], 44, 1, 497; 1926, [vii], 1, 845; A,, 663.62 2. Physik, 1924, 29, 36; A , , 1926, ii, 97.53 2. physikal. Chem., 1926, 123, 406; A., 1105.Physikal. Z . , 1921, 22, 1 ; A., 1921, ii, 179; ibid., 1932, 23, 9, 44820 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.constants of polyatomic molecules.The following equation forthat part of the chemical constant which is dependent on rotationalenergy, i, = log (8x2~kfh2u), where f is the geometrical mean ofthe moments of inertia of the molecule and u a symmetry factor,has been obtained in a number of ways 54 [compare equation (3)].A. Eucken, E. Karwat, and F. Fried55 determined the chemicalconstants of a number of gases and compared them with the valueobtained by adding the above term to the “ monatomic ” constant,using optical values of I and ignoring the factor u. The resultsshowed no concordance, which might be ascribed to the absenceof the factor a. Mention may be made of recent determinationsof chemical constants of the following : Chlorine,66 bromine,57iodine,ss and hydrogen halides.Sg No satisfadtory agreement hasbeen obtained between the values (between which large discrepanciesoften occur) and the theory.In the Seckur-Tetrode calculation, the quantum theory isimplicitly applied to the translational motions of gases, whilst incalculations of chemical constants it is assumed that that part ofthe heat capacity which depends on the translational energy is aconstant down to the absolute zero. W.Nernst 6o employed adegradation theory according to which the heat capacities of gasesfell off a t low temperatures in the same way as do those of solids,and obtained a value i = log ((2m)3’2k5’2/&3}, which is almost indis-tinguishable numerically from the Sackur-Tetrode value.Theconditions which must be fulfilled by a gas the heat capacity ofwhich falls off to zero at absolute zero have been examined byK. Bennewitz,61 whilst the difficult question of the applicabilityof quantum theory to the translational motions in gases has beendiscussed by several authors.62 F. I. G. Rawlins 63 has recently64 Ref. (37). Also M. Saha and R. Sur, Phil. Mag., 1926, [vii], 1, 279;A., 234; K. SzBll, 2. Physik, 1926, 36, 292; A., 570.6 6 2. Physilc, 1924, 29, 1 ; A., 1925, ii, 98; ah0 A. Eucken and E. Karwat,2. phyeikal. Chem., 1924, 112, 467; A., 1924, ii, 820.6 6 R. R. S . Cox, Proc. Cantb. Phil. SOC., 1926, 22, 491; A., 1025, ii, 645.6 7 R. Suhrmann and K. von Liide, 2. Physik, 1924,29, 71 ; A., 1925, ii, 96;sn K.Jellinek and R. Uloth, ibid., 161, 157; A., 463.00 Z. Ekktrochem., 1916, 22, 185; A., 1916, u, 469.e2 A. Einstein, Sitzungsber. Preuss. Akad. Wisa. Berlin, 1924, 261 ; 1925, 3,18; A., 1925, ii, 405, 624; M. Planck, ibid., 1925, 49; A., 1925, ii, 495; A.Schidlof, Arch. Sci. phys. nat., 1924, [v], 6, 281, 381; A . , 1925, ii, 483;ibid., 1926, [v]. 8, 5 ; A., 463; E Schrodinger, Sitzungaber. Preusa. Akad.Wias. Berlin, 1925, 434 ; A+, 1926, ii, 951 ; Physzkd. Z., 1926, 27, 95; A,,463.K. Jellinek, 2. anorg. Chem., 1926, 152, 16; A,, 569.F. I. G. Rawlins, Trans. Fwaday Soc., 1926, 22, 233; A., 1087.2. phyrikal. Chem., 1924, 110, 725; A , , 1925, ii, 97.Proc. Physical Soc., 1916, 38, 176; A., 567GENERAL AND PHYSICAL CHEMISTRY, 21summarised some aspects of the present state of knowledge ofspeoific heats a t low temperatures and chemical constants.Solutions of Electrolytes.In continuation of the1925 Report,l the following investigations for the purpose of furthertesting the Debye-Huckel theory of strong electrolytes may benoted.The limiting law for tervalent ions has been confirmed bysolubility measurements of [Co(NH3) a)"'[Co(CN)6]"' in sodiumchloride solutions.2 The effect of the dielectric constant of themedium has been confirmed by measurements of the activitycoefficients of hydrogen chloride in aqueous glycerol ~olutions,~and by similar measurements in sucrose solutior~s.~ The effect oftemperature as predicted by the theory has been confirmed bysolubility measurements of silver iodate a t 75".The theory hasbeen tested in certain non-aqueous solvents.has studied the freezing-point depressions of some salts in aceticacid and in liquid ammonia, obtaining results which are mainlyin agreement with the theory. Similar measurements with cyclo-hexanol as solvent show good agreement with the equations.'In his extension of the theory to concentrated solutions, it willbe remembered that E. Huckel attempted to take into account theeffect of varying dielectric constant of the solutions, and, on theassumption that the dielectric constant varies linearly with the ionconcentrations (i.e., D = Do - S c ) , he found that the correspondingterm in the expression for log f was approximately proportionalto the concentration.8 G.Scatchard9 has tested this equationfor aqueous and alcoholic solutions of hydrogen chloride, and findsthat it is in good agreement with the data up to 1M. H. S. Harned 10has studied the activity coefficients of hydrogen chloride in con-centrated chloride solutions with the same object, and finds thatthere is " remarkable agreement between the observed resultsand the general theory of Debye and Huckel. In fact, nothingAnn. Report, 1025, 22, 27.J. N. Bronsted and N. J. Brumbaugh, ,J. Amer. Chem. SOC., 1026, 48,2015; A,, 907.W. W. Lucasse, 2. phyaikal. Chem., 1926, 121, 254; A., 796; J. Amer.Chem. SOC., 1926, 48, 626; A., 474.G. Scatchard, ibid., p. 2026; A., 911.W. P. Baxter, ibid., p. 616; A., 474.Ibid., p.2263; A,, 1102. ' E. Schreiner and 0. R. Frivold, Z. physikal. Chem., 1926, 124, 1 ; A,,* Ann. Report, 1925, 22, 34, equation (6).J. Amer. Chem. SOC., 1926, 47, 2098; A., 1925, ii, 971.Rapid progress continues in this field.Thus T. J. Webb1208.io .Tbid., 1926, 48, 326; A,, 35422 ANNUAL REPORTS ON THE PROQRESS OF CHEMISTRY.seriously contradictory to their general theory has developed fromthe numerous results on chloride solutions considered,’’ It isfound that in solutions of constant total ionic strength logfH,,is proportional to its concentration up to 3M. Values of 6 for thesalts are obtained from the Huckel expression, and making thearbitrary assumption that BE. = Sa,, relative values are obtainedfor the ions. In the case of lithium and hydrogen chlorides, thesevalues are so great as to lead to negative values of the dielectricconstant in solutions above 4M.It is suggested that the linearvariation of log f with concentration (when interionic electricaleffects according to the simpler theory have already been takeninto account) has a deeper significance than Hiickel’s theory implies.G. Akerlof has made a similar study of sulphate solutions.11 Thevalue of 6 for the sulphate ion is negative, ie., it is more polarisablethan water and increases the dielectric constant of the medium.All the available data of single and mixed salt solutions are collectedin a paper by H. S. Harned and G. Akerl6f.l2 Good agreementwith the Huckel expression is exhibited in solutions of singleelectrolytes, but only moderate agreement in mixed electrolytes.kerlof 13 has further put forward the idea that the solubility ofa salt is higher the greater its effect (positive or negative) on thedielectric constant of the medium, Using the values of 6 obtainedabove, he shows that there is a close parallelism between the twoquantities.The linear variation of log f with concentration has also beenconikmed by E.Guntelberg 1* for hydrochloric acid in (HC1, MCI)mixtures of constant total-ion concentration. This is shown tobe a consequence of J. N. Bronsted’s rule l5 of the linear variationof the osmotic coefficient in such solutions, and to apply only tomixtures of salts of the same ion-type. The same author hasdiscussed BrBnsted’s principle of the specific interaction of ions lSand its relation to the Debye-Hiickel theory.According to thisprinciple, the activity coe&cient of an ion is made up of two factors :(1) a coeficient of interaction between the ion and other ionspresent, and (2) a “ salting-out ’’ coefficient depending solely onthe other ions present. I n factor (l), it is supposed that ions areuniformly influenced by ions of their own sign and that specificeffects arise only from the interaction of ions of opposite sign.The physical basis of this principle is found in the Debye-Huckell1 J. Amer. Chem. Soc., 1926, 48, 1160; A,, 688.Physikal. Z . , 1926, 27, 411; A., 796.l3 J . Physical Chem., 1926, 30, 1585.l4 2. phpikal. Chem., 1926,123, 199; A., 1207.l6 J.A m . Chem. Soc,, 1922, 44, 877; A,, 1932, ii, 481; ibid., 1923, 45,2898; A., 1924, ii 94GENERAL AND PHYSICAL CHEMISTRY. 23conception, according to which there is in the immediate vicinityof any one ion, a great preponderance of ions of the opposite signand these only are responsible for the specific effects. The Debye-Huckel theory appears to be superior in that it obtains directlythe interionic electrical effects of all kinds. Bronsted‘s formulationis, however, advantageous in the interpretation of relations incertain types of mixed salt solutions (e.g., solubilities of slightlysoluble salts in solutions of various ion-types).I n the last Report, it was pointed out that there is a differencebetween the Milner and the Debye and Hiickel calculations of theinterionic electrical energy (the former being two-thirds of thelatter).This difference has now been elucidated. E. Q. Adamshas pointed out that the quantity obtained by Debye and Hiickelin their first calculation is the free energy change (AF) due tointerionic electrical forces, in the trawfer of ions from a givensolution t o a very dilute solution in which electrical forces arenegligible. Debye and Huckel directly evaluated, in fact, theelectrical work done in removing an ion from its ion atmosphere.Milner, on the other hand, calculated the electrical work done inseparating the ions of a given solution to an infinite distance fromone another. This is the maximum (electrical) work done in aninfinite dilution ( A ; Adams’s AA).Since the latter is two-thirdsof the former, the discrepancy is explained.Debye and Huckel regarded the quantity obtained by themas the mutual potential energy of the ions in solution (U,) andattempted to determine the corresponding work term by meansof the Gibbs-Helmholtz equation AIT = - J U e / T 2 . dT. Inorder to get a result of the correct form, they were obliged to treatthe dielectric constant as independent of the temperature. SinceU, is itself a free-energy quantity, it is necessary to reverse thisprocess to get the true total-energy change. In this way, E. Q.Adams and N. Bjerrum 17 h d that the heat of dilution of a saltsolution is given by AU = - +A(1 + d log Did log T). N. Bjerrumapproaches the matter on the basis of Debye’s second calculation,in which he obtained the electrical work of charging all the ionsin the solution (reversibly) simultaneously.This corresponds to A ,the electrical work of dilution. Debye calculated the correspond-ing free energies of transfer of ions by obtaining the differential ofA for a small addition of one ion species :SA/Sni = Ai = - ~ ~ u z i 2 / 2 0 .Bjerrum greatly simplified the derivation by showing that thel6 J . Amer. Chent. Soc., 1926, 48, 621; A., 474.l7 2. physikal. Chern., 1926, 119, 146; A,, 47624 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.same result may be obtained by considering the electrical work ofcharging a single ion in the given solution. J. A. V. Butler I* hasshown by an independent argument that the quant.ity so obtainedis in reality a free-energy quantity.There appears to be considerable uncertainty about the valueof d log Did log T above; Adams gives - 1.5, Bjerrum - 1.315.Apart from this, Bjerrum compared recorded heats of dilution ofsalt solutions with this equation.The experimental figures (neces-sarily referring to moderately concentrated solutions) are highlyspecific and show little relation to the calculated value. W. Nernstand W. Orthmann l9 have determined the heats of dilution ofsome salts a t very low concentrations. They find even among saltsof the same ion-type no agreement with the equat,ion; in fact,some give positive and others negative values. The theory ofthe heat eflects corresponding to the free-energy changes is thereforeunsatisfactory.that Milner’s theoryaccounts better than Debye’a for the activity coefficients of hydrogenchloride in methyl alcohol is disputed by G.Scatchard.21 Theformer authors, however, questionz2 his method of dealing withthe data. G. NonhebelB has investigated the activity coefficientsof hydrochloric acid a t extreme dilutions. He finds that theequation log,, f = - 0.39fi best fits the results; the Debye-Hiickel theory gives logl, ,f = - 0*5051/& whilst Milner’s givesapproximately log,, f = - 0.37dC.The problem of the determination of the activity coefficients ofan individual ion-species in a salt solution has received some atten-tion. If the activity coeEcients of one kind of ion (e.g., chlorineion) of a salt were known, it would be possible, by correlating thesalts, to determine them in all cases. D.A. MacInnes 24 attemptedthis method by making the assumption that the two ions of potassiumchloride (which have nearly the same weight and mobility) havethe same activity coefficients a t each concentration. G. N. Lewisand M. Randall adopted the same assumption.26The individual activity coefficients could be measured directlyin a concentration cell ‘( with transport ” if the value of the liquid-junction potential were known, since the E.M.F. of such a cellThe claim of G. Nonhebel and H. Hartley18 Phil. Mag., 1927, [vii], 3, 213.1) Sitzungsber. Preuss. Akad. Wias. Berlin, 1926, 51; A,, 579.20 Ann. Repurt, 1925, 22, 33.2 1 Phil. Mug., 1926, [vii], 2, 577; A., 1006.22 IW., p.586; A., 1006. Is Ibid., p. 1085.24 J . Amer. Chem. Soc., 1919, 41, 1086; A., 1919, ii, 385; ibid., 1921, 48,‘ 5 “ Thermodynamios,” 1923, p. 381.1217; A., 1921, ii, 619QENERAL AND PFIYSICAL CHEMISTRY. 25(e.g., H,(HClcllHClc21H2) is given by RT/F . log al/a, + EL,where EL is the liquid-junction potential. If. S. Harned26 hassubjected the '' thermodynamic method " of computing liquid-junction potentials, first used by D. A. MacInnes and J. A. Beattie,27t o a rigorous analysis and has obtained data for the individual ionactivities in mixed chloride solutions.According t o the theory of electrolytic dissociation as formulatedby Arrhenius, the degree of dissociation of an electrolyte is givenby a = &/Am. In the case of strong electrolytes, a decisive massof evidence indicates that dissociation is complete at all dilutions,and variations in the equivalent conductivity A, must be ascribedto changes in the ionic mobilities with concentration.The dis-sociation of weak electrolytes, formerly calculated by the sameformula, must now be corrected for variations in the ionic mobilities.M. S. Sherrill and A. A. Noyes 28 have considered several cases of'' moderately ionised " acids. The true degree of dissociation isgiven, not by &/A, but by A,/&, where A, is the value of theequivalent conductivity for complete dissociation a t the particularconcentration measured. Values of A, are obtained by the Kohl-rausch rule from the equivalent conductivities of completely ionisedsubstances a t the same concentrations, thus :(&)c HA = HC1 f NEA - NaCI.The ionisation constants obtained from the true degrees of dis-sociation are further corrected for the effect of electrical forces bymultiplying each ionic concentration by its activity coefficient,thus : KHr = (fH.a)(fAp a ) / ( l - a)c. In this way, satisfactoryconstants are obtained for the first atage of ionisation of phosphoricand sulphurous acids, and for the second stage of ionisation ofsulphuric acid, assuming in the last case that the first hydrogen iscompletely ionised. D. A. MacInnes 29 has applied similar methodsto a number of weak acids and obtains excellent constants, exceptin the case of acetic acid, in which the values show a definite trendwith concentration. This may be due to inaccurate data, or, it issuggested, to the effect of variations in the dielectric constant ofthe solution, which are not taken into account.The variation of the ionic concentration of water in salt solutionshas been studied.The true equilibrium constant of the ionisationof water is the activity constantKw = UH. . ~ O H . / ~ H , O = fH* . foHI . mw2/aHa0,where m, is the concentration of hydrogen and hydroxyl ions in26 J . Physical Chem., 1926, 80, 433.27 J . Amer. Chern. SOL, 1920, 42, 1117; A , , 1920, ii, 466.Ibid., 1926, 48, 1861; A,, 1006. *I IM., p. 2068; A., 90686 ANNUAL REPORTS ON THE PROORISS OF CHEMISTRY.the solution. An increase of the dissociation of water and otherweak electrolytes on the addition of salts was predicted by J.N.Br8nated.30 Since the activity coefficients of ions initially decreasewith increasing total-ion concentration, the concentrations rn,must increase in order to maintain the equilibrium constant. E.Schreiner31 made some exact calculations of the effect on thebasis of equations representing the effect of salt concentration onactivity coefficients. The older electromotive methods of deter-mining the ionic product of water involved cells with liquid junctions.A new method of determining relative values of the “activitycoefficient product,” fH. . foBt/aRIO, from a combination of datafrom cells without liquid junctions, has been developed.32 Whenthis quantity is known, the ionic concentrations can be determined,suce m, = mB.= may. = u, =. . on. axso). e dissociationof water in solutions of potassium and sodium chlorides,32bromides,33 and sulphates 34 and of lithium chloride 35 has beendetermined in this way. The curves for the alkali-halide solutionsare given m Fig. 1. The dissociation rises t o a maximum a t aboutao J . Amev. Chem. SOC., 1920, 42, 781; J., 1921, 119, 574.31 2. anorg. Chem., 1924, 135, 3 5 7 ; A., 1924, ii, 524.aa H. S. Harned and G. M. James, J. Physical Chem., 1926, 30, 1060; A.,s4 G. Akerlof, Zoc. cit., Ref. (11).36 H. S. Harned and F. E. Swindells, J. Amer. Chem. Sot., 1926, 48;126;l/K-l(f- -~-.~ --- ThH. S. Harned, J . Amer. Chem. SOC., 1925, 47, 930; A , , 1925, ii, 538.907.A,, 246GENERAL AND PHYSICAL CHEMISTRY.270 4 N . I n the sulphate solutions, the maximum value is greaterand the curve flatter.J. Colvin 36 has determined the ion-activity product of water inaqueous glycerol solutions, up to 40% glycerol, by means of electro-motive measurements involving liquid junctions. He h d s thatthe dissociation constant of water remains practically unchangedover the whole range.Ion Hydration in Aqueous Xolution.A number of determinations of the degree of hydration of ionsin aqueous solutions, by means of distribution experiments, haveappeared. The principle of the method, first employed by J. C.Philip,37 is that if the ions are combined with water, the amountof " free water " available for dissolving another substance isreduced.The distribution of a suitable substance between a non-aqueous solvent and the salt solution is studied. Assuming thatthe true distribution coefficient between the solvent and the " freewater " is the same as in pure water, the amount of " free water )'can be determined, and hence the amount combined with the ions.J. N. Sugden38 has made an extensive series of measurements ofthe distribution of acetic acid between amyl alcohol and salt solu-tions, and has deduced the corresponding hydration figures. Exceptin the case of sulphates, the hydration values so obtained arepractically independent of the concentration and, further, areadditive for the ions of salts. Nitrates and chlorates were foundto have negative hydration values, i.e., they increase the apparentamount of water.Relations between the hydration figures andthe viscosity and also the molecular conductivity a t infinite dilutionwere found. For these reference must be made to the paper.Similar measurements have been made by 8. Glasstone and col-l a b o r a t o r ~ , ~ ~ who have determined the solubilities of ethyl acetatein salt and other solutions, and by H. A. Tayl~r,~O who determinedthe partition ratio of hydrogen chloride between benzene and saltsolutions. The latter concluded that there is no appreciabledifference between " free " and combined water, the aqueoussolutions behaving like pure water.It should be observed that the validity of this method dependsa s J., 1925, 127, 2788; A., 246.3 7 Trans. Faraday SOC., 1907, 3, 140; A., 1907, ii, 935; J ., 1907, 91, 711.a s J . , 1926, 174; A., 244.88 S Glasstone and A. Pound, ibid., 1925, 12'7, 2660; A,, 1926, 18; S.Glasstone, D. W. Dimond, and E. C . Jones, ibid., 1926, 2936; S. Glasstone,D. W. Dimond, and E. R. Harris, ibid., p. 2939.Compme J. W.Corran and W. C. McC. Lewis, J . Amw. Chem. SOC., 1922, 44, 1673; A., 1922,ii, 691.J . Physical Chem., 1926, 29, 995; A , . 1925, ii, 85828 ANNUAL REPORTS ON TEE PROGRESS OX CEEMIBTRY.entirely on the truth of the assumption that the solubility in the'' free " water of a salt solution is the same as in pure water. Themeasurements give primarily the relative activity coefficiente ofthe solute employed in various salt solutions, and the relationsfound are not necessarily to be interpreted aa the result of hydration,The problem is identical with that of the " salting-out " effect ofelectrolytes on non-electrolytes, which has recently received muchattention.In many cases, in dilute solutions a t any rate, the effect of anelectrolyte on the solubility of a non-electrolyte is given by V.Rothmund's equation,41 log so/s = kc, where so is the solubilityin water, and s that in a salt solution of concentration c.J. 8.Carter 42 has found that the solubility of iodine in salt solutionscan in most cases be represented by this equation. K. Linder-strom-Lang 43 has made an extensive series of determinations ofk for hydroquinone, quinone, boric acid, and succinic acid. Ageneral explanation of the effect has not been found. A.McKeowniound,44 using P. C. L. Thorne's that there was a correlationbetween the effect of sodium chloride on the solubility of ether inaqueous solutions and its effect on the heat of solution, a relationwhich has a statistical basis. Linderstrom-Lang finds that thisis not general.According to P. Debye and J. McAulay4s the effect is due tothe influence of the electric field of ions on other components of asolution, which causes the more polarisable molecules to amassthemselves round the ion, and the less polarisable molecules to bedisplaced from the vicinity of ions. McAulay4? has consideredthe efiect of non-electrolytes on the solubilities of salts from thesame point of view. He deduces a relation between the dielectricconstant of the solvent and solubility, which accounts fairly wellfor the solubilities of aalts in alcohol-water mixtures.He furtheroutlines a theory suggested by Debye, of which greater detail ispromised later, in which the distribution of water and alcoholmolecules is given as a function of the distance from an ion. Thecurves show that the proportion of molecules of water (the morepolarisable constituent) to alcohol increases rapidly a t 1-2 A.V.from the ion.A new approach from which, it appears, conclusive evidence41 2. physikal. Chem., 1900, 33, 401; d., 1900, ii, 467; ibid., 1909, 69,623; A . , 1909, ii, 980; also Setschenov, ibid., 1889, 4, 117; A . , 1889, 1044.J . , 1925,137, 2861; A,, 236.J . Amcr. Chem. Sococ., 1922, 44, 1203; A ., 1922, ii, 552.43 Compt. rend. Trav. Lab. CarBberg, 1924, 16, 1 ; A., 1925, ii, 30.45 J . , 1921, 119, 262. '' J . Physical Chem., 1926, 30, 1202; A., 1089.4 8 d n n . Report, 1926, 22, 35QENERAL AND PHYSICAL CHEMISTRY. 29as to the nature of the hydration of ions may be obtained, has beenopened up by the study of the energy changes in the solution ofgaseous ions. These may be determined from certain atomisticdata.40 W. M. Latimer 49 has made some new calculations of theenergy of solution of gaseous ions in water, making use of his ionicentropies, and finds a remarkable agreement between his valuesand those calculated by the expression of M. Born,50 AE = (e2/2r)(l -l/B), wherer is the radius of an ion.of charge e , and D is the dielectricconstant of the solvent, using the ionic radii calculated by W.H.and W. L. Bragg from crystal measurements. This equation is asimple electrostatic expression for the energy change in bringinga charged sphere into a medium of dielectric constant D. Latimer’srelation, already described,51 that the entropies of solution ofgaseous ions of one sign vary linearly with the game radii, againshows that the energy effects on the solution of gaseous ions aredetermined by their size and charge. In very dilute solutions, thereis no evidence of specific ion-water combinations, though in con-centrated solution specific effects depending on the nature of theion may come in.T. J. Webb has attempted a direct calculation of the free energiesof solution of gaseous This quantity is regarded as beingmade up of two parts : (1) the difference between the energyrequired to charge the ion in the solution and in a vacuum ; and(2) the work done in compressing the solvent owing to the effectof an electric field on the solvent “ dipoles.” The free energy ofhydration is obtained as a function of the radius of the ‘‘ cavity )’containing the ion in the solution.This radius is obtained byuse of the partial volumes of salts in solution. The apparentvolume of a salt in solution is equal to the volumes of the ion cavities,less the contraction caused in the solution (electrostriction). Anexpression is deduced for the last quantity and by a combinationof the equations it is possible to determine the radii of the ioncavities and the free energies of hydration.The values are checkedby determining some corresponding lattice-energies of solid saltsand electron affinities of halogens. It may be also observed thatK. Jabtczyhki determined limiting volumes of salts in solutionand found values in agreement with the crystal measurements ofBragg.Compare A. Gyemant, 2. Physik, 1924, 30,540.4 6 Ann. Report, 1920, 17, 3.49 J . Amer. Chm. Soc., 1926, 48, 1234; A., 684.so 2. Physik, 1920, 1, 46.I2 PTOC. Not. A d . Sci., 1926, 12, 624; A., 1008; J. A m r . Chem. Soc.,6B Rcoz. Chem., 1923, 3, 362; A.. 1926, ii, 33.61 This Report, p. 17.1926, 48, 2689 j A.. 120890 ANNUAL REPORTS ON THE PROGRESS OF CHB3IISTRP.Velocity of Reaction in Solutions.As indicated in previous Reports,l research in this field, includingthe study of ion catalysis and salt action, has been much concernedwith the significance of thermodynamic activity as a factor deter-mining reaction velocity.Although this question is still open,there appears to be a fairly general conviction that activity is animportant factor. The bearing of the modern theory of electrolytesis beginning to be explored.J. N. Bronsted2 has attempted a general formulation of thefactors governing the rate of ionic reactions in dilute solutions,especially the kinetic salt effect, which is, broadly speaking, muchgreater in reactions between ions than between neutral moleculesor neutral molecules and ions. Thermodynamical considerations,supplemented by the hypothesis that the rate of a reaction A + B =C + D i~ determined by the rate of formation of an unstableintermediate complex A,B (“ critical complex ”), lead to an expres-sion for the velocity, v = k .C A C B , f&fB/fn,B (f is the activitycoefficient), provided that a change of the medium (as, e.g., inchange of ion concentration) involves only activity, not concen-tration, change of the substrate. The charge of A,B is the algebraicsum of that of A and B. Taking the activity coefficients of ionsto be determined only by their charges and the total ion con-centration, and assuming A,B to behave as an ordinary ion, thesign and approximate magnitude of the activity factor F = fzAfa.f(8A+cg) can be evaluated from activity data or from the approxim-ate relation 3 log f = - z2di, where x is the charge of the ion andthe ionic strength, whence v = kCACBe2zAzbdi approximately.For a reaction between a neutral molecule and an ion, F evidentlyrepresents the salt effect on the activity of the former, which, indilute solution, is relatively small and approximately linear.Forreactions between ions, considerable (exponential) salt effects areindicated-positive if the reacting ions have the same, negative ifdifferent signs. Experimental data agree with the theory, butnot always quantitatively.4 The influence of ions increases rapidlywith their valency. In accordance with Bronsted’s ii principle ofthe specific interaction of ions,” the activity coefficient of a1 Ann. Report, 1922, 19, 18; 1924, 21, 34; H.S. Taylor, “PhysicalChemistry,” p. 779.a 2. physikal. Chem., 1922, 102, 169; A , , 1922, ii, 699; ibid., 1925, 115,337; A., 1925, ii, 681.J. N. Bronsted and V. K. La Mer, J . Amer. Chem. Soc., 1924, 46, 555;A,, 1924, ii, 306.A large number of examples are given by J. N. Bronsted, lac. c i t . , ref. (2).6 See this Report, p. 22GENERAL AND PWSICAL CHEMISTRY. 31reactant ion is chiefly influenced by ions of the opposite sign,especially if multivalent.Although recognising its practical value, N. Bjerrum6 andJ. A. Chriatiansen 7 criticise the theoretical basis of Bronsted’sformula, which, however, the former deduces by assuming a differentmechanism of reaction, and also from the kinetic theory. Christian-sen obtains an expression in formal agreement with Bronsted’sby applying the kinetic equation for a gas reaction to solutions,8account being taken of the increased “ inactivation factor,” andespecially of the effect of interionic forces in modifying collisionfrequency and concentration near an ion.The nature and difficultiesof the problem are further exemplified in relation to a study of thereaction between hydrogen peroxide and iodine in which thesalt effect-slightly positive for the salt type Kc1, slightly negativefor the type K,SO,, positive and greater for the type BaCl,-isattributed to changes in the proportion of hydrogen peroxide towater molecules around an iodine ion following the influence onits electric field of the surrounding cations.Factors such as therelative volumes, polarisability, and dipole properties of thesemolecules may be 0perati~e.l~has given a very general kinetic interpretationof activity by which he claims to justify the expression of reactionrates in terms of activities when rates are defined as “ moles trans-formed in 1 mole of all components.” With this modification, heis in agreement with the Bronsted expression.Brief reference may be made to recent studies of reactions betweenions :(1) lorn of the Sffime sign (Strong positive salt effect).-(@) Ter-molecular reduction of ferric chloride by stannous chloride : l2bivalent have twice the effect of univalent cations, and the reactionis bimolecular a t high salt concentration. (6) Bimolecular reactionbetween the cations of mercuric nitrate and chloropentammino-cobaltic nitrate : 13 anions are much more effective than cations.G .Scatchard2. physikal. Chem., 1924, 108, 82; A , , 1924, ii, 240; ibid., 1925, 118,251; A., 131. ’ Ibid., 1924, 113, 35; A., 1925, ii, 47.Previously considered by M. Trautz, 2. anorg. Chem., 1919,106, 149; A.,J. A. Christiansen, 2. physikal. Chem., 1925, 117, 433; A., 1926, 33.See in this connexion Ann. Beport, 1925, 22, 35; this Report. p. 28.J. Amel. Chem. SOC., 1923, 45, 1681; A., 1923, 5, 626,U’. F. Timofbev, G. E. Muohin, and W, G. Gurevitsch, 2. physikal. Chem.,l3 J. N. Bronsted and C. E. Teeter, J . Phyaicul Chem., 1924, 28, 670; d.,1919, ii, 327.1935, 115, 161 ; A., 1926, ii, 686.1924, ii, 74532 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.( G ) Oxidation of iodide by ferricyanide.14 (d) Saponification ofesters of dibasic acids : l5 the first stage shows a small (linear) salteffect, the second a large positive (exponential) effect-the cationiccharge is the chief factor and the activity factor P calculated fromthe ionic strength accounts for the observed rates.( e ) The photo-decomposition of uranyl formate in formic acid : 16 the magnitudesof salt effects are in good accord with Brbnsted’s theory.(2) Ions of Opposite sign (Strong negative salt effect).-@) Re-action between hydrogen, iodine, and iodate ions; here the salteffect is quantitatively accounted for by the factor F = 1 0 - 2 . 2 0 J 2 ~over a considerable range of ion concentration.The factor 2.20is greater than the value calculated from the Debye theory. Thereaction in acetate buffers is accounted for in a similar way.17( b ) Reduction of ferric salts by thiosulphate.l*When the reacting system contains a weak electrolyte the additionof neutral salt may displace its equilibrium,19 and the consequentchange of concentration gives rise to a “secondary salt effect,”the “primary effect” being due to activity change on1y.m Theformer depends on salt effects on the activity factor in the expres-sion for the dissociation constant of the weak electrolyte :K = (~Ac*l[B,I/~(AB),l)(f,f,/f,) ;such activity effects can be calculated approximately on t,he basisof the interionic-attraction theory. The salt action is positive ornegative according to the type of weak electrolyte.Writing theequilibrium as A + B =e C + catalyst ion, the general rule is :As the sum of the squares of the ionic charges of the reactants isgreater or less than this sum for the resultants, so the secondarysalt effect is negative or positive. This principle has been experi-mentally verified.20 The catalytic decomposition of nitrosotri-acetonamine by hydroxyl ions shows, e.g., a positive effect in thepresence of piperidine, negative in the presence of phosphate , andvery little effect, as expected, in the presence of sodium amino-acetate 2 1 (NH,CH,GOO’ + H,O + NH,*CH,*CO,H + OH’).14 C. Wagner, 2. physikal. Chem., 1924, 113, 201; A., 1925, ii, 49.1 5 J. N. Bronsted and A. Delbanco, 2. anorg.Chenb., 1925, 144, 248; A , ,1 6 G. Berger, Rec. trav. chim., 1925, 44, 47; A., 1925, ii, 313.1 7 E. Abel and F. Stadler, 2. phpikal. Chem., 1926, 122, 49; A,, 1009.18 J. Hollute and A. Martini, 2. anorg. Chem., 1924, 140, 206; 141, 23;19 J. N. Bronsted, J . , 1921, 119, 674.20 Ref. (13); J. N. Bronsted and C. V. King, J . Amer. Chem. Soc., 1925, 47,2 523; A., 1925, ii, 1171; J. N. Bronsted and K. Pedersen, 2. physikal. Chem.,1924, 108, 186; A . , 1924, ii, 331.1925, ii, 684.1925, 144, 321; A , , 1925, ii, 305, 215, 702.11 ill. alpatrick, J . Amer. Cheat. Soc., 1926, 48, 2091; A., 919GENERAL AND PHYSICAL CHEMISTRY. 33(3) Ions and Neutral Molecules.-It is in the large class of reactionsbetween neutral molecules and ions, including ion catalysis, thatthe question of the significance of activity has received the mostattention.The unirnolecular decomposition of hydrogen peroxide 22in bromine-bromide solutions (virtually, catalysis by hydrogenbromide of constant concentration) is given by the equat'ion- d[H,O,l/dt = kJH,O,I[H'I"r'] ,fkmfor ionic strengths not exceeding 1.0 ; the * ' concentration !' velocitycoefficient k, (in contrast with the " act,ivity ? ' velocity coefficient,k,) shows a marked drift,. Similar relations apply to the chlorine-chloride reaction.22 J. A. Christiansen % has criticised this formul-ation in the particular case of the above react'ion. Thc conversionof 3-chloroacetanilidc into p-chloroacet,anilide 24 is exactly pro-portional t o the activit'y product of t'he hydrogen chloride catalyst.The rate of addition of hydrogen chloride to quinone in ethyl-alcoholic solution is stated 25 to be governed by the activity productof the hydrogen and chlorine ions. Proportionality between rateand activity is also supported in studies of the reaction betweenformic acid and bromine or iodine.268.W. Pennycuick 27 has attempted to settle the disputed questionwhether the inversion of sucrose follows strictly the unimolecularlaw. His very accurate measurements 28 show a small increaseof k during reaction. Postulating that water molecules are activ-ated by association with hydrogen ions, w = k [sugar mols. per mol.H,0][H',nH20], the last term being assumed proportional to thehydrogen-ion activity which does apparently increase slightlyduring inversion.Previous investigators 29 found no evidence ofthe latter, but T. W. J. Taylor and It. F. Bomford30 observed a7% increase in the presence of salt. G. Scatchard's31 analysis2 z W. C. Bray and/or R. S. Livingston, ibi&., 1913, 45, 1251; A , , 1923,ii, 473; ibid., p. 2048; A . , 1023, ii, 747; ibid., 1915, 47, 2069; A . , 1925,ii, 981; ibid., 1926, 48, 46, 53, 406; A., 246, 251, 364.23 2. physikal. Chem., 1925, 117, 448; A., 1926, 33.24 H. 8. Harned and H. Seltz, J. Amcr. Chem. rSoc.. 1922, 44, 1476; A . ,1922, ii, 631; A. C. D. Rivett, Z. phpikal. Chem., 1913, 82, 201; 85, 113;A . , 1913, ii, 205, 1041; G. Akerkf, Medd. I<. Votenskapsakad. Nobel-Znsl.,1922, 6 , No. 2.z 5 L. Ebert, 2.Etekhmltem., 1966, 31, 113, 209; A., 1995, ii, 408, 586.28 D. L. Hammick, W. K. Hutchison, and F. R. Snell, J., 1925,127, 2715;D. L. Haminick and M. Zvegintzov, J., 1926, 1105; A,, 691.2 7 J . Amer. Chem. Soc., 1926, 48, 6 ; A., 949.2 8 Ann. Repolt, 1924, 21, 14.l8 H. A. Feles and J. C. Morrell, J. dmer. Chem. Soc., 1912, 44, 2071; A . ,Jo J., 1924, 125, 2016; A., 1924, i, 1256.81 J. Amer. Chem. SOC., 1926, 48, 2259; A,, 1107.A,, 1926, 32.1922, ii, 832; C. M. Jones and W. C. McC. Levis, J . , 1920, 117, 1120.REP.-VOL. XXIII. 34 ANNUAL REPORTS ON THE PROQRESS OF CHEMISTRY.of Pennycuick’s data indicates, however, constancy of rate towithin a few parts per 1000, the observed increase being attributedto a systematic error. Scatchard32 has come to the conclusionthat the difficulties attending the accurate electrometric measure-ment of hydrogen-ion activity in sucrose solutions are such as torender inconclusive the previous attempts of himself and others 34to determine the mechanism of the inversion process by fitting therates of reaction with formuls containing this activity.It mayhere be noted that the same author, discussing the correlationof reaction rate and viscosity, indicates the great experimentaldifficulties involved, and shows that the kinetic theory requiresno viscosity effect. A viscosity correction has been employed byW. C. McC. Lewis and others.35The acid catalysis of lactone formation, which shows all thecharacteristic features of hydrolytic reactions, has been studiedin water, ether, and water-ether mixtures by H.S. Taylor andH. W. Close.as New evidence is found for believing that the rateis determined by the hydrogen-ion activity only, the activity,viscosity, and hydration factors employed by previous investig-ators 37 being regarded as very uncertain.According to M. Kilpatrick 38 the rate of decomposition of nitroso-triacetonamine by alkali is decreased in the presence of glycerolto about the same relative extent as the decrease of the hydroxyl-ion activity in J. Colvin’s30 measurements of hydrogen- andhydroxyl-ion activities in glycerol-water mixtures ; the increasedactivity of the hydrogen-ion in such mixtures would explain theaccelerating effect of glycerol in hydrogen-ion catalysis.The theories of salt action mentioned above refer in the firstplace to dilute solutions.G. Grube and G. Schmidm find thatthe salt effect on the hydrolysis of cyanamide by dilute nitric acidin solutions of nitrates (linear a t low salt concentrations) is ex-ponential for concentrations from 1N to saturation ; k = k,,ercwhere k and k, are velocity coefficients for solutions of the same32 J. Amer. Chem. Sac., 1926, 48, 2026; A., 911.a3 Idem, ibid., 1923, 45, 1581; A., 1923, ii, 626; ibid., 1921, 43, 2387;A., 1922, i, 230.* I T. Moran and W. C. McC. Lewis, J., 1922, 121, 1613; C. M. Jones andW. C. McC. Lewis, ref. (29).35 Ref. (29), and Ann. Report, 1942, 19, 19; W. H. Garrett and W. C. MoC.Lewis, J. Amer. Chen. Soc., 1923, 45, 1091; A., 1923, ii, 47fi; J.Colvin,Trans. Faradau Sac., 1926, 22, 241; A., 1109.a s J. Physical Chem., 1025, 29, 1085; A., 1926, ii, 1070.87 Uarrett and Lewis, ref. (35).as Ref. (21).40 2. physikul. Chem., 1926, 118, 19; A,, 474; also 0. Schmid and R.This Report,, p. 27, ref. (36).Olsen, ibid., 124, 97GENERAL AND PHYSICAL CHEMIBTRY. 35acidity containing respectively c and 0 equivalents of salt, and Tis the " specific salt effect." This relation is valid for other reactions,whilst a similar relation, a = aoe''c, applies to the salt effect onthe thermodynamic activities 41 except a t low concentrations( < 1 W ) where, owing to interionic forces, a lowering of ion activityoccurs. This law is considered incompatible with the "dualtheory )) of catalysis.The fact that T and r' are independent oftemperature 42 does not agree with Bjerrum's theory that catalysisis determined by the equilibrium H',nH,O =$ H' + nH,O. WhilstGrube and Schmid's relation is in agreement with Huckel's activityexpression,43 Schmid and Olsen 42 prefer to account for deviationsfrom the exponential law (activities) a t low concentrations, not bythe interionic-attraction theory, but on the basis of G. Tammann'stheory of internal pressure.44 From the measured external-pressureeffect on the hydrogen-electrode potential (in the absence of freehydrogen g a ~ ) , ~ 5 and assuming internal-pressure changes due t othe salt to exert the same effect on the electrode as external pressure,the true salt effect (total effect less pressure effect) on the hydrogen-ion activity is in agreement with the exponential equation a t lowas well as a t high salt concentrations.G.&erlof,46 in a very recent paper, gives strong evidence infavour of the general rule that the velocity always follows theactivity of the catalyst ion for hydroxyl- as well as hydrogen-ioncatalysis in salt solutions. I n the hydroxyl-ion catalysis of thedecomposition of diacetone alcohol the curves expressing thechange, with salt concentration, of the reaction velocity and ofthe hydroxyl-ion activity are, for a series of chlorides, in the sameorder, just as in the acid catalysis of the N-chloroacetanilide trans-f~rmation.~' The salt effect on the hydroxyl-ion activity, thermo-dynamic and catalytic, is the reverse of that on the hydrogen-ionactivity, and an attempt is made to relate reaction velocities inacid and alkaline salt solutions to the water equilibri~m.4~ b e r -lof 49 has found the relation klk, = (cb/a,JDIC''* for the I\.'-chloro-acetanilide transformation in acid-salt solutions (D is a constant ;C concentration of salt; and a , a,, the hydrogen-ion activities41 For a review of the literature see ref.(40).45 G. Schmid and R. Olsen, ref. (40), where further references and a dis-43 Ann. Report, 1923, 22, 34, equation (6); this Report, p. 21.44 G . Tammann, " Uber die Beziehungen zwischen den inneren Krilften4 5 G. Tammann and H. Diekmann, 2. anorg. Chem., 1926, 150, 129; A.,46 J . drner. Chem. Soc., 1926, 48, 304C.4 7 Refs.(24) and (46).48 Medd. K . Vetenskapsakad. NobeLIwt., 1926, 6, No. 2, 1 ; A., 1926, 126.See also this Report, p. 21.cussion of Bjerrum's theory are given.und Eigenschaften der Losungen " (Hamburg and Leipzig, 1907).360.4 B This Report, p. 2636 ANNUAL REPORTS ON THE PROQRESS OF CITEMIISTRY.with and without salt, respectively). His earlier relation 50 E = cvafor ester hydrolysis has been questioned.51Following A. L a p w ~ r t h , ~ ~ N. ’Bjerrum 53 and others, F. 0. Riceand associates advocate a theory of unhydrated-ion catalysis(‘( protions,” present in small concentration), which they extendto a general theory 55 that the velocity is determined by the con-centration of (‘ residual )’ molecules in equilibrium with othercomponents of the system.The theory is largely based on acomparison of the temperature coefficients of similar reactions.The affinity for water of the hydrogen ion being greater than thatof the hydroxyl ion, neutral solutions are “ catalytically alkaline,”and the catalytic minimum point for reactions catalysed by bothions should be at practically the same acidity for all such reactions.This minimum is in fact often found 56 a t about pE 5. Incon-sistencies with the theory are indicated in that the minimum(pH 4.8) for the autocatalytic reaction between iodine and acetonein aqueous solution is not affected by temperature and neutralsalts,ss and that the p H values for benzamide and acetamidehydrolysis are higher than predicted, viz., 598 and 6.2, respe~tively.5~Further support has been given to the theory 58 that substancessubject to hydrolytic reaction in the presence of both acid andalkali (e.g., esters) are weak ampholytes, the rate being determinedby the concentration of the positive or negative ester ion, whichis increased respectively by the acid or alkaline catalyst, and iscalculable from the two equilibrium constants K , and Kb.Assum-ing equal reactivity of these ions, the relation between rate and p ,5 O Ann. Report, 1922, 19, 19.61 Gmbe and Schmid, ref. (40); also ref. (46).6* J., 1908,93, 2187; also J. Kendnll and P. M. Gross, J . A ~ E T . Chem. ~Soc.,1921, 45, 1416; A., 1922, ii, 32.6a 2. anorg. Chem., 1920, 109, 275; also E. Sohreiner, ibid., 1922, 121, 321 ;A., 1922, ii, 468; ibid., 1924, 135, 333; A ., 1924, ii, 524.54 F. 0. Rice and M. Kilpatrick, J . Amer. Chem. SOC., 1923, 45, 1401; A.,1923, ii, 548; F. 0. Rice and W. Lemkin, ibid., p. 1896; A., 1923, ii, 678;F. 0. Rice, ibid., p. 2808; A . , 1924, ii, 98; F. 0. Rice, C. F. Fryling, andW. A. Wesolowski, ibid., 1924, 46, 2405; A , , 1925, ii, 48; F. 0. Rice andC. F. Fryling, ibid., 1925, 47, 379; A . , 1925, ii, 556.6s The general character of this theory has been disputed; see C. N. Hinshel-wood, Chem. Revieuw, 1926, 3, 230 ; idem, ‘‘ The Kinetics of Chemical Changein Gaseous Systems,” 1926, p. 155; R. C. Tolman, J . Amer. Chem. SOC., 1925,47, 1626.61 For collected data see M. Bergstein and M. Kilpatrick, J . PhysicalChem., 1926, 30, 1616.I. Bolin, 2.anorg. Chem., 1925, 143, 201; A , , 1925, ii, 411.6 8 H. von Euler and 0. Svanberg, b. physiot. Chem., 1921, 115, 139; A.,1922, i, 219; H. von Euler and E. Rudberg, 2. anorg. Chem., 1923,127, 244;A., 1923, ii, 840; 2. Physik, 1923,16, 64; A , , 1923, ii, 647GENERAL AND PHY SIOAL CHEMISTRY. 37is given by a symmetrical U-curve with a minimum a t the isoelectriopoint :v = ko + k,,t.[E'l + kdE'1 = Lo + k.,,t.Ka[H']/k,~ + Em.Ka/[HIwhere E' and E' are the ester ions and A and B are constants.Recent work59 is in good agreement with the theory. Contraryto earlier observations,60 the two limbs of the curve are of equalslope. Ethyl benzenesulphonate (non-ampholyte) shows quitedifferent behaviour. Some doubt attaches to the significance ofko ; possibly it gives the activity of the ' * zwitterions." Salts havevery little effect on the catalytic-minimum pH.The inversion ofsucrose has been discussed from the same point of view.61Studies on the catalytic minimum of the iodine-acetone reaction(referred to above), in buffer solutions, have been made by H. M.Dawson and associates.62 Not only is support found for the" dual " theory of catalykis, which has found little favour in recentyears, but it is extended to the anion, the observed rates beinggiven by the equation v = kH.[H'] + k,,[HA] + k,.[A'] with theaddition of the term koH,[OH'] a t low hydrogen-ion concentration.Assuming complete dissociation of the salt, and also the validityof the concentration " expression for the dissociation constant,K,, of the weak acid, a symmetrical U-curve is theoretically pre-dicted when v is plotted against pa, in excellent agreement withexperimental data.Catalytic activity is proportional to volumeconcentration of the catalyst calculated from K,, and no oonnexionis found between velocity and thermodynamic activity.Mutarotation.Recent research on the mechanism of mutarotation of the sugarsis of interest in relation to the claim of J. W. Baker, C. K. Ingold,and J. F. Thorpe63 to have obtained conclusive proof that thisphenomenon is purely a tautomeric change involving (contrary tothe previously accepted view) no intervention of water. Accord-ing to T. M. Lowry and E. M. Richards,64 the experimental results= k o + B I H ] + A / [ H ] .. . . * (4)58 K. G . Karlsson, Z. anorg. Chem., 1925, 145, 1; A,, 1925, ii, 877.E o IbLd., 1931, 119, 69; A., 1922, ii, 40; Bnn. Repart, 1922, 19, 19.61 H. von Euler and A. Olander, 2. anorg. Chem., 1926,156, 143; A., 1108.6 3 H. 31. Dawsonand J. S. Carter, J . , 1926, 2382; A., 1108; H. M. Dawsonand N. C. Dean, abid., p. 2872 ; H. &I. Dawson and C. R. Hoskins, ibid., p. 3166.83 Ann. Repmt, 1924, 21, 13; J., 1924, 125, 268; A., 1924, i, 262. Theseauthors based their conclusions on a mathematical analysis of the dynamicsof mutarotation, end on the observation that very small amounts of waterhad no effect on the velocity of mutarotation of tetra-acetyl glucose dissolvedin ethyl acetate, and of glucose in methyl alcohol.J., 1925,127, 1386 ; A., 1925, i, 886 ; Bee also T.M. Lomrg, zbid., p. 1371 ;A . , 1925, 1, 886 (a reply to Baker, Ingold, and Thorpe, and a general dis-cusaion of the meohamsm of mutarolabon)38 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY,of these authors were largaly invalidated by the presence of unknowncatalytically-active impurities, in the absence of which muta-rotation can generally be suspended in a dry solution. Further, int’he presence of the very small amounts of water used by Baker,Ingold, and Thorpe, the value of dk/d[H,O] should be so small as tobe experimentally indistinguishable from the zero value which theyfound and regarded as incompatible with the ‘‘ hydrate theory.”Lowry 64 has re-examined the whole question, and, on the basisof modern views on valency, has extended his mechanism for acidand alkaline ester-hydrolysis to the analogous mutarotation of thesugars, thus going far towards a reconciliation of previously con-flicting views.Both phenomena are regarded as ionic in character.The former proceeds through the formation of bi-polar molecules(ewitterions) by addition of H+ and OH-, one of these being derivedfrom the acid or alkali, the other from water, thus :P + F1OH H OHCH,-CO.O.CH, =+= CH,*$:-?*CH, =+= CH,*C + HOCH,.The latter is attributed to the formation, by a similar ionic mechan-ism, of an intermediate aldehyde form of the sugar; but as this isnot necessarily hydrated, it may be produced by isomeric changewithout addition of water. Since the hydroxyl ion does not thenplay any essential part in this change, the proton transfer (‘i proto-tropic change ”) can proceed in any medium which is capable of(1) accepting a proton from one part (OH group) of the sugarmolecule, and (2) giving a proton to another part (C-0-C group).Regarding an acid as a ‘‘ proton donator ” and a base as a “ protonacceptor,” an effective solvent for mutarotation should thus beamphoteric in character, e.g., water; acidic and basic solventsshould be effective only in the presence of water, or of each otherif water is absent.This view has received striking experimentalsupport.s5 In general, pure, dry, neutral solvents are ineffective,whilst pyridine and cresol, ineffective when dry, become active inthe presence of water, and develop great catalytic activity whenmixed in the dry state.The “ hydrocatalysis )’ theory has thusbeen not only maintained but extended.H. von Euler’s theory of ester hydrolysis, referred to above, hasbeen applied to the mutarotation of glucose.66 The U-shapedk-pE curve is nearly symmetrical, with a shallow minimum at theT. M. Lowry and I. J. Faullmer, J., 1925, 127, 2883; A., 1926, 148.6 5 Refs. (58), (59), (61); H. von Euler, A. Olander, and E. Rudberg, 2.anorg. Chem., 1925,146, 45; A , , 1925, ii, 876; H. von Euler end A. Olander,ibid., 1926, 152, 113; A., 580GENERAL AND PHYSICAL CHEMISTRY. 39isoelectric point pH 5 ; k changes little between pH 2 and pE 8.The two dissociation constants of the amphoteric sugar are of theorder K , = 10-13, Kb = 10-ls, whence can be calculated the con-centration of sugar anions and cations t o which the rate is pro-portional ; between p , 2 and p E 8 the determining factor is regardedas a function of the zwitterions or neutral molecules.Equation (4)reproduces the experimental data.07 The nearly-equal slope ofthe two arms of the curve indicates approximately equal reactivityof the two sugar ions, kcat. and kan. being a t least 1000 times greaterthan k,. R. Kuhn and P. Jacob 68 are in general agreement withvon Euler, but, from a study of salt action, they believe that thevelocity of mutarotation depends on activity rather than on con-centration of the reactants, and they therefore find evidence forthe conclusions of Baker, Ingold, and Thorpe in the fact that thevelocity remains unchanged in solutions varying from 2%--50% ofsugar in spite of a 200/, change in the activity of water.I n thisconnexion, it may be noted that G. G. Jones and T. M. Lowry 69find no relation whatever between the velocity of mutarotation oftetramethyl glucose in water-acetone mixtures and the aqueousvapour pressure of such mixtures ; they conclude that the catalyticeffect of water is proportional neither to its concentration nor toi t 3 activity.Optical Activity.In the last Report on this subject,l prominence was given tocriticisms of T. M. Lowry’s well-known system of classifying rotatorydispersion as “ simple ” or “ complex,” according as it can orcannot be expressed by a one-term Drude equation. The systemwas regarded as lacking justification on practical as well as theor-etical grounds, and a return to the older classification into “ normal ”and “ anomalous ” rotatory dispersion was considered desirable.These conclusions were largely based on H.Hunter’s examinationof the two-term Drude formula = ko/(h2 - hO2) + kJ(X2 - h?),which indicated that a sharp distinction between simple and com-plex rotatory dispersion would be difficult, except when the complexdispersion was also anomalous, and impossible if the componentpartial rotations of the coinplex dispersion were of similar sign?Recent work has, however, proved that the difficulties in the6 7 C. S. Hudson’s empirical formula is thus given a theoretical significance;J . Ante?. Chem.Soc., 1907, 29, 1672; A., 1907, ii, 942.6 8 Z. phipikal. Chem., 1924, 113, 389; A., 1926, ii, 49.J . , 1926, 720; A., 481. Ann. Report, 1924, 21, 3, 61.2 J., 1924. 125, 1198; A., 1924, ii, 645.3 ‘‘ I n practice it will be impossible to detect the departure of the I/= - pcurve froiii linearity when k, and k, are both positive. If the rotation con.stants are of opposite sign, and if b,>b, when ,&,>A, detection will be possibl40 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.practical application of Lowry‘s system are by no means so greatas Hunter suggested. Complex rotatory dispersion was easilydemonstrated in ten halogen derivatives of ~amphor,~ althoughonly one of them showed anomalous dispersion. With one exception(where a more complex equation was required), all these dispersionscould be represented by two-term equations, the terms being.ofsimilar sign in three cases and of opposite sign in the others ; butonly in one case were the conditions fulfilled that the rotationconstants should be opposite in sign and Ic,<k, when h,71,.3Further, the undesirability for practical reasons of abandoningthe classification of rotatory dispersion as simple and complex, infavour of the normal and anomalous grouping, is evident from theconsideration that, in critical cases, the latter depends on knowingwhether a reversal of sign would occur if the dispersion-curve couldbe followed into the infra-red region (usually impracticable a tpresent), whilst the former can be checked by direct observationup to the limit of transparency in the ultra-violet.For example,the rotatory dispersion of P-bromocamphor is complex but normal,5since k,>k, when Ao>hl, but the margin is so narrow that thecalculated curve only just fails to cross the A-axis ( L e . , CL just failsto suffer reversal of sign); any doubt as to the validity of theequation would a t once make the extrapolation into the infra-redregion so uncertain that it would be impossible to decide whetherthe rotatory dispersion were normal or anomalous.6 As a practical,and in the first place empirical, method of Classification, Lowry’ssystem seems to be justified.The question of its theoretical significance as distinct from itspractical utility has been recognised in the attempts to correlateonly in very rare cases.The only condition under which the experimentaldata can be expected to show the effect whieh Lowry and Dickson regard asevidence of ‘‘ complex ” dispersion is when the rotation constants are oppositein aign and k,<k, when Ao>A,.”4 J. 0. Cutter, H. Burgess, and T. M. Lowry, {., 1925, 127, 1260; d.,1925, ii, 743. For other examples see E. M. Richards and T. M. Lowry,ibid., p. 1512; A., 1925, ii, 934.(Ann. Report, 1924, 21, 3.)6 T. M. Lowry and J. 0. Cutter, ibid., pp. 606, 608; A., 1925, ii, 356.T. M. Lowry has introduced the term ‘‘ quasi-anomalous ” t o describecases of ‘‘ complex but normal ” rotatory dispersion (e.g., camphor), in whichalthough Iso and k, are of opposite sign, the resulting dispersion-curve showsno obvious anomalies, merely because the relative magnitudes of k, and k,are not such a@ to give rise to a reversal of sign.See ref. (5), p. 608 ; T. 31.Lowry, J. Chint. physique, 1926, 23, 6 6 5 ; Nature, 1926, 117, 274.T. M. Lowry and E. M. Richards, J., 1924,125, 2511; A., 1925, ii, 265 (areply to Hunter’s criticisms and a discussion of the practical and theoreticaljustification of the use of the Drude formula).* See R. H. Pickard and H. Hunter, ibid., 1923, 125, 436, and Ann. Report,1923, 20, 15 et segUENERAL AND PHYSICAL CHEMISTRY. 41the wave length 7b0 of the dispersion constant in the Drude formula(as determined from rotatory-dispersion measurements only) withthat of the head of the dominant absorption band 1,.Such acomparison has been made in the case of ~ a m p h o r , ~ camphor-q ~ i n o n e , ~ and nine halogeno- and five sulphonic 9 derivatives ofcamphor; h,, always exceeds ha by roughly 100-150 A.V. Thediscrepancies are, a t any rate in part, accounted for by the dis-placement of h, due to superposition of selective and generalabsorption, and these results are regarded as affording some justi-fication for the use of the Drude formula from the themetical stand-point, since, according to the theory h, represents the wave-lengthof the band controlling rotatory dispersion.sA summary and discussion of the types of optical superposition,any of which may cause complex or anomalous rotatory dispersion,has been given by T. M. Lowry and J.0. Cutter.lo Six classesare now distinguished, viz., those of : (a) Two separate media;(6) two mixed, stable, fluid media; (c) two molecular types derivedfrom one optically-active compound, one type being generally thatcomposing the crystal, the other being produced either (i) bypolymerisation, dissociation, or isomeric change of the solute, or(ii) by chemical reaction with the solvent ; ( d ) radicals of oppositeactivity in one molecule; ( e ) induced asymmetry of double bondsin an asymmetric molecule ; (f) possibly two natural frequencies(i) in a single crystal, (ii) in a single molecule. A recent study4of the mono- and di-halogeno-substitution products of camphorstrongly supports the general validity of the principle of opticalsuperposition, the different asymmetrical centres in a moleculecontributing independent partial rotation to the observed total.11E. Darmois,12 reviewing physical theories of optical rotation,concludes that none of them can explain the considerable effectsof solvent, concentration, and temperature, and that physico-chemical theories [e.g., of dynamic isomerism, class ( c ) above]provide a satisfactory mechanism.Support for the isomeridetheory is found by A. Haller and R. Lucas l3 in the approximateCOnStanCy of the ratio ([.]A - [ctIB)/([alA - [.IC) over the range4358-6708 A.U. for various derivatives of camphor in five solvents,including phosphoric acid l4 (A, B, and C refer to different solvents).This rule, a consequence of Biot's law of mixtures, is accurately8 E.M. Richards and T . M. Lowry, J., 1925, 127, 1503; d., 1925, ii, 934.lo Refs. (6) and ( 6 ) .l1 See criticisms by T . 8. Patterson, Nature, 1926, 117, 786, and remarksl* J . Phys. Radzum, 1925, [vi], 8, 232; d., 1926, ii, 1119.13 Compt. rend., 1925, 180, 1803; R. Lucas, ibid., 181, 45; A . , 1925, ii, 742.l4 Idem, ibid., 1926, 182, 1022; A., 662.by T. M. Lowry, ibid., p. 787.B 42 ANNUAL REPORTS ON THE PROGRESS OZF CHEMISTRY.obeyed when B is a mixture of A and C. Again, the dextrorotationof camphor, less in formic acid than in benzene, becomes a slightlsvorotation in concentrated nitric or phosphoric acid, and a stronglaevorotation in concentrated sulphuric acid.15 Camphor is there-fore considered to exist in solution as an equilibrium mixture oftwo forms, a and p, of opposite rotatory power, the two terms ofthe Drude formula for camphor 5 representing the effects of theseisomerides.The approximate agreement of the positive term withthe rotation constant for crystalline camphor suggests the identityof the or-isomeride with crystalline camphor, as in the case of tartaricacidsfs According to L. Longchambon,17 there is no justificationfor regarding the Drude terms as characteristic of such CL and pisomerides, but R. Lucas14 maintains that as a first approxim-ation they may be so regarded. It may here be noted thatLowry and his associates have obtained strong evidence that incamphor the superposed optical effectB are (1) that of the fixedasymmetry of the saturated carbon atoms, -and (2) that of theinduced asymmetry of the ketonic group, since in most camphorderivatives the positive partial rotation is controlled by a dis-persion constant corresponding approximately with the wave-lengthof the ketonic absorption band.6T.M. Lowry and W. R. C. Coode-Adams 1* have measured withthe greatest possible accuracy the rotatory power from infra-redto ultra-violet (25170-2263 d.U.) of a quartz column nearly50 cm. long. The dispersion formula- 0.1905, 9.5639 2.3113h2 - 0,0127493 - h2 - 0*000974 a =which is valid for the whole range, postulates the existence ofbands of selective absorption a t 1130 and 310 d.U., the influenceof infra-red bands being covered by the small constant, - 0.1905.In spite of numerous attempts to find a general physical theoryof optical activity which can be experimentally tested, it cannotbe said that any great success has yet been attained.The incor-poration by Drude of a rotation term in his theory of dispersionnecessarily provided for optical rotation, but no real explanationof the phenomenon was thereby aff orded.12 Further, the theorytook no account of solvent and concentration effects. The latterwere associated with the refractive index of the medium in theLorentz-Livens theory, which, however, did not explain the con-R. Lucas, Compt. rend., 1926,182, 378; A., 337.l0 Ann. Report, 1924, 21, 59.1' Compt. rend., 1926,182, 769; A., 559.la Roy. Soc., Dec., 1926 (in press); Nature, 1926, 118, 861GENERAL AND PHYSICAL CHEMISTRY.43nexion between rotation and molecular asymmetry. The latertheories of M. Born,1Y C. W. Oseen,20 F. Gray,21 and A. Land622were, on the other hand, definitely based on molecular asymmetry;they agree broadly in ascribing rotation to unsymmetrically-disposedelectron resonators coupled together, i.e., reacting by mutualinduction. The relations obtained are complex and do not permitof estimating the order of magnitude of the effect. (Sir) J. J.Thornson's theory,23 although physically and mathematicallysimpler, involves molecular magnitudes at present unknown.A new attack on this problem has recently been made by R. deMallemann,24 who has extended the ordinary dispersion formulsby the introduction of the single notion of molecular asymmetry ;his analysis involves the orientation theory put forward by Lan-gevin in connexion with the Kerr effect.The problem of calculatingoptical rotation appears thus to have been brought appreciablynearer solution. The rotation calculated for a tetrahedral moleculeof the type CHClBrI is of the right general order of magnitude,which is all that can be hoped for a t present. Complete solutioninvolves a fuller knowledge of molecular structure than we yetpossess. Optical rotation, according to this theory, (1) dependson the geometrical form only of the tetrahedron which is deter-mined by the atoms a t the apices (the analysis does not call forknowledge of the forces producing the structure), (2) is proportionalto the product of the refractivities of the four atoms, thus accountingfor the known influence of heavy atoms and of double bonds.Itappears, further, that as regards rotation an asymmetric group ofatoms behaves almost independently of the rest of the molecule.The analysis indicates great sensitiveness of optical rotation t omolecular structure, so that failure to express the experimentalvariations by any simple law is not surprising.Electrification at Surfaces."It has long been realised that the Helmholtz conception of theelectrical double layer a t surfaces as two layers of ions of oppositecharges confronting each other a t a 6xed distance (condenser19 Ann. Physik, 1918, [iv], 55, 1 7 7 ; A , , 1918, ii, 283.22 Ann. Physik, 1918, 56, 225; PhysibaE. Z., 1918, 10, 300.*3 Phil. Mag., 1920, [vi], 40, 713.*' A,nn. Physique, 1924, [XI, 2, 5 ; 1925, [XI, 4, 456; A . , 1926, ii, 1029;Compf. rend., 1923,177, 427; 1925,181, 106, 298, 371; A., 1925, ii, 840, 935,1030. See also ref. (12). * See the Faraday Society's discussion on electrification at surfsoes(Trans, Pa'oraday SOC., 1926, 22, 434). Some of the papers contributed &rereferred-to below.Ibid., 1915, 48, 1. 21 Physical Rev., (Z), 1916, 7, 47244 ANNUAL REPORTS ON THE PROQRESS OF CHEMISTRY.fashion) is inadequate. J. Billiter and G. Gouy suggestedthat ions in the liquid form a diffuse layer. D. L. Chapman3applied the Boltzmann equation to obtain the distribution of ionsin a diffuse layer, but his equations have been shown to be in-adequate.4 0.Stern 5 has therefore postulated a combination ofthe two types-a (‘ condensed ” double layer near the surface ofseparation ; beyond it, in the liquid, a ( ( diffuse ” layer of ions.The “ thermodynamical )’ potential difference (E) measured acrossthe surface is the total P.D. due to both layers. On the otherhand, electrokinetic measurements give the P.D. (l) across thatpart of the interface which is capable of displacement parallelto the surface, i.e., the .‘ diffuse ’) layer. The two P.D.’s have beenmeasured by H. Freundlich and co-workers,B at glass surfaces in avariety of solutions. Not only do they differ, but they may be ofopposite sign. Whilst the E P.D. is not much influenced by thesalt concentration, the 4-c curves are very characteristic for saltsof different types.There is no satisfactory theory of the relationbetween [ and C, since Stern’s equation cannot be applied to actualcases.H. Lachs and J. Kronman,’ however, find that these potentialscan only be reproduced within 14%. It is to be expected thatonly P.D.’s which depend on a thermodynamical equilibriumbetween the two phases are definite and reproducible (thus a metalonly gives a definite P.D. in solution containing its ions), and theabove cases do not come within this category. Measurements ofc and 1 a t the surfaces of slightly soluble salts and solutions con-taining their ions are therefore of greater value. A. Gyemant *has made such measurements with barium sulphate, and R. Labeswith barium sulphate, zinc oxalate, lead chromate, and silver1 2.physikal. Chcm., 1903, 45, 307; A , , 1904, ii, 18.J. Physique, 1910, [iv], 9, 457; Ann. Physique, 1917, [ix], 7, 129; A.,Phil. Mag., 1913, [vi], 25, 47.5. Also K. F. Herzfeld, Physikal. Z . , 1920,* A. Frumkin, Phil. Mag., 1920, [vi], 40, 376; A . , 1920, ii, 578; 0. K.1917, ii, 291.21, 28.Rice, J . Physical Chcm., 1926, 30, 1501.2. Elektrochem., 1924, 30, 508.H. Freundlich and P. Rona, Sitzungsber. Preuss. dkad. Wiss. Berlin,1920, 20, 397 ; H. Freundlich and G. Ettisch, 2. phys-ikal. Chem., 1925, 116,401 ; A., 1925, ii, 873. Summary of results by H. Freundlich, Trans. FaradaySOC., 1926, 22, 440.Bull. Int. Acad. Polonaise, 1925, A , 289; A., 1926, 803.* 2. physikal. Chem., 1922,103, 260 ; d., 1923, ii, 52.The 6 P.D. betweensolid salts and their solutions was first realised by F. Haber, Ann. Physik,1908, [iv], 26, 927 ; .4., 1908, ii, 802. A. Oyemant has discussed the theoryof ionic adsorption applied to such cases, 2. physikal. Chem., 1924,108, 387 :A., 1924, ii, 391.9 Ibid., 1925, 116, 1 ; A , , 1925, ii, 796GENERAL AND PHYSIUAL CHEMISTRY. 45chloride. The latter has worked out a detailed theory. Sinceions of opposite charge to the solid accumulate near the surface-and to a greater extent the greater their concentration in thesolution-the electrokinetic potential is small in concentratedsolutions. I n more dilute solutions, specific effects are observable,and in the absence of specific adsorption of ions, the theory indicatesthat an ion influences the electrokinetic potential the more thesmaller the solubility product of the salt which it forms with eitherof the component ions of the solid.This conclusion is confirmedby the experiments.A. Prumkin and associates have made measurements of theP.D. a t the surface of aqueous solutions by F. B. Kenrick’s method,1°in which the P.D. is measured between the solution flowing downthe inside wall of a cylindrical tube and a stream of a standardsolution flowing down its axis. In salt solutions,ll the outersurface is in nearly all cases negatively charged ; the predominanceof anions, thus indicated near the surface, is greater the less theirenergy of hydration, and the effect on the P.D. is in the sameorder. Similar measurements have been made with organic com-pounds.The results are in accordance with the orientation ofmolecules in the surface layer, and give valuable information asto their polarity. Aliphatic alcohols, esters, amines, etc.,12 increasethe positiveness of the surface owing to their orientation with therelatively positive alkyl groups outwards. Strong acids and neutralsalts have the opposite effect, owing to the greater attraction ofwater for cations than for the carboxyl group. I. Traube’s adsorptionrule (viz., that as the number of methyl groups increases in arith-metical progression, the adsorption from solutions of the sameconcentration increases roughly in geometrical progression) holdsalso for these P.D.’s. Aromatic compounds show similar relations.13The effect of methyl groups is, however, less than in aliphaticcompounds and the presence of polar groups in the nucleus mayreverse the effect.This method is only applicable when the surface equilibriumis quickly reached.A method has been devised l4 for use withla 2. physikal. C’hem., 1896, 19, 625; A., 1896, ii, 460.l 1 A. Frumkin, ibid., 1924,109,34 ; A., 1924, ii, 462. Compare A. Frumkin,8. Reichstein and R. Kulvarskaya, Kollcid Z., 1926, 40, 9 ; A., 1091. A.Frumkia and A. Donde (2. physilcal. Chent., 1926, 123, 339; A., 1104) findthat mercury can be substituted for the standard solution.A. Frumkin, ibid., 1924, 111, 190; A . , 1925, ii, 109.l3 A. Erumkin, A. Donde and R. Kulvarskaya, ibid., 1926, 123, 321; A.,1092.l4 A.Frumkin, ibid., 1925, 116, 485; A., 1926, ii, 873; Kolloid Z., 1924,35, 340; A . , 1925, ii, 544; Trans. Kurpcv. Inst. Chem. [Russia], 1925, No. 4,66; A., 1926, 109346 ANNUAL REPORTS ON THE PROGRESS OF CHEMISTRY.solutions giving insoluble unimolecular films, in which the P.D.is measured between the stationary solution and either a glowingwire or a wire containing some radioactive material, in order tomake the air-gap sufficiently conducting. In these cases, theP.D. is proportional to the amount adsorbed until a completeunimolecular layer is formed, after which it remains constant.has worked out an elaborate statistical theory ofthe surface charges of inorganic electrolyte solutions, and is ableto account for Frumkin's results. A. Garrison l6 has used a con-denser method to determine the surface charges of electrolytes.R. D.Kleeman and C. R. Pittsl7 have ako studied the sign ofthe charge furthest from the solution by another method. H. W.Gilbert and P. E. Shaw l8 have recently summarised the literatureon the determination of electric charges a t gas-liquid interfaces.The study of the surface phenomena of mercury in electrolyticsolutions promises to give particularly valuable information abouteIectrification a t surfaces and also about the effect of an electricfield on the constituents of the solution, for it is the unique casein which the P.D. can be varied a t will by polarisation and theeffects on the surface tension observed a t the same time. Theclassical equation of Gibbs and Helmholtz, dy/dV = - e, whichequates the rate of change of surface tension with applied P.D.to thecharge on the double layer e, has been obtained in numerous ways.R. K. Schofield19 has identified e with the amount of adsorbedmercury ions and has directly determined this amount by aningenious method, obtaining results in good agreement with theequation.lQa A. Frumkin 20 has discussed the effect of the adsorptionof anions and cations and of neutral capillary-active substances onthe electro-capillary curve. In the latter case, variations of surfacetension are given by dy = - e . dV - BTAdpA. The first termon the right represents the effect of electrification, the second(in which PA is the amount of adsorbed substance A , and pA itschemical potential in the solution) the lowering of surface tensionproduced by the capillary-active substance.Since ra is itself aW. Wessel1 5 Ann. Physik, 1925, [iv], 77, 21; A., 1925, ii, 795.16 J . Physical Chem., 1925, 29, 1617; A,, 1926, 130.1 7 Ibid., p. 608; A , , 1926, ii, 659.18 Proc. Physical Soc., 1925, 37, 196; A., 1925, ii, 798.10 Phil. Mag., 1926, [vii], 1, 641; A., 672; Trans. Faradcay Soo., 1926,22, 452. Compare A. Frumkin, Z. physika2. Chem., 1922, 103, 65; A . ,1923, ii, 64.1- W. A. Patrick and P. W. Bachman ( J . Physical Chem., 1926, 30, 134 ;A., 239) and J. E. Rosenburg and G. Stegeman (ibid., p. 1306 ; A,, 1201) alsohave investigated the adsorption of ions at the mercury surface.*o Phil. Nq., 1920, [vi], 40, 363, 375; A., 1920, ii, 678; also ref. (19)GENERAL AND PHYSICAL CHEMISTRY. 47function of V , this equation does not give the complete variationof y with V , Frumkin21 has applied the equation Ay=A log (Bcfl)for the lowering of surface tension produced by an active substanceand has obtained B as a function of the electric-field strength inthe form B = B,e+lRT, where 4s is the additional electrical workof adsorption due to the electric field, On this basis, the effectof amyl alcohol on the electro-capillary curve is satisfactorilyaccounted for. Capillary-active neutral substances in general onlylower the surface tension in the vicinity of the electro-capillarymaximum, i.e., when the electric field strength is low. The amountadsorbed is therefore diminished by increasing the P.D. a t theinterface in either direction. It has been found by direct measure-ment 22 that the adsorption of n-octoic acid a t the surface of silveriodide increases to a sharp maximum a t about the isoelectricpoint.0. K. Rice 23 has investigated the surface tension of chargedsurfaces, obtaining the expression dy/dV = - e - Eridpi/dV, inwhich the second tcrm represents the effect of the adsorption ofions (pi is the chemical potential in the superficial layer of ionsof the i t h kind). These terms are interpreted from the point ofview of electrostatic theory. A detailed analysis of the changesproduced by electrolytic polarisation a t the mercury surface andthe therinodynamical theory of their effects on the surface tensionhas been given by J. A. V. Butler.24 It is held that Gibbs’sequation by itself is inadequate to account for the electrocapillarycurves, an electrostatic effect in addition having to be taken intoaccount.dyldT‘ = - 2e - aHg.FHg. - Pd{SI’,dpz}/dT’,in which the first term represents the electrostatic effect, thesecond the effect of adsorbed mercury ions, the third the effect ofother adsorbed ions or molecules. I n the third term rs itselfvaries wi+.h Ti, and this variation can only be calculated by kineticmethods. An application of the theory of ionic adsorption isoutlined which accounts quantitatively for the electro-capillarycurves in iodide solutions and is capable of accounting qualitativelyfor all types of curves exhibited by salt solutions.0. K. Rice 25 has examined the application of various theoriesof the electrolytic double layer to the electro-capillary curves.Chapman’s equation 26 is inadequate. As an alternative to Stern’sThe following equation is obtained,2 1 Z. Physik, 1926, 35, 792; A,, 347.52 A. Frumkin and A. Obrutshewa, Nature, 1926,117, 790; A., 674.2s J. Physical Chem., 1926, 30, 1348; A., 1202.24 Proc. Roy. SOO., 1927, [A], 113, 694.25 J . Physical Chem., 1926, 30, 1501. 28 Compare ref. (3)48 ANNUAL REPORTS ON THE PROURESS OF CHEMISTRY.theory of a " condensed " double layer a t the surface and a diffuselayer in the solution, i t is suggested that the electronic charge inthe mercury may not reside entirely a t the surface but may also bediffuse. The two assumptions give very similar results but are notentirely adequate, E. Liebreich 27 has put forward evidence forthe belief that the maximum of the electro-capillary curve corre-sponds with the formation of hydroxide or basic salt on the surfaceof the mercury by cathodic polarisation. P. L. Usher2* hasexamined electro-capillary curves in salt solutions in connexionwith the electrokinetic behaviour.J E. COATES.J. A. V. RUTLER.27 Z. Elektrochem., 1926, 32, 162; A,, 478. Compare E. Liebreich and28 J. Phyeical Chem., 1926, 30, 954; A,, 803,W. Wiederholt, %bid., 1924, 30, 263; A , , 1925, ii, 44