ANNUAL REPORTSON THEPROGRESS OF CHEMISTRY.GENERAL AND PHYSICAL CHEMISTRY.1 . THE KINETICS OF ELECTRODE PROCESSES.THE Faraday Society Discussion on Electrode Processes,l in April 1947,showed how wide a range of problems in this field has attracted attention inrecent years. Without attempting a classification, it is possible todistinguish two rather different, though complementary, trends : ( a ) Theinvestigation of a greater variety of reactions, electrode materials, andsolvents, and the extension of measurements to higher current densities.( h ) The more intensive study of a few " classical " reactions, notably thcelectrodeposition of hydrogen on mercury 2, and p l a t i n ~ m , ~ in which,4. N. Frumkin and his colleagues have played tEe major part.T t is becoming increasingly evident that hydrogen and oxygen do nothold the outstanding position as regards high overpotential that has some-times been ascribed to them.Highly irreversible electrode reactions are notuncommon. Among others, the Kolbe and the Hofer-Moest reaction, forwhich equilibrium potentials are given by W. M. Latimer,4 the deposition ofthe azide ion (p. 30), and the large number of irreversible reductions dis-dosed by polarographic investigation^,^-^ may be noted.The quantity of available material makes i t impossible to review thewhole field adequately in this Report ; several subjects, in particular thedeposition and passivity of metals, have been omitted entirely. Thoseincluded have been chosen on the grounds of recent development or ofobvious, though long-standing, importance ; in the latter case a certainamount of recapitulation of an earlier Report is unavoidable.Many of thetopics with which the present Report is concerned have been discussed byJ. A. V. Butler in his book ; 10 recent work on hydrogen overpotential has alsobeen reviewed by J. W. Smith.llTram. Faraday SOC., 1947, 43, A , 111 the press (summerised by V. Gold, Nalwc,1847, 160, 306).Acta Physicochens. U.R.S.S., 1943, 18, 23.Trans. Faraday SOC., 1948, 44,I. M. Kolthoff and J. J. Lingane, " Polarography ", Interscience, 1941.J. Heyrovsky, " Polarographie ", Springer, 1941.F. P. Bowden and J. N. Agar, Ann. Reports, 1938, 35, 90.* " Oxidation Potentials ", Prentice Hall, 1938.' 0. H.Muller, Chem. Reviews, 1939, 24, 95. J. J. Lingane, ibid., 1941, 29, 1.11 Scirnce Progress, 1947, 35, 675. l" '' Electrocrtpillarity ", Methuen, 19406 GENERAL AND PHYSICAL CHEMISTRY,(i) Experimental Methods.The usual object of investigations of electrode kinetics is to elucidate themechanism of the reaction occurring at the electrode-solution interface. Ingeneral, therefore, it is necessary that experimental methods should be able todistinguish (a) '' activation overpotential " * (qR),Q9 l2 which has its origin insome " sluggish " stage(s) of the interfacial reaction, from " concentration "and " resistance " overpotentials. (qc and rlr), which arise from associatedprocesses in the solution iiettr the electrode; ( b ) the various stages possiblyresponsible for qa from one another.Both problems may be attacked by studying the behaviour of electrodesa t which the potential and/or current is varying with respect to time; suchexperiments may be made either by passing an alternating current throughthe cell, or by suddenly changing the current from one steady value toanother and following the subsequent change of potential.The electrodepotential generally lags behind the current, and the system is analogoup to anelectrical network containing resistances and capacities. The resistancesrepresent the various " slow " &ages in the overall process, and the chargeson the Capacities represent " accumulations " of certain components of thesystem at one or other of these stages.The early " commutator " method l3 of distinguishing qa and -qc from-qr is based on this principle, the assumption being made that the resistanceoverpotential decays almost instantaneously when the current is cut off,whereas t,he major part of other types of overpotential persists for anappreciable time.I n recent years, the availability of improved apparatus,combined with a better understanding of the nature of electrode processes,has made possible a considerable development of both oscillographic andA. C. methods.(a) The Use of Alternating Current.-The A.C. behaviour of an electrodemay be investigated by including the electrode, together with a suitable largeand relatively unpolarisable reference electrode, in one arm of an A.C.bridge and thus measuring its (complex) impedance.Various othermethods w 2 0 have also been used to compare the amplitude and phase of theE.M.F. between the working electrode and a reference electrode with that ofthe current flowing through the cell. A separate D.C. polarising circuit is12 J. X. Agar and F. P. Bowden, Proc. Roy. SOC., 1938, A, 169, 206.l 8 See S. Glasstone, " The Electrochemistry of Solutions ", Methuen, 1938, p. 423.l 4 G. Jones and S. M. Christian, J . Anier. Chenz. SOC., 1935, 57, 272.1 5 D. C. Grahame, ibid., 1941, 63, 1207.1 6 P. Dolin and B. Ershler, A c t a Physicochinz. U.R.S.S., 1940, 13, 747.17 B. Ershler, see ref. ( I ) . J. E. B. Randles, see ref. (1).Trans. Furaday Xoc., 1935, 31, 110; T. Borissova and M. Proskurnin, ActaPhysicoclLint.U.R.S.S., 1936,4, 819; 1940,12, 371.20 Conapt. rend. Acad. S c i . U.R.S.S., 1939, 24, 915.* " Overpotential ", 7, is defined as the potential difference between a workingelectrode and the appropriate reversible electrode in the same solution. I n this Report77 is taken to be a positive quantity, and is written 171 where any confusion regardingthe sign is likely to ariseAQAX : THE KINETIUS OF ELECTRODE PBOUEYYEY. 7usually incorporated, so that the D.C. or mean potential of the electrode maybe varied as desired.Although an electrode may be regarded as a network of resistances andcapacities, it should be noted that the system is likely to be highly non-linear,i . e . , the voltage across a resistance (capacity) is not proportional to thecurrent (charge).If a pure sinusoidal current flows through an impedance ofthis type, the resulting voltage generally contains a series of harmonics.The percentage of harmonics may be reduced to negligible proportions bykeeping the voltage amplitude sufficiently small, and amplitudes of a fewmv. (i.e., small compared to RT/F) have been found satisfactory.l6S l6, 18, l9The resistance and capacity associated with any stage of the electrodeprocess are thus " slope " or differential quantities, defined byR = aV/ai and C = ?q/aVwhere V represents the voltage drop associated with this stage, i thecorresponding current density, and q the corresponding charge per sq. cm. ;R (ohm. and C (VF. cm,-2) refer to 1 sq. em. of electrode surface.Of the systems so far studied, the simplest is the mercury electrode under" completely polarisable " conditions.Provided the solution contains noreducible solutes, there is a considerable range of potential in which noelectrolysis can take place, so that any current flowing through the electrode-solution interface in -these circumstances serves only to charge the doublelayer.* Under suitable conditions, concentration changes and the resistanceof the solution (&, Fig. la) may be neglected, and the electrode behavessimply as a condenser, having the double-layer capacity, C L (Fig. la). Thefirst reliabIe measurements of CL by this method, in which due regard waspaid tto possible contamination of the interface, were made by A. Frumkin andM. Proskurnin,lg using a stationary mercury surface and 50 cyclee/sec.A.C.M. Proskurnin and M. Vorsina20 subsequently extended the method tovery dilute solutions ( 10-4~) ; in these solutions the resistance Bs is no longernegligible in comparison with the impedance of CL a t 50 cycles/sec., but thedifficulty can be avoided by using very low frequencies (1 cycle/sec.).At more negative potentials the double-layer condenser develops a" leak ", since electrolysis, e.g., electrodeposition of hydrogen, becomesappreciable. This situation is shown in Fig. lb.al As before, Rs representsthe resistance of the electrolyte and concentration overpotential is neglected.A. Frumkin has pointed out 39 22 that a condenser (C,) in parallel with aresistance (Re) will represent the behaviour of any electrode a t which thereis only one slow stage; in such cases the rate of all stages of the reaction isalways uniquely determined by the instananeous value of the metal-solutionpotential difference. The slope resistance Re can thus be obtained from the21 Cf.B. Breyer and F. Gutmann, ref. (30); G. Falk and E. Lange, 2. Naturforscii.,1946, 1, 388.22 Acta Phy&ochitta. U.R.S.S., 1940, 13, 799.* This is the usual view, but there is no a p i o r i reason why other transient processes,e.g., deposition of adsorbed hydrogen atoms shouId not occur, even thongh continuouselectrolysis does not take place (see p. 26)8 GENERAL AND PHYSICAL CHEMISTRY.current-potential relation under steady current conditions ; for an electrodetvhich obeys the Tafel relahion :i = i0e~7~fl/R7' or yi = b(1og i - log io) .. . * (1)i.I(C)FIG. 1.where i (amps./cni.2) is the current density, i, is a constant, and b = 2.303ItTluP. we haveat rooin temperature, if u = 0.5.%Fig. l b has a particularly simple interpretation when the discharge ofions, rather than any subsequent stage, is the rate-determining step, becausethe capacity C, is then merely the double-layer capcity, CL. But if thedischarge process is rapid in comparison with some later stage, so thatz3 Cf. Frumkin, ref. (2), p. 41AGAR THE KINETICS OF ELECTRODE PRGCESSES. 9equilibrium is maintained between the ions and the (adsorbed) atoms formedby their discharge, e.g., H+ + E- + H(ads.), the capacity C, arises partlyfrom the accumulation of adsorbed atoms on the electrode, and will begreater than CL.It should be noted that the measured electrode capacity C,always includes CL, so that the reversible accumulation of adsorbed atoms williiot be detected unless the charge required to deposit them is comparable tothat required to alter the potential of the double layer.= If the value20 p ~ . c m . ~ is adopted for the double-layer capacity on a negativelycharged mercury surface, about 2 x coulomb/cm.2 are required tochange the double-layer potential by 0.1 v . ; this charge corresponds to1 or 2% of a monolayer of hydrogen.A.C. methods have been used by Dolin, Ershler, and others 16) lT> 25, 26 toinvestigate the kinetics of deposition of hydrogen ions on platinum.Theirexperiments refer to platinum electrodes at potentials more positive thanthe reversible hydrogen potential, and the conditions are such that (a) acoiisiderable fraction of the surface is covered with adsorbed hydrogenatoms, ( b ) the reaction Hr + E - =+ H(ads.), though fairly rapid, proceedswith measurable speed, and (c) the final stage (formation of free H2) does notoccur to any appreciable extent. The relation between the equilibriumpotential, V,,, of such an electrode and the amount of adsorbed hydrogen,q,[, expressed as coulombs per sq. em., is known from other investigations;it is thus possible to define a capacity C, = ?q,/aV,. Dolin and Ershler showthat the simplest possible picture of this system (for a homogeneous surfaceor a heterogeneous surface with unrestricted mobility of adsorbed atoms) isthat given in Fig. l c .As before, CL is the double-layer capacity, and Rd isthe “ resistance ” associated with the process H+ + E- + H(ads.). Ifthis process takes place a t the rates 5 J , in the two directions underequilibrium conditions (at the particular mean potential in question), it maybe shown l7 thatRd = RT/PJ, . . . . . . . . (2)Observations a t different hequencies 16, 25 indicated that Fig. l c did nottruly represent the A.C. impedance of the electrode ; the experimentalresults actually correspond to a more complicated circuit of the type ofFig. I d , which represents a heterogeneous surface, having different resistancesRd, Rd‘, Rd” . . , and capacities C,, C,’, Ca” .. . a t different points,together with restricted mobility, represented by resistances r , r’ . . .The influence of the local concentration changes produced by alternatingcurrents has been studied by J. E. B. Randles and by Frumkin, Dolin, andEr~hler.~’ It was shown theoretically many years ago 28 that a sinueoidalcurrent passing through an electrode would cause the concentration of anysubstance taking part in the electrode process to oscillate about a meanvalue, with the same frequency as the current but different phase. Theamplitude of the concentration change is a maximum at the electrode-’‘ -4. Hickling, Trans. Ir’araday SOC., 1941, 37, 532.l 5 K. Kosenthal, P. Dolin, and B. Ershler, Acta Physicockiwr. U.H.S.S., 1946, 21, 213.2b B.Ershler and 31. Proskurnin, ibid., 1937, 6, 196. 2 7 Ibid., 1940, 13, 793.A 10 GENERAL AND PHYSICAL CHEMISTRY.solution interface and falls off exponentially with distance from the interface.For a reaction having negligible activation overpotential and involving unitvalency change, and provided the amplitude of the concentration oscillationsis small, the A.C. component of the concentration overpotential isA- cos (at -;) . . . RT iylc=---l@ col/Da (3)where D is the diffusion coefficient of the reacting ion, co is the meanconcentration, and the alternating current density is i = iA cos at It willbe seen that the potential lags behind the current density a t all frequencies.The relation (3) is equivalent 17, 28 to a capacity C, and a resistance R, inparallel, or l8 to a capacity +C, and a resistance $Iic in series, where(in farads and ohm respectively).The fact that the system can be represented, at all frequencies, either by aseries or by a parallel arrangement of resistance and capacity is surprising;i t arises from the dependence of C, and R, on a.A similar result is obtained when the activation overpotential is notnegligible,l83 27 but it is now necessary to include an additional resistanceRe, characteristic of the interfacial reaction and related to the equilibriumexchange rate Jo in the same way as Rd (eqn.2). Ershler’s final expressions 17are equivalent to Fig. l e ; they have been applied to the systemHglHg2(C10,),, 0 . 0 1 ~ ; HCIO,, 2 ~ , using frequencies up to 5000 c.P.s.; tothe platinum-hydrogen electrode under conditions such that local changes inconcentration of dissolved hydrogen are important,27 and, in a rather morecomplicated form, to the determination of the rate of adsorption of ions onmer~ury.1~ Randles l8 has investigated the deposition of various metallicions a t amalgam electrodes, where there are two diffusion processes-in thesolution and in the mercury-and has evaluated the rate constant for thereaction Zn++ -+ Zn (amalgam) ; it is strongly dependent on the natureof the anion.-Further experiments, using 50 C.P.P. A.C. at a mercury-jet or droppingelectrode, have been carried out by J. Heyrovsky and his co-workers,6~29and by B. Breyer and F. Gutmanm30 Heyrovsky’s results indicate thatmost single-electron deposition processes and some two-electron processestake place very rapidly, although the deposition of Zn, of many other bivalentions, and also of Bi++-+, Sb +++, and In+++ from certain solutions, is distinctlyirreversible.(b) Charging Curves and Decay of Overpotential : Oscillographic Methods.-The first work in this field in which attention was paid to the elimination of28 F.Kriiger, 2. physikal. Chem., 1903, 45, 1 ; T. R. Rosebrugh and W. Lash Miller,J . Physical Chem., 1910, 14, 816.29 See ref. ( 1 ) ; 2. physikal. Chem., 1943, A , 193, 77 ; Coll. Czech. Chem. corm^., 1947,12, 11.30 Trans. Faraday SOC., 1946, 42, 644, 650; and see ref. (1)AGAR : THE KINETICS OF ELECTRODE PROCESSES. 11impurities appears to be that of F.P. Bowden and E. K. Rideal31 and ofE. Baars32 who measured the decay of hydrogen overpotential on opencircuit; Bowden and Rideal3l also studied the increase or decrease ofoverpotential when the current was increased or reversed. More recently,P. P. Bowden and K. E. G r e ~ , ~ 3 using very low current densities, havefollowed the correspondingly slow change of potential on a mercury cathodewith a quadrant electrometer, and several investigations have been made,with the aid of the cathode ray oscillograph,34f 35 of the more rapid changesof potential at higher current densities.The results for mercury cathodes may be interpreted in terms of Fig. l b ;if the conditions are correctly chosen, leakage through the resistance Re isnegligible, and a linear change of potential with time (at constant C.D.) isobserved, from which the electrode capacity may be derived.When thepotential of the electrode approaches its final steady value, Re can no longerbe neglected. A correction derived from the y-log (steady current) relationmay he applied; 31 an alternative method of deriving this correction, fromcharging and decay curves in combination, has been described by B.Kabanovand S. J ~ f a . ~ ~Similar methods have been used to study the deposition of monolayers ofhydrogen or oxygen on platinum.37It was shown by G. Armstrong and J. A. V. Butler 38 that the decay ofhydrogen overpotential on mercury at low C.D.s was in good agreement withan equation of the formwhere t is the time after stopping the current and B is a constant.Usingthe Tafel equation (1) in conjunction with Fig. l b , and assuming C, to beconstant, it may easily he shown thataF i,t eaqlF'Rl' - eaqlF,'R1' = -R T c ? * - - -where -ql is the initial overpotential and i, is defined by (1) ; this equationreduces to the logarithmic form (4) for large values of t . An analogousequation is given by F r ~ r n k i n , ~ who quotes unpublished experiments on amercury cathode by Fedotov in support of it ; the values of C, observed were18-20 P F ~ , and thus in good agreement with the accepted value of thedouble-layer capacity a t more positive potentials (see Table, p. 18).The decay of overpotential on other metals has been extensively studiedn 1 Proc. Roy. Soc., 1928, A , 120, 59.32 Sitzungsber.Ges. Beford. Naturwiss. Marbury, 1928, 63, 213.33 See ref. (1).34 E.g., Butler and Pearson, ref. (120) ; Barclay and Butler, ref. (73) ; Hickling,35 K. F. Bonhoeffer et al., 2. Elektrochem., 1941, 47, 147, 441, 536; E. Newbery36 Acfa Physicochim. U.R.S.S., 1939, 10, 617.37 See p. 26.R * Trans. Faraday Soc., 1933, 29, 12til ; cf. Butler, ref. (10).ref. (43).el al., l's-ar~s. Faradny SOC., 1947, 43, 12312 GEXERAL AND PHYSICAL CHEMISTRY.by A. L. Ferguson and his co-workers s99 40. *1 and by A. Hickling andP. W. Salt.42 From their results, there is little doubt tlhat the phenomenaare often more complex than the above equations suggest. There is. as yet,no adequate explanation of all the observations, but Hickling and Saltconclude that there are two distinct processes, one operative at high C'.D.sand responsible for the rapid, initial, part of the decay curve, and anotherresponsible for the slower, long-period, decay.High-speed charging and decay curves have usually been determilied by'' single-sweep " oscillographic methods, but a repetitive method, giving astationary picture on the oscillograph, has been used by A.H i ~ k l i n g . ~ ~Another instrument developed by the same author 44 makes i t possible tostudy rapid decay processes without an oscillograph. The instrumentmeasures the lowest potential attained during a known and adjustableinterval of time; for a continuously decreasing potential, this must be thepotential at the end of the interval.(ii) The Electrolytic -Double Layer.It is obvious that the structure of the double layer, i.e., t'he tlistributioiiof charged particles and of neutral molecules at the electrode-solution inter-face, is a question of major importance to the understanding of electrodereacti0ns.~~9 46 The methods of investigating the double layer may beclassified under five headings : 47 (1) Electrocapillary (including measure-ment of contact angles in the case of solid 48 (2) Measurement ofcharge per unit surface area by the dropping electrode.(3) Measurement ofelectrode capacity, by charging curves or A.C. methods. (4) Directmeasurement of adsorption from the solution. (5) Electrokinetic methods.Recent work on frictional 493 50 and other mechanical properties 51 ofmetals in aqueous solutions suggests the possibility of an additional methodof studying the metal-solution interface.Methods ( l ) , (2), and (3), which are closely related to one another by thefundamental equations of electrocapillarity, are at present the mostimportant, although mainly restricted to mercury electrodes.The exactthermodynamic treatment of the electrocapillary curve, due originally to39 ?'runs. Electrochletw. SOC., 1939, 76, 113.40 A. L. Ferguson and H. Bandes, ibid., 1942, 81, 103, 123.I1 See ref. ( 1 ) .4 2 Trans. Faraday Xoc., 1941, 37, 460.43 Ibid.. 1940, 36, 364; cf. T. Erdey-Grk and (1. Kromrey, %. physikal. Chew.,4 4 Trans. Faraday ~ o c . , 1937, 33, 340; see also ref. (421).4 5 A. Frumkin, " Coliche double, Electrocapillarite, Surtension ", ActualitPs4 6 A.Frumkin, Trans. Faraday Soc., 1940, 36, 117.4 7 Cf. Butler, ref. (10); Frumkin, ref. (46).4a See also A. Frumkin and A. Gorodetskaya, Acta Physicochisn. U.R.S.S., 1938, 9,48 F. P. Bowden and D. Tabor, dim. Reports, 1945, 42, 32.j0 R. E. D. Clark. Trans. Puruday SOC., 1946, 42, 449.1931, A , 157, 213.scientifiques et industrielles, No. 373 (1936).313, 327F. 0. Koenig 52 and to S. K. Craxford, 0. Gatty, J. StL. Philpot,and. H. A. McKay,= has been reviewed by Craxford,54 and a rather simplerderivation, following Koenig, has been given by D. C. Grahame andR. B. W h i t n e ~ . ~ ~ ? 55a Exact relations for concentrated solutions have beenworked out by S. Jofa and A. F r ~ m k i n , ~ ~ who refer potentials to a suitablereversible electrode in the same solution, e.g., a reversible hydrogen electrodein hydrochloric acid.The earlier discussions usually imply that the potentialis measured with respect to a standard reference electrode, and that theliquid-junction potential between this electrode and the solution underinvestigation can be eliminated.For a “ completely polarisable ” electrode 523 54, 55 the most importantrelation is the Lippman equation :(+/a+)s,c = - Q . . . . . (6)where y is the interfacial tension, C# the metal-solution potential difference,and q the charge per unit area on the metallic side of the interface; thesubscripts s and c imply constant area and constant composition of so1ution.sThe value of + is always ambiguous to the extent of an unknown additiveconstant, but this presents no real difficulty.The charge q is the differencebetween the number of positively charged univalent ions in t’he metal and thenumber of electrons.The differential capacity, C, of the electrode is defined byc = (a(I/aC#),, c . . . . . . . (7)(;2y/2+2)& c = - c . . . . . * (8)whence it follows thatThese equations are entirely general and do not involve any assumptionsabout the distribution of the charges at the interface; 54 they show (a) thatthe charge (I is always zero at the electrocapillary maximum; ( b ) thatmethods (l), (2), and (3) are to a large extent equivalent. ,4lthough theearlier work suggested discrepancies, recent experiments have confirmedthis inter-re1ati0n.l~~ st A.Frumkin and M. Vorsina 5 7 9 58 have pointedout that capacity measurements usually give more detailed information thanmethods (1) or (2), even for mercury surfaces; for solid metals theiradvantages are obvious.Further equations may be derived connecting y, 4, and the concentration51 E.g., P. Rehbinder and E. Wenstrom, Acta Physicochim. U.R.S.S., 1944,19,36.jn J . PhysicaE C’liesn ., 1934, 38, 1 1 1, 339 ; Wien-Harms, “ Handb. d. Experimental-physik ”, 12(ii), 380 (1933) ; N. K. Adam, “ The Physics and Chemistry of Surfaces ”,Oxford, 1938, p. 344.53 Phil. Mag., 1933,14,849; 1934,17, 54; 1935,19,965; 1936,22, 359.j4 Trans. Faraday SOC., 1940, 36, 85.55n D. C. Grahame, Chem. Reviews, 1947, 41, 441. (This review appeared while theprevent Report was in the press; it is not possible to deal fully with its contents, whichdiffer in some respects from the views of other workers.)5 6 Acta Ph?ysicochint.U.R.S.B., 1939, 10, 473; see also S. Jofa et al., J . PhysicalC ’ ? t p t ) i . Russia, 1939,13, 931, 934.* a .4( tn PhyRicochini, Tr,R.S,S., 1943. 18, 242.5 5 J . Amer. Chem. SOC., 1942, 64, 1548.j8 Ibid., p. 341. .14 GENERAL AND PHYSTCAL CHEMISTRY.or activity.52~ ** 55n- 56 The information to be obtained from the comparisonof electrocapillary and capacity data a t different concentrations has recentlybeen discussed in detail by GraharneeSEa It is possible, for example, tocalculate the adsorption of cations and anions, separately, at the metal-solution interface.The corresponding equations for non-polarisable or “ partially ” polarisahlcinterfaces are discussed by Craxford FA and by Grahame and Whitney.66At first sight, method (Ti) would appear attractive, but two difficultiesarise in its application : (a) The theory of electrokinetic effects at metallicsurfaces is at present unsatisfact~ry,~~ because it is not possible to allowadequately for the deflection of current from the solution to the metallicconductor; the well-known equations of D.C. Henry 60 are derived onthe assumption that it is determined by the conductivities of the two phases,but it has been pointed out that polarisation phenomena a t the metal-solutioninterface are probably more ( b ) The exact relation betweenthe electrokinetic < potential and other quantities concerned (e.g., thepotential discussed below) is not clear.6fIn the case of mercury or other liquid metal, there is an additionaldifficulty, since the motility of mercury droplets in an electric field ariseslargely from a circulation within the drop set up by the differing interfacialtensions a t various points of its surface.62 The subject is discussed byA.Frumkin and B. Levich.s3Direct measurements of adsorption, (4), have not been widely used, butthe method has been employed in the study of silver,64 charcoal,65 andplatinum surfaces. 66The detailed structure of the double layer is usually discussed in terms of0. Stern’s theory,67 which may be regarded as a synthesis of the earlierviews of Helmholtz with those of D.L. Chapman and G. G o ~ y . ~ ~ Sternintroduced three new concepts :(i) The overall potential difference between metal and solution is5s A. Frumkin and’ B. Levich, Acta Phyaicochint, IJ R.S.S., 1945, 20, 769; see alsoH. R. Kruyt and J. Oostermann, Kolbid-Beih., 1938, 48, 377.Proc. Roy. SOC., 1931, A , 153, 106.81 E.g., F. Urban and H. L. White, J . Physical Chem., 1932,36,3157; W. G. Eversoleet al., J . Chem. Physics, 1943,11, 63, 156.62 See B. Bruns, A. Frumkin, et al., Acta Physicochim. U.R.S.S., 1934, 1, 232;1938, 9, 359; H. J. Antweiler, 2. Elektrochem., 1937, 43, 596; 1938, 44, 719, 831, 888;M. von Stackelberg, ibid., 1939, 45, 466; T. Krjukova, Acta Physicochim. U.R.S.S.,1947, 22, 381.63 ] b i d . , 1946, 21, 193.64 M.Proskurnin and A. Frumkin, 2. physikal. Chem., 1931, A , la, 29; V. I.Veselovsky, Acta Physicochim. U.R.S.S., 1939, 11, 816; see also H. R. Kruyt andJ. T. G. Overbeek, Trans. Faruday SOC., 1940,36,110.6 5 A. Frumkin et al., Acta Physicochim. U.R.S.S., 1940, 12, 796.6 6 A. Slygin, A. Frumkin, and W. Medwedowsky, ibid., 1936, 4, 91 1 ; A. FrumkinSee also J. J. Bikerman, Phil. Mag., 1942, 33,and A. Slygin, ibid., 1936, 5, 819.384, and ref. (552).2. Elektrochem., 1924, 30, 608.68 See Butler, ref. (10)AGAR : THE KrNETICS OF ELECTRODE PROCESSES. lfidivided into two parts ; one, is the potential difference between a distantpoint in the solution and the centre of an ion in contact with the metal, whilethe other, (+ - is the potental difference between the centre of such anion and the interior of the metal.(ii) The charge in the metal, q per unit area, is given byq = K ( + - $ h l ) .. . . . (9)where K is the (integral) capacity of the “ Helmholtz ” part of the doublelayer.(iii) The charge in the solution, which amounts in all to - q per unitarea, is divided into two parts. The first, - ql, is supposed to consist of ionsoccupying adsorption sites on the electrode surface, and the number of suchions per unit area is evaluated by an application of Langmuir’s adsorptionequation, the adsorption energy being of the form @ & $lP, where I[, is the“ specific adsorption potential ” of the ion in question. The second, - q2,is a diffuse distribution of charge, of the type originally postulated by Gouy.This distribution is calculated 6 7 9 69 by methods similar to those employed inthe Debye-Huckel theory ; the non-linear Poisson-Boltzmann differentialequation in this case can be integrated directly without further approxim-ations.A. S. Coolidge and W. Juda 7O use a different method of calculation.It should be noted that the capacity K relates the total charge to a partof the potential difference-that between the metal and the layer of ions incontact with i t (the “ Helmholtz ” layer) ; K gives no direct informationabout the charge of the Helmholtz layer.68The two charges ql and q2 may be evaluated in terms of #1, the specificadsorption potentials, the concentration, c, and certain known constants ofthe system, and on equating (ql + q2) to - q a rather complicated relationbetween the various quantities is obtained.67 The equation can be simplifiedif the specific adsorption potentials may be neglected and if the ions in theHelmholtz layer occupy only a small fraction of the available sites.For ami-univaIent electrolyte, we then have 46q = K(+ - ,J~) = 2cdP sinh * 1 P + 4c - P sinh -L, * P . . (10) RT K 2Rlwhere K is the reciprocal of the Debye-Huckel characteristic length and dis the diameter of a water molecule, which appears in consequence of theassumption that the number of available dtes in the Helmholtz layer is equalto the number of water molecules in contact with the surface. According to(lo), + and t,hl are both zero at the electrocapillary maximum, where q = 0.Analogous equations may also be derived for electrolytes of other valencyty~es.5~9 7 1When 4 is not too close to zero, it follows from (10) that t,bl is practicallyindependent of 4, though dependent on c.Consequently, if the potential of apolarisable electrode is altered in a solution of constant concentration, the69 S. M. Neale, Trans. Faraday SOC., 1946, 42, 473.l o J . Amer. Chem. SOC., 1946, 68, 608.‘1 A. Frumkin, 2. physikd. Chem., 1933, A , 164, 121 ; see also ref. (57)1 t i C: ENERAL AND PHYSICAL CEIEMTSTRY.change of the Helmholtz potential, A(+ - $1), is practically equal to thechange of the total potential, A$. Furthermore, the observed double-layercapacity, CL = aq/2+, becomes equal to K , which may thus be found bymeasurement of C, in an appropriate range of potential.When K ia known,may be calculated by using (lo); alternatively, may be calculatedfrom (9), using experimental values of the total charge q and of K.463 575 58With the same restriction on the value of 4, i t may also be shown that= remainsconstant, becoming numerically greater as the concentration is reduced.These two well-known results are particularly important in applications tothe kinetics of electrode processes.(RT/F) A In c if the concentration is varied while (+ -K-*.I \I \I \ . - - _ - -IK+I I0.5 1.0FIU. 2 .Potentia/ v. N- ca/orne/ e/ectrode.The capacity of the electrode in the neighbourhood of the electrocapillarymaximum (+ = 0), where CL =i= K , may also be calculated from 573 58But a difficulty arises because the value of K for a negatively chargedelectrode, where the Helmholtz layer consists mainly of positive ions, differsfrom that for a positively charged electrode in contact with a layer of negativeions, and it is not clear which capacity should be used when the charge issmall and the layer contains comparable numbers of both ions.Expressionstaking the two capacities, K+ and K-, into account have been given byFrumkin 463 575 58 and by J. StL. P h i l p ~ t . ~ ~Measurements of the capacity of mercury electrode^,^^^ 573 583 737 74 and72 Phil. Mag., 1933, 13, 775.73 I. i\f. Barclay and J. A. V. Butler, Trans. Faraday Soc.. 1940, 36, 12s.D. C. Grehame, J . Anwr. Ghem. SOC., 1946, 68, 301ACAR : THE KINETICS OF ELECTRODE PROCESSES. I 7related electro-capillary investigations 54, 72 in solutions of ions that do notshow marked specific adsorption are in general agreement with Stern’stheory. The variation of capacity with potential in dilute solutions isusually of the type indicated in Fig.2.469 571 58 The values of K , and K - ,for cation and anion respectively, are given by the two *’ plateaux ”. I n theneighbourhood of the electrocapillary maximum there is a minimum, whichbeconies cieeper and wider as the concentration is reduced, in agreement withtheory. The actual value of the minimum, however, has been found to behigher than that given by the the0ry.4~9 57 The sharp rise in capacity on theextreme left-hand (positive) side probably indicates incipient formation of asolid salt or dissolution of the electrode, and in many solutions, particularlya t higher concentrations, it tends to obscure the true negative ion capacity.Grahame l5 has found i t impossible to fit the curve in this region by a Sternequation including a constant specific adsorption potential.*In more concentrated solutions (e.g., l.0N-potassium chloride) anomaliesappear in the region of the capacity minimum, including a subsidiarymaximum on the left-hand branch near the point of zero ~ h a r g e .l ~ l ~ ~ , 74At intermediate concentrations (e.g., 0-1N-potassium chloride) there is analmost uniform transition from K - to K , , without maximum or minimum.A subsidiary maximum on the right-hand branch appears in solutionscontaining multivalent cations, and is clearly observable in, e.g.,10-3~-HCl + 10-5N-LaC13.Such observations indicate that multivalentcations enter the Helmholtz layer in greater quantities than the Stern theorysuggests as soon as an appreciable negative charge is present on the metaI.The structure of the double layer is thus less diffuse than that pictured bySmall maxima on both sides of the usual minimum have recentlybeen reported 55a for 0.001N-perchloric acid and 0.001N-sodium fluoridesolutions without addition of multivalent ions.Rather different anomalies appear when the solution contains capillaryactive anions, such as iodide. They have been discussed by Vorsina andFrumkin 58 and by 0. Essin and R. Markov; 75 a somewhat differenttreatment of this subject was given by J.A. V. Butler.76 The capacity ofmercury electrodes in the presence of capillary-active organic molecules hasalso been in~estigated.1~~ 55a7 i 3 j 7 iData on the change of ymax with concentration are given by Craxford 54(KNO,, NaCl, KI, CaBr,) and by Frumkin and J ~ f a . ~ ~ From these values,the amounts of electrolyte adsorbed on an uncharged surface may becalculated by the Gibbs adsorption equation. For potassium nitrate andsodium chloride (N and 0 . 1 ~ ) they are positive, though small(< 1 x 10-l0 mol./cm.2) ; larger positive values are obtained when the salt(KI, CaBr,) contains a readily adsorbable anion.5P I n concentrated57A d a PILysicochinL. U.R.X.S., 1939, 10, 353. ’’ .l’r*OC.Ro?~. XOC., 1927, A , 113, 594.i i A . Ksenofontov, R t . Proskurnin, and A. Gorodetslmyn, Actn Physicor.liini. U.R.S.S.,* See also ref. (Eiha).1938, 9, 39; A. Gorodetskap, ibid., 1940,12, 3091s GENERAL AND PHYSICAL CHEMISTRY.hydrochloric acid the adsorption appears to be negative.56 Experimentalresults for sodium chloride solutions a t various concentrations and potentialshave been analysed by Grahame.55a He finds that the specific adsorptionof the chloride ion on a positively charged mercury surface may considerablyexceed the net negative charge of the solution side of the double layer.Some recent values of the capacities of mercury electrodes are given inthe Table.Capacities of mercury electrodes (VF./cm .2).Solution.K-. Minimum. K,. Mothod. Ref.0,00l~-HCl 39 * 8.0 (5.5) 17.2 A.C. (1 c.P.s.) stationary 6TO-OlN-HCl - 9 , 9 9 O-OO~N-HC~ + 39 * 12.9(7*2) 18.6-19.6 ,, ,,7.2 17.5 * I 7 , 58 0-001N-NaOH -0*001N-H2SO4 41 * 8.1 17.3 *0.1 N-KCl N 36 - - 19 460.1 N-NaCl - n!) 1 8-1 I) A.C. y240 to 500G'c.p.s.). 7 1Slowly-forming drop.-_ N 22 Single-sweep osc. (le3 73to lea see.). Exact1 .ON-H,SO,electrode area uncer-tain.C.D.electrode.14.7 (10.5) -0.00 IN-ThCI, (max. 27.8)} N 50 1 *ON-HCI0.2N-HsSO4 - - 20.2 5 2 Slow charging at low 33O-IN-KCI 42.2 - 22.3 Dropping electrode 780.001 to 0.16N-HCl 53.7 1.7 -- 23.3 & 0.5 9 , 9 , 72Hf, K+, Ca++, Al+ I + - - 19 E lectrocap. curve. 540- 1 N - NaC 1 57.3 _ - 23.6NO,- (0.001 to IN) 24 I , 9 ,c104- (0-2N) 26 9 1 9 , so,- (0.01 to 1N) 40 1 , 9 9Figures inparentheses in the third column are theoretical minimum capacities given by Stern'stheory.(iii) Theories of Hydrogen Overpotential.Since theoretical aspects of electrode reactions were last discussed in thesereport^,^ H.Eyring, S. Glasstone, and K. J. Laidler 79 have put forward anew theory of hydrogen overpotential, which may also be adapted to explainoxygen overpotential. Developing the ideas of J. Horiuti and M. Polanyi,sothey assume that the rate-determining step, at least for one class of electrode,is a prototropic reaction * in the neighbourhood of the electrodesolutioninterface. But whereas Horiuti and Polanyi envisaged the processrepresented byEyring, Glasstone, and Laidler suppose that : (i) the proton comes from anH,O molecule (not an H30+ ion), in both acid and alkaline solution; (ii) the- -- -- -* Indicates values derived from curves given in the references cited.OH3+ +Me--+OH, +H-Me .. . . (A)7 8 D. Ilkovic, Coll. Czech. Chem. Comm., 1936, 8, 170.i 9 J. Chem. Physics, 1939,7, 1053; Trans. Electrochem. SOC., 1939, 76, 145.Acta Physicochim. U.R.S.S., 1935, 2, 605; cf. A. Frumkin, 2. physikal. Chent.,1932, A, 160, 116; J. A. V. Butler, Proc. Roy. SOC., 1936, A, 157,423.* Prototropic reactions in general, and the various ways in which they may bepictured, are disciissed by R. P. Bell, " Acid-Base Catalysis ", Oxford 1941 ; see alsoR. P. Bell, Trans. Faraduy SOC., 1941, 37, 493AGAR : THE KINETIC'S OF ET,ECTRODE PROCESSES.19rate-controlling proton transfer occurs between an K,O molecule in thesolution and a layer of adsorbed water on the electrode; (iii) the adsorbedwater is more or less split up into H and OH, separately adsorbed on tiheelectrode. The complete scheme may thus be writtenIH2°-iMnH I - H- H i - 0- H- IH 0-H + 0- Me --+ 0-. . . H ~ . . .o- Me --+ I + HH-Initial state. Activated state. Final state.In their first ~apers,7~ Eyring, Glasstone, and Laidler supposed that theelectrode potential, V , including any overpotential, was developed betweenthe H20 in solution and the adsorbed HO and H on the metal, and assumedthat a fraction aV of the potential determined the free energy of the activatedcomplex; if the proton in the activated state is situated approximatelyhalf-way across the double layer, a will be about 0.5.By a simple applicationof the absolute reaction rate theory, it is shown that the rate of discharge isproportonal to e-aVRW',* whereas the rate of the reverse process isproportional t o efpVF/RT, where a + p = 1 . 7 In a later form of thetheory,Q 82 in order t o explain the fact that q (not V ) is independent of[Ht] in solutions of acids without added salts, it was assumed that : (iv) thepotential V is developed across two double layers; the overpotential iseffective over the inner or " electrode " layer considered above, while thereversible part of V operates over an outer or " solution " layer. Theinfluence of electrode material on y is ascribed to the differing strengths ofthe M-H and M-OH bonds assumed in (iii).The theory has been criticised by A.Frurnkin.,? 84 Although (iv)roughly corresponds to the diffuse and Helmholtz double layers of theStern theory in a solution containing an acid alone, it does not do so whensalts are present in excess. Under such conditions (see later), q definitelyvaries with [H+], and the experimental results indicate that the reactingspecies in acid solutions (though not in alkaline) is H,O rather than H,O.However, the substitution of H,O' for H20 in (i) does not, perhaps,fundamentally change the theory, and it remains to consider suppositions(ii) and (iii), which represent a profound modification of the usual ideasconcerning the structure of a mercury-solution interface.It is difficult t osee how they can be reconciled with electrocapillary and related data.,Eyring, Glasstone, and Laidler were originally led to postulate H,O as thereacting species by a comparison of a few observations for other metals inacid and alkaline solutions; the data on which they base their conclusionS. Glasstone, K. J. Laidler, and H. Eyring, " The Theory of Rate Processes ",Proc. Imp. Acad. Japan, 1939, 15, 39.81 G. E. Kimball, S. Glasstone, and A. Glassner, J . Chent. Physics, 1941,9, 91.McGraw-Hill, 1941 (Chap. X).84 Acta Physicochim. U.R.S.S., 1940, 12, 481.* European sign convention.t A more general relation between forward and reverse rates hrts been derived by.I . Horiuti and M. Ikusima.820 C4NN E RAT, AN 1) PHYSTCAT, CHEMISTRY.are very limited, and it has been criticised on other grounds byJ.A. V. Butler.85G. E. Kimball R6 has applied the theory of absolute reaction rates toion-discharge reactions in a more general manner and has considered theeffect of diffusion processes. Somewhat similar relations have also beenderived by R. A ~ d u b e r t . * ~ A different point of view has been advanced bj-.J. Weiss,8a who supposes that electronic transitions froin the interior of theiiietal to the solution arc sluggish because the electrons have first to beraised to the relatively high surface energy levels.Much attention has been paid to the * ‘ electro-chemical ” mechanismsuggested by Horiuti et aLs9 The reaction in question is usually writtenH,O 4- H-Me-+ H,O 4.- H, + Me .. . . (B)although Horiuti himself sometimes considers 90 a, different, bnt related,process :H, + Xe+ H, -{- MeTt was originally supposed 89 that the adsorbed hydrogen atoms, H-Me,are in equilibrium with the solution, i.e., that the reaction H,O 1- + Me- +H-Me is fast. This assumption leads to conclusions (values of or> 1) incontradiction to experiment if the fraction of the surface, 8, covered byhydrogen is small; 91* 92 it may easily be shown, however, that lower valuesof a are to bs expected if 8 is large.More recently, the possibility has been considered that the reactionsandH,O +Me-+H-Me . .+ H-Me- -+ H, -1 Me H,O. . . (A). . * (R)are both irreversible.l61 25, 91, 93- 94 Neglecting the interaction between theadsorbed atoms, it may be assumed (cf.9k93) that the two reaction rates(current densities), are given byi , == k., [H 3 ( 1 - 0) e-abP,RT *85 J .Chem Physics, 1941, 9, 279.8 7 J . .Phys. Radium, 1942, [8], 3, 81 ; see G. Champetier, “ La Recherche chimique88 See ref. ( 1 ) .89 J. Horiuti, G. Okamoto, and K . Hirota, S c i . Papers Inst. Phys. Chenz. Res. To~!Jo,1936, 29, 323; G. Okamoto, J . Pac. Sci. Hokkaido I m p . Univ., 1937, (iii), 2, 11.5;J. Horiuti, S c i . Papew Inst. Phys. Chern. Res. Tokyo, 1940, 37, 374.8 6 Ibid., 1940, 8, 199, 815, 820.en France ”, 1940-1945 ” (SOC. chimique de France, 1946).E.g., K. Hirota and J. Horiuti, Bull. Chenz. SOC. Japan, 1938, 13, 238.9 1 A. Frumkin, Acta Physicochim. U.R.S.S., 1937, 7, 475.92 A.Frumkin, Sci. Pdpers Inst. Phys. Chem. Res. Tokyo, 1940, 37, 473.93 P. Lukovtsev, S. Levina, and A. Frumkin, Acta Physicochim. U.R.S.S., 1939, 11,21 ; A. Legran and S. Levina, &id., 1940, 12, 243; see also P. Lukovtsev and s. Le\,ina,J . Physical Chem. Russia, 1947, 21, 589, 599.O‘ P. Dolin, B. Ershler, and A . Frumkin, Acta Pliy~icochi?>a. U.R.X.S., 1940, 13. 779.* Strictly speaking, these eqiiations are correct only when the difference betweenneed not be tftken into the overall potential 4 %nil the Helmholtz potential (4account,AGAR THE KINETICS OF ELECTR0I)E PROCESSES. 21andAs soon as a steady current is established, ill = ib, so thati,: k H [H’] f) e - a ’ P H l ’111 general, 8 inay either increase or decrease with 4, but if a’ = a , as inaywell be approximately the case, 0 becomes independent of-\ rather different situation arises if the reaction proceeds by thedtcrnativ-c “ catalytic ” mechanism : 895 95followed byand of i.H,O -+ Me- --+ H-Me (irreversible) (A)(irreversible) (C) 2H-Me ---+ H, + NC‘I’ht: rate of the latter is indepeiidcrit of the potential, so that thereshould cxist a maxiwzunz C.D., corresponding to 0 = 1.96 If‘ the current isincareased beyond this value, some other mode of formation of H,, e.g., (B),must come into action.A somewhat different, cliscwssiori of thc subject has been gil-cii byA.Hickling and F. W. Salt.g7 They assume that thc first stage (A) israpid and reversible, and that the amount of hydrogen adsorbed is determinedby either the Freundlich or the Langmuir isotherm.By suitable choice ofthe exponent in the Freundlich isotherm, it is possible to explain the observedvalues of the Tafel factor u on the basis that (C) is the slow stage, and i t issupposed that the reaction proceeds via (C) at low C.D. At high C.D. thcreaction (B) must also be considered. Assuming thnt it i.s equally probablethat a hydrogen ion will be discharged on an adsorbed H dona as on a vacant site,they conclude that q will become independent of C.D. at high C.D., theavailable adsorption area being 50 yo covered under these conditions.I t is clear from studies of adsorption of gaseous hydrogen on metals 98that the behaviour of the monolayer formed is profoundly affected by themiitual repulsion of the adsorbed atoms.As far as the hycirogen-electrodereachtioil is concerned, this factor uras first taken into awount by Horiuti~t r 1 1 . , ~ ~ 7 90, 95 who coilsidered the effect of repulsive forces 011 adsorbed atomsand on activated complexes of the type H - . . . Hall.., and Had<. . . . H<L,l..corresponding to (B) and (C) respectively. A simpler method hasbeen. developed by Dolin and Ershler, and by Frumkin andN. A41adjalova,16- 253 943 99 following M. Temkiii and V. Pyzhev.100 T t isasslimed (a) that repulsion between the adsorbed particles, or alternativelJ7,inhomogeneity of the suface, causes the energy of adsorption of H atoms toJ. Horiuti and G . Okamoto, Sci. Papers I n s t . Phys. C‘henr. lies. Tokyo, 1936, 28,231 ; Bull.Chem. SOC. Japan, 1938,13, 216.9G E q . , Butler, ref. (80).B* E.g., J. K. Roberts, “ Some Problems in Adsorption ”, Cambridge, 1939.99 Acta Physicochim. U.R.S.X., 1943, 19, 1.loo Ibid., 1940, 12, 327; see also J. Physical C‘hem. Russia, 1940, 14, 1153; 1941,97 Trans. Paruday Soc., 1942, 38, 474.15, 29022 GENERAL AND PHYSICAL CHEMISTRY.fall off linearly with 8, and (b) that the change in activation energy for thevarious processes considered is proportional to the change of adsorptionenergy. It follows from the first assumption that the activity (fugacity) ofadsorbed hydrogen is proportional to efe, where f is a constant,* and thisrelation has been confirmed experimentally by the electrochemicalinvestigation of the equilibrium properties of adsorbed hydrogen on platinum.If a numerical factor al, relating change in activation energy to change inadsorption energy, is introduced, it follows that the rate of deposition ofhydrogen on a partly covered surface (reaction A) isAnalogous relations may be derived for the reverse reaction, and for the" electrochemical " process (B) .94 In subsequent applications it has usuallybeen assumed that al = a, and in some cases, additionally, that al = a = 0.5.Calculations on these lines have led to several interesting results, of which thefollowing may be mentioned :(i) I n some cases the rate of deposition of hydrogen (reaction A) may beindependent of potential.l6> 25 This situation may arise if 8 increases as +become more negative, so that the changes in the two exponential terms in(12) compensate one another.More negative potentials tend to acceleratethe deposition, whereas an increase in 8 leads to an increased repulsiveenergy, which tends to make it slower.(ii) If hydrogen atoms are ultimately removed from the electrode bythe electrochemical mechanism (B), the conclusion that 8 should beindependent of i, already discussed for a simpler model in which interaction isneglected (cf. ll), also holds under certain conditions for the morecomplicated case.94(iii) If hydrogen atoms are ultimately removed by the catalyticmechanism (C), or by diffusion into the metal, the overpotential should beadditively composed of two parts, one characteristic of an equilibriumbetween the adsorbed hydrogen and the solution, and the other depending onthe kinetics of the deposition stage (A).99on the depositionof hydrogen ions (A), and on the corresponding reaction in which thereacting particle is a water molecule, has been further considered byFrumkin.21 37 46, 719 919 93 When the reacting particle is an H,O+ ion, it isassumed that the rate of deposition iswhere [H#Is is the hydrogen-ion concentration a t the interface, ($ - $J isthe potential across the Helmholtz layer, and F represents some function,which, on experimental grounds, may be expected to have the formi=k[H+]e-aIfee-aQFRT .. . . . (12)The influence of the diffuse double-layer potential,i = [H+lSw$ - $1)F(+ - = k: e- 4 4 - h)P/R2'* The relation given apparently implies that the difierential free energy of adsorptionis linearly dependent on 8 ; Temkin and Pyzhev actually consider the heat of adsorption,but the distinction is probably not important provided f is reasonably large and 6 is closeneither to 0 nor to 1AGAR : THE KINETICS OF ELECTRODE PROOESSES.23Provided that [H+lS is not too large, we have[H+Is = [H+], e-JllFIRTwhere [H'], is the bulk concentration. It follows that lo1RT . 1 - R RT 1 - RI'1-q I = --In z - (,-) ln[Ht]o + (,") t,hl - = I n k . (13):l: aPFor a mercury cathode, #1 is normally negative, and, as a < 1 , any reductionof its numerical value, e.g., by addition of neutral salts, should increase -4.On the other hand, if #1 remains constant while [ H - ; - ] , is varied, r ) shouldincrease by 2.303[(1 - a)/cr]RT/Pv. for each tenfold reduction in [H*],,.But if a solution of an acid alone is diluted with water, the ensuing changesin (cI1 and (RT/F) In [H+], cancel one another and q remains unaltered.If the reacting particle is H,O inst,ead of H,O-i, (13) no longer holds, andthe corresponding equat,ion isRT . RT RTaF P O aP 171 =-- In z + _ _ I n [H-'-] - # - -- ln k' .. . (14)The effects of change of [H+], (at constant +1) and of change of 1,h1 (at coiistttnt[H+l0) are thus in the opposite direction to those given by (13).These relations were originally worked out for the deposition of hydrogenand have been mainly used in connection with this reaction, but theprinciples involved should be applicable to other cases.45- l01The definition of the heat of activation in electrode reactions has beendiscussed by J.N. Agar,lol who also considers the possible temperaturevariation of a. It has been shown that the relation between heat ofactivation E' and overpotential discovered by F. P. Bowden : lo2and easily explicable if the rate-controlling stage is of the type (A), alsoholds if it is of the type (C).E = wo - aP(iv) Experimental Investigations of the Deposition of Hydrogen fromAqueous Xolutions.(a) Mercury Cathodes.-Although most investigators have confined theirattention to current densities between and amp./cni.2, somemeasurements have been made at lower and at higher C.D.s; the latter arediscussed in another section. Using a special technique to exclude oxygen,F.P. Bowden and K. E. Grew 103 studied the deposition of hydrogen from0*2~-sulphuric acid and found that the Tafel relation (1) held down to10" amp./cm.2, although the value of b was slightly greater than that usuallyobserved a t higher C.D. A. Mituya lo4 also made measurements in this1°3 See ref. (1).Io1 J. K. Agar, see ref. (1).lo2 Proc. Roy. Soc., 1929, A, 126, 107.lo4 Bull. Inst. Phys. Chem. Res. Tokyo, 1940, 19, 142; A . , 1940, I, 324.* Comparison of (1 3) or (14) with the empirical '1'afel equation ( 1 ) shows that the" a "s in the two cases are not strictly the The empirical a includes acontribntion, usually small,71 arising from the fact that 4, varies slightly with 4 (or v).'24 GENERAL AND PHYSICAL CHEMJSTRT.range, but his work has been criticised by Frumkin,2 who points out that hisresults for the higher C.D.s do not agree with established values and suggeststhat the electrode was contaminated by platinum, as appears possible in theapparatus used.I n the more usual range of current densities, 8.Jofa, A. Kolychev, andL. Shiftman lo5 have resolved a long-standing disagreement between theresults for stationary and dropping electrodes ; lo6 they show that identicalvalues of q are obtained by the two methods provided the dropping-electrodevalues are corrected for the non-faradic current and for changes in dropvolume as the potential becomes more negative. Measurements of hydrogenoverpotential on a mercury-jet electrode are also in agreement with those forstationary surfaces.lo7Several workers have confirmed 2y 33 l o 7 9 lo8 that the overpotential isindependent of concentration in dilute solutions of acids without added salts.On the view that the overpotential is due to reaction (A), this is in agreementwith (13), but it can also be explained in other ways.In more concentratedsolutions (> 0 . 1 ~ ) of hydrochloric, hydrobromic, sulphuric, and perchloricacids, a fall of -q is observed with increasing [H+],; l o 7 7 log, 110 in many casesthe q-log i curves are no longer linear, and there is a general tendency for theoverpotential to be more nearly independent of concentration a t thc morenegative electrode potentials., Frumkin and Jofa 2. 33 110 explain theseobservations as an effect of the penetration of anions into the double layer,giving rise to a more negative value of t,hl than the Stern theory, in its simpleform, predicts.in some of the solutions used, although the changes in ^r) are somewhat lessthan would be expected from the $i values.2Concentrated solutions of sulphuric and phosphoric acids have beenstudied by A.J. de Bethune and G. E. Kimball,los who also observe a fall ofoverpotential, which they ascribe to reaction of undissociated acid molecules.Such an effect is, perhaps, to be expected, but it would appear difficult toexplain the observations for perchloric acid in this manner.3The influence of addition of salts on the hydrogen overpotential was firstdemonstrated by S. Levina and V. Sarinsky,lll who added small amounts ofLaCI, to dilute HC1 solutions and observed an increase of overpotential,which is greater than that given by (13) when t,hl is calculated from Stern'stheory [eqn.(lo)] but somewhat less than expected if is obtained froincapacity data. The results have been discussed by Frumkin.2, 46The influence of additions of potassium and sodium chloride tohydrochloric acid solutions (constant [H '-I,,) has been investigated byThere is independent evidence of high negative values of105 Acta Physicochina. U.R.S.S., 1940, 12, 331 ; cf. Frumkin, rcf. (2).106 J. Heyrovsky, Chem. Reviews, 1939, 24, 125.107 A. Rius and J. Llopis, Anal. Fis. Quinz., 1946, 42, 897.108 J . Chem. Physics, 1945, 13, 63.1OQ 5. Jofa, Acta Physicochinr.U.R.S.S., 1939, 10, 903 ; J . Physical ChenL. Russia,110 Acta Physicochiin. U.R.S.S., 1943, 18, 183; see also J . Physical C'he7n. Russia,1939, 13, 1435.1944, 18, 268. ll1 Acta Physicoclbim. U.R.X.S., 1937, 7 , 485AGAR : THE KINETICS OF ELECTRODE PROCESSES. 25Bagotsky 112 and by J. Llopis and J. N. Agar.ll3 For these two salts verysatisfactory agreement with equation (13) is obtained when +1 is calculatedfrom Stern’s theory (or a modification of it).112 There also appears to befair agreement for additions of calcium ch10ride.l~~It has also been shown l l 2 9 113 that the overpotential in acid solutionsincreases by 0.058 v. per pH unit when [H-;], is decreased, provided the total(univalent) cation concentration, “a7, K+] + [Hi],, remains constant ;under these conditions is also constant, and, since u = 0-5, the result is inagreement with (13). Rather similar results have been obtained in moreconcentrated solutions (total cation concentration = 4M) by Jofa andFrurnkin,llo who also note that there is no correlation between the over-potential and the activity coefficient of hydrochloric acid, which dependsconsiderably on the nature of the salt (LiCI or KC1) present.The behaviour in alkaline solutions is entirely different. Kxperiments insuch solutions are difficult, owing to amalgam formation, and the observationsare less reliable, but i t has been confirmed 113 that a = 0.25 in NaOHsolutions, and an investigation of the influence of [OH-] in NaOH-NaClmixtures, with [OH-.] + [GI-] = constant ( O - ~ N ) , shows that -q in this casedecreases by 0.058 v.per unit increase of pH, a result to be expected if thereacting particle is H,O rather thaii H30 + [cf. eqn. (14)].Although addition of salts normally raises the overpotential in acidsolutions, the reverse effect may occur under some conditions if the anion ofthe added salt is strongly adsorbed on the electrode; 2. 11* an effect of thissort occurs with bromides a t low overpotentials. The influence of the iodideion has also been investigated ; 114 i t brings about a large lowering (ca. 0.2 v.)of q a t low C.D., but a t more negative potentials, where the iodide ions are nolonger adsorbed, the overpotential rises t o the usual value. A markedhysteresis effect is observed, which suggests that the adsorption anddesorption of iodide ions (on the negatively charged metal) is a relativelyslow process.Addition of certain capillary-active cations (e.g., tributyl-ammonium) to acid solutions raises the overpotential; 11* the effect may beascribed to the positive charge carried by the ions, but is possibly due in partto a siiiiplc blocking of the surface. J. O’M. Bockris and B. 1E. Conwayhave shown, however, that many alkaloids can Lower the hydrogen over-potential. 115The reliable experimental evidence now available indicates very stronglythat the rate-determining step in acid solutions is reaction (A), at least a t(2.D.s up to amp./cm.2.The main arguments leading to this conclusion may be summarised asfollows : 2 7 (i) Electrocapillary and capacity measurements over a wideraiigc of potential, both in acid and in alkaline solution, show that the112 Unpublished results quoted by Prumkin, ref.( 3 ) .113 Anal. Pis. Quin2. (in the press).llp S. Jofa, 13. Kabanov, E. Buchinski, and F. Chistyakov, Acta PhysicocltinL.115 Nature, 1947, 159, 711.U.R.S.S., 1939, 10, 31726 GENERAL AND PHYSICAL CHEMISTRY.mercury-solution interface corresponds closely to the ionic double layersenvisaged in Stern’s theory. There is no sign that adsorbed hydrogen atomsare at any time present in quantities even remotely approaching a completemonolayer. (ii) The only process that will give the observed value of aunder these conditions is (A). (iii) Measurements of the influence of changesin [H1 lo and of addition of salts show that in acid solutions H30+ participatesin the rate-controlling reaction.For alkaline solutions, the less extensiveevidence suggests that the corresponding particle is H,O.(b) Phtinum Cathodes.-Several recent investigations 947 116, 117 haveshown that the hydrogen overpotential on really clean, bright platinum ismuch lower than has generally been supposed. Platinum electrodes may becleaned or “ activated ” in situ by a brief anodic polarisation, and instringently purified solutions their activity does not change appreciably inperiods of the order of an hour. If the solution has not been purified, or iftraces of poisons (e.g., As203) have been added to it, the activity decays veryquickly, and the decay is accelerated by 117 This shows that theloss of activity is primarily due to deposition of some constituent of thesolution, and not to a slow “sintering ’’ of the metallic surface.Thenecessary purification of the solution may be carried out by leaving it incontact for some hours with large sheets of platinised pIatinum.At such electrodes, in acid solutions, the activation overpotential is of theorder of only 1 mv. a t 1 ma./cm2, and in unstirred solutions considerableconcentration overpotential is observed, arising from supersaturation of theliquid near the electrode with hydrogen. This overpotential can be decreasedby coating the electrode with a few monolayers of a long-chain fatty acid,which facilitates the removal of hydrogen as b~bb1es.l~~ The activationoverpotential in alkaline solutions is somewhat higher than in acid.94* 1 1 7The formation of adsorbed layers of hydrogen or oxygen on platinised andbright platinum a t potentials between the reversible hydrogen and thereversible oxygen value has been carefully investigated by Frumkin and hisco-workers,169 173 251 26, 66, 1181 119 by means of slow-charging curves and byother methods.Similar results have been obtained a t higher currentdensities, using a cathode-ray oscillograph to follow the more rapid changes ofpotential; 1 1 7 9 120, 121 this method has also been used to study gold 122 andsilver 123 electrodes, where rather different effects are observed. Althoughthe slow-charging curves approximate fairly closely to equilibrium conditions,comparison of observations made during deposition of the adsorbed film withthose made during its removal show that the process is not completelyreversible ; the irreversibility is probably more marked at higher currentI l 6 L.Kandler, C. A. Knorr, and C. Schwitzer, 2. physikal. Chem., 1937, A , 180, 281.1 1 7 G. C. Barker, private communication ; Diss., Cambridge, 1947.11* B. ErshIer and A. Frumkin, Trans. Furaduy SOC., 1939, 35, 464.119 A. Frumkin, A. Slygin, B. Ershler, and G . Deborin, Acta Physicochim. U.R.S.S.,lao J. D. Pearson and J. A. V. Butler, Trans. Furaday SOC., 1938,34, 1163.121 A. Hickling, ibid., 1946, 41, 333. 12? Idem, ibid., 1946, 42, 518.123 A. Hickling and D. Taylor, see ref. (1).1935,3,791; 1937,7,325; 1938,8,565; 1939,11,45AGAR : THE KINETICS OF ELECTRODE PJWCESSES.27densities. In acid solutions the equilibrium charging curves show threedistinct regions; starting with an electrode at or near the reversiblehydrogen potential they correspond to (i) removal of approximately amonolayer of hydrogen, (ii) charging the double layer on an almost baresurface, (iii) deposition of a layer of oxygen. I n alkaline solution thedistinction between the three regions is not so clear. The observed linearrelation between potential and quantity of electricity passed in region (i)shows that the heat of adsorption of hydrogen must decrease considerablyas the fraction of the surface occupied increases, and this has been confirmedby measurements of the differential heat of adsorption of gaseous hydrogenon platinum black.124 The bonds between the metal and the adsorbedhydrogen or oxygen atoms appear to have appreciable dipole moments, theiiegative ends being directed towards the solution.66 In the case of oxygenlayers the potential difference arising from the dipoles may .be greater thanthe overall metal-solution potential difference ; in consequence, the double-layer potential, and the 7: potential, are reversed, as may be shown byelectrokinetic e~perirnents.~~The distinction between the " double layer " region, and the two(hydrogen and oxygen) " adsorption " regions is shown very clearly by thecoefficient of friction between two platinum surfaces, which is much higher inthe double layer region than at lower or higher potential~.~~1 117The kinetics of formation and removal of adsorbed hydrogen have beenstudied by the alternating-current method 16, 1'9 25 (see p.9). In theregion of the reversible potential, the rate of deposition is almost independentof the potential [cf. p. 22, (i)] and is 10-20 times greater than the rate ofthe complete process H+ --+ H,, as measured with steady currents.94 Ittherefore appears that stages of the process subsequent to deposition ofadsorbed atoms have an important influence on the kinetics in this case.Similar investigations have been made in heavy water; 25 undercorresponding conditions, the rate of formation of adsorbed deuteriumproceeds a t about half the speed of formation of adsorbed hydrogen.( c ) Other Metals.-A careful investigation of hydrogen overpotential onlead cathodes in acid solutions has shown that the overpotential is evengreater than on mercury; 367 125 it also seems that clean lead electrodes givea value of cc close to 0-5, although earlier work 126 generally indicated lowervalues of a, and of the overpotential.36 Anomalous results are obtained ifthe potential of the electrode is allowed to become sufficiently positive foradsorption of anions (e.g., SO,=) or formation of lead salts to occur, or if highcurrent densities, which cause disintegration of the surface, are used.It appears that the reduction of lead salts (e.g., the sulphate), when oncethey have been formed, is a somewhat slow process, and this may explainI z 4 1,.Rfaidanowskaja and B. Bruns, Acta Physicochir,b. U.R.S.S., 1938,9, 927.lZB See also A. Frumkin and Y. Kolotyrkin, ibid., 1941, 14, 469; S. Jofa, J . PhysiculCheut. Russia, 1945, 19, 117; Y. Kolotyrkin and N. Bune, ibid., 1946, 20, 667; 1947,21, 581. alZ8 E.g., T. Erdey-Grriz and H. Wick, 2. physikal. Chem., 1932, A , 162,5328 GENERAL AXD PHYSICAL CHEMISTRY.the discrepancbies to be found in previous results for this metal. A similar'* slow reduction " effect may occur on iron e1e~trodes.l~'Lukovtsev, Levina, Legran, and Frumkin 93 have found that the hydrogenoverpotential on nickel cathodes increases with increasing pH in acidsolutions, but decreases with increasing pH in alkaline. Addition of neutralsalts lowers the overpotential in alkaline solutions, but may produce either aslight increase or a slight decrease in acid solntions, according to the currentdensity used.These observations show that the rate-controlling stagesinvolve H ' ions in acid solutions and, probably, H,O molecules in alkaline ;they can be explained qualitatively in terms of a slow deposition processfollowed by irreversible forination of H, by the electrochemicalniechanism (R) .Frumkiri and A l a d j a l o ~ a , ~ ~ and H. P. Stout,12* using a palladiu,i/diaphragm polwised on one side only as cathode, have demonstrated that aconsiderable part of the overpotential " comes through " the diaphragm tothe unpolarised side within a few minutes of starting the current ; similarobservations have been reported for irod29 Prumkin and Aladjalova showthat the overpotential 011 the polarised side is additively composed of twoparts, *tjl and rjZ; ql arises probably froiri the deposition of hydrogen aboms,is rapidly established, and is milch larger in alkaline than in acid solutions;q2 is characteristic of the concentration of hydrogen dissolved in the metal[cf. p.22 (iii)] and is transmitted to the unpolarised side of the diaphragm.Measurements of hydrogen overpotential on thallium have been made byT. M. Le Barrori and A. It. C h ~ p p i n , l ~ ~ using sulphuric acid solutions from04001 to 0 . 5 ~ ; the temperature coefficient of -q was also determined.Several less common metals (Ni, Cu, Pb, Mo, Tu, Nb, Be, In, and T1) havebeen studied by J.O'M. Bockris,l31 who has also shown that, for a largenumber of metals, there is a negative correlation between overpotential andthermionic work function. There is, as yet, no satisfactory explanation ofthe correlation.(d) High Cuwent Den,sities.-An extensive investigation of hydrogenoverpotential on many nietals at high ciirrent densities ( to 1 amp./cm.2)has been carried out by A. Hickling and P. W. Salt.42. 9s. 132 I n order toeliminate resistance overpotential, the potential was measured after thccurrent was cut off, using a specially designed electronic interrupter andmeasuring circuit. In many cases (notably for mercury) the ?-log i curvesare non-linear, and show a tendency to approach a limiting overpotentialat high C.D. It has, I n some cases (e.g., lead) the curves have a maximum.Iz7 8.Levina et al., J . Physical Chetji. Russiu, 1947, 21, 32.5 ; Frumkin, ref, (3).12@ H. H. Uhlig, N. E. Cam, and P. H. Schneider, Tram. Elecfrochcw. SOC., 1941,130 dbid., 1940, 77, 289.131 il'ature, 1947, 159, 539; Trans. Faruday Soc., 1917, 43, 417; see also V. S . Joffe,Cspekhi Khinr., 1943,12, 438.132 Trans. Faraday SOC., 1940, 36, 12%; 1941, 37, *24, 319, 333; see also Hickling,ibitl., 1937, 33, 1540.See ref. (1) ; also R. M. Berrer, 7 ' r a ~ s . Furada!j SOC., 1940, 36, 1235.79, 11AGAR : THE IEINE'I'ICS OF ELECTRODE PROCESSES. 29however, been shown that the decay of overpotential during the shortinterval between interruption of the current and measurement of thepotential may be considerable; 2 the exponential character of the decaymakes it impossible to extrapolate decay curves to zero time graphically,hut if the extrapolation is carried out by equation ( 5 ) , Hickling and Salt'sobservations for mercury agree with the usual linear ?-log i relation found a tlower current densities.2011 other inetals, the clec.,zy of overpotciltial limy be less i-ztpicl, and theerror in Hickling and Salt's measurements mny therefore be smaller.. 111support of this view, Bockris l31 has shown hhat for several metals theq-log i curves measured by the " direct " method also flatten off a t highcurrent densities.No such effect was, however, observed by B. K a b a n o ~ . ~ ~ Measurements have also been made of the hydrogen overpotential onplatinised platinum cathodes a t high current densities ; in this caseconcentration overpotential is important, but it does not provide 8 1 1explanation of the very high overpotentials sometimes observed.It hasbeen suggested 134ct that they may be due to a slight inequality in theconcentrations of positive and negative ions near the electrode.135(v) Anodic Processes.The evidence in favour of the hydrogen peroxide theory of anodicoxidation has been reviewed by S. Glasstone and A. H i ~ k l i n g , ~ ~ ~ who havealso disccused the Kolbe synthesis and allied reactions.137 A. Hickling 138has dram1 attention to the interesting fact that the potentials and pH atwhich the Kolbe reaction proceeds with good yield should also bring aboutrapid evolution of oxygen, which is not observed.In criticism of thehydrogen peroxide theory, it has been pointed out that hydrogen peroxide isformed anodically only in exceptional circumstances, and that i t is readilydestroyed by anodic oxidation.139The electrodeposition of oxygen from 0 . 1 N-sodium hydroxide on platinuinanodes: has been investigated by H. P. Sto1Lt,l4O who finds a linear -4-log irelation with o! = 1.0; the energy o€ activation a t the reversible oxygenpotential, derived from the temperature coefficient of overpotential, is25.3 kcals.Measurements of oxygen overpotential on several other metals in alkalinesolutions show that the behaviour of the electrodes is often very complicated,especially a t high current densities.141V. IT.Slender, J . Appl. Chem. Russia, 1946,19, 1303.133 Acts PhysicociLiw. U.R.S.S., 1936, 5, 193; see also A. G. I'echerskaya and134 ( a ) G. E. Coates, J . , 1945,484; ( b ) P. M. Bryant and G. E. Coates, see ref. (1).135 Cf. R. M. Fuoss and M. A. Elliott, J. Amer. Cheni. SOC., 1946,67, 1339.136 C'hem. Reviews, 1939, 25, 407.l S i T'rans. Electrochem. Soc., 1939, 75, 333.139 Eq., W. D. Bancroft, Tram. Electrochent. Soc.. 1937, 71, 1%; M. Haissinsky,140 See ref. ( 1 ) ; cf. -412n. Reporfs, 1938, 35, 101.l4I A. Hickling and 8. Hill, see ref. (2).13* See ref. ( 1 ) .see ref. (1)30 GENERAL AND PHYSICAL CHEMISTRY.The electrodeposition of the azide ion on platinum, palladium, andiridium anodes has been shown 142 to require an overpotential of about 4volts a t measurable current densities; this is probably the highest over-potential yet recorded. The value of a is approximately 1, but increasesslightly with rise in temperature, and the C.D.a t a given potential isproportional to [N3-]. The emission of light a t the anode during electrolysisof azides has been reported by R. Audubert.143(vi) Non-aqueous Solvents.In agreement with the observations of S. Levina and M. Silberfarb,lUI. S. Novoselski 146 has found that the hydrogen overpotential on mercurycathodes in ethyl and methyl alcohols is somewhat less than that in aqueoussolutions. A similar decrease of overpotential has also been reported fornickel cath0des.~3Hydrogen and oxygen overpotentials in mixtures of organic solvents andwater have also been 14’ In the case of hydrogen depositionfrom acid solutions in methyl alcohol-water mixtures,146 using a leadcathode, the overpotential is found to have a maximum value at ca.50% ofwater, and to be much lower in the pure alcohol than in pure water ; in someother solvent mixtures, minima are observed. On nickel cathodes, thesolvent effect is much smaller and the intermediate maxima or minima areeither absent or much less marked.At certain current densities, the oxygen overpotential on platinum inN-sulphuric acid solution in dioxan-water mixtures also appears to passthrough a maximum at intermediate concentrations ; 147 with pure dioxanor pure acetic acid as solvent, it is higher than in aqueous solution.Hydrogen overpotential on nickel cathodes in liquid ammonia has beenfound to be higher than in aqueous solutions ; 148 lead and mercury electrodesseem to be unsuitable in this medium, possibly owing to “amalgam ”formation.V. Pleskov has also discussed the anodic evolution of nitrogenfrom liquid ammonia.149(vii) Diffusion and Convection Processes.It has been customary to discuss mass (solute) transfer between thesurface of an electrode and a moving solution in terms of a “diffusionlayer ”; 1% this concept is useful because it circumvents some difficult142 H . P. Stout, Trans. Faraday SOC., 1945, 41, 64; see also R. Audubert andE. T. Verdier, J . Chim. physique, 1942,39, 48; C m p t . rend., 1941,213, 870.143 Bull. SOC. chim., 1940, 7 , 907; E. T. Verdier, Compt.rend., 1942, 214, 617; 1943,216, 183.144 Acta Physicochim. U.R.S.S., 1936, 4, 275; see also Bowden and Grew, ref. (1).145 J . Physical Chem. Russia, 1938, 11, 369 ; A., 1938, I, 576.146 J.O’M. Bockris, Nature, 1946, 158, 584; see ref. (1).14’ Idem, aid., 1947, 159, 401; see ref. (1).148 V. Pleskov, Acta Physicochim.. U.R.S.S., 1939, 11, 305.140 Ibid., 1945, 20, 578.160 W. Nernst, 2. physikal. Chem., 1904, 47, 52AGAR : THE KINETICS OF ELECTRODE PROCESSES. 31hydrodynamical problems, but it is unsatisfactory in several respects andseems also to have been frequently misunderstood. The original diffusion-layer theory implied that there was a stationary layer of liquid in contactwith the electrode.; within the layer only diffusion is operative, whereasoutside it the concentration is supposed to be kept uniform by convection,I n actual fact the liquid in the layer is not stationary, although its motionmay be largely parallel to the electrode surface, so that there is littleconvective transfer of solute to or from the electrode.A great advance has recently been made by B.Levich,l6191a who hasdeveloped the fundamental theory of convective diffusion a t electrodes,using modern hydrodynamical concepts, and following, in general, the lineson which the closely analogous problems in heat transfer have been treated.Dimensional methods have also been used ; 153,156 such methods do not givea complete solution, but the gaps may be filled by the use of comparativelyfew experimental results, including heat- transfer mea~urernents.~~~Calculations have been carried out for laminar and turbulent forcedc o n ~ e c t i o n , ~ ~ ~ ~ 152 and for natural convection arising from changes in thedensity of the solution near the electrode.l5l> The results are inagreement with experiment, particularly in the ease of a rotating-discelectrode, which is hydrodynamically simple.For such an eleotrode,Levich lS2 finds that the conventional Nernst diffusion layer thickness, 6 ,is given byD * + 8 = 1*62(--) (f) em.where D is the diffusion coefficient, v the kinematic viscosity, and w theangular velocity. This equation is in accordance with the more generaldimensionless equation : 163const.(Pr)-?h (Re)-m i =where I is a characteristic length (e.g., the radius of the disc), Pr (Praiidtl’snumber) = v/D, Re (Reynold’s number) = UZ/v, and U is a charaoteristiclinear velocity (e.g., the peripheral velocity).It appears that the valuesn = 4 and m = 3 hold for laminar motion and high values of Pr in manysystems ; the relation between the quantities is different when the motion isturbulent. J. N. A.151 Acts Physicochim. U.R.S.S., 1942,17, 257; 1944,19, 117, 133.162 See ref. (1).153 J. N. Agar, see ref. (1).154 N. Y. Buben and D. Frank-Kamenetsky, J. Physical Chem. Russia, 1946,20, 225.lS5 Cf. C. V. King and P. L. Howard, Id. Eng. Chem., 1937, 29, 76; S. Uchida,J. SOC. Client. Ind. Japan, 1933, B, 36, 416; A. W. Hixson, Ind. Eng. Cliem., 1944,36, -18833 GENERAL AND PItYSICAL CHEMISTRY.2.FAR ULTRA-VIOLET SPECTRA AND RELATED TOPICS.In recent years there have appeared a number of excellent reviews ofelectronic spectra in general and of work in the near ultra-violet region inparticu1ar.l Important reviews have also appeared of the far ultra-violet33 * Of these, the first is particularly useful for experimental methods,the second contains most useful tables of spectra reported before 1941, ttndthe third brings these tables up to date to 1944. Since 1044 a considerablefurther volume of work in the far ultra-violet region has been published,justifying a further review. Not since 1939 has a survey of the regionappeared in these report^.^ The present Report collects together some ofthe recent work on electronic spectra, with primary (but, since there is nosharp dividing line between spectra in the far and near ultra-violet regions,not exclusive) stress on the wave-length region below 2000 A.A summaryof attempted applications of some of the data to chemical problems hasappeared elsewhere,6 as has also a simplified account of far ultra-violetspectra and of the theory underlying their interpretation.’Two of the major developments since the last Report have been (1) theextensive determination of molecular ionisation potentials by Price and hisschool, and (2) the beginning of much greater stress on intensities ofabsorption. The ionisation-potential determinations have usually beencarried out by observation of Rydberg series, but have been helped byelectron-impact work performed in conjunction with the spectroscopictechnique; * the first method gives the greater accuracy, but the secondhas the advantage of indicating clearly the existence of an ionisation limit.W.C. Price gives a list of many of the ionisation potentials so far determined.The stress on intensities dates from a most important series of papers byR. S. Mulliken in 1939,lO in which he showed the great value of intensitymeasurements for interpreting spectra and in which he appealed for furtherdata. The war meant a lapse of some years before his cry could be answered,but, latterly, increasing numbers of workers have been turning their attentionto the experimental problem of absolute intensity measurements. Manyexamples of these two outstanding developments will be found scatteredthrough this Report.* E.J. Bowen, Ann. Reports, 1943,40, 12; W. R. Brode, “ Chemical Spectroscopy,”2nd ecltn., Wiley, 1943; R. N. Jones, Chern. Reviews, 1943, 32, 1 ; E. A. Braude, Ann.Reports, 1945, 42, 105; K. Bowden, E. A. Braude, and E. K. H. Jones, J . , 1946, 94s;A. Maccoll, Quart. Reviews, 1947, 1, 16.For experimental methods see also a J. C. Boyce, Rev. Mod. Physics, 1941, 13, 1.R . A. Sawyer, “ Experimental Spectroscopy,’’ Prentice-Hall, 1944.H. Sponer and E. Teller,’Rev. Mod. Physice, 1941, 13, 76.J. R. Platt and H. B. Klevens, ibid., 1944, 16, 182.W. C. Price, Ann. Reports, 1939, 36, 47.A. D. Walsh, V. Henri Memorial Vol., Desoer, Likge, 1947.Idem, Quart. Reviews, 1948, 2, 73.* T. 31.Sugden, in the press.lo .J. Chena. Physics, 1939, 7, 14, 30, 121, 339, 353, 356, 364, 670;Chenb. Reviews, 1917, 41,For summary, see R. S. Mulliken and C. -4. Rieke, Rep. Prog. Physics, 104857., 8, 331.940, 8, 234\VALSH : &AH. ULTRA-VlOLET SPECTEA ANL) RELATED TOPICS. 33Ethylene, Allcylethylenes, and Alkylation Red Shifts.-The far ultra-violet spectra of light and heavy ethylene, propylene, trans-but-2-ene,and trimethyl- and tetramethyl-ethylene were described by Price and W. T.Tutte.ll At low pressures the ethylene absorption begins abruptly at1745 A. with a series of bands which undoubtedly represent a first transitionof a Rydberg series leading to the ionisation potential at 10.50 v. Super-imposed upon these is a weaker region of absorption stretching from 2000 A.to beyond 1600 A.with a maximum a t 1630 A. Its characteristics agreewell with those expected for an N , V transition of a x electron,12 i e . , atransition from the ground state to an orbital with an extra node betweenthe carbon nuclei. With increasing methyl substitution, the r=-l ionisationpotential decreases and the N , V transition shifts to longer wave-lengths.The ionisation potential decrease can be attributed largely to the “ inductiveeffect” of the methyl group. This effect is sometimes called “ chargetransfer ”, because, when H in a bond H-X is replaced by CH,, the bondelectrons move nea.rer to X, i.e., transfer of negative charge to the regionround X occurs. The ionisation potentials of the group X will therefore bedecreased because of the repulsion between electrons.In the case ofethylene and propylene, in terms of hybridisation of valencies, the effectmay be described as follows.13 Replacement of H in C,H, by the lesselectronegative CH, group evokes more s character in the carbon vadencytowards the CH,, and therefore more p character in the carbon valencyinvolved in the CF bond of the C=C. The CF electrons of the C=C group thusbecome more weakly bound. The repulsion between them and the outlyingx electrons therefore increases, with the consequence that a x electron ismore easily removed. This raising of the ground state orbital in consequenceof charge transfer must be part of the reason for the N,V shift to longerwave-lengths. As Mulliken points out,12 one would expect the charge -t;rensfer effect to cause a smaller raising of the Y than of the iV state, becauseof the larger size of the excited orbital.Computation of the term valuesfor the V state readily shows that they d9 show decreases with alkylation,these decreases being smaller in absolute magnitude than the ground-statechanges. Consequently, since the effect means a diflerential raising ofthe two states, if we believe charge t,ransfer to be largely responsible forthe ground state changes we must believe that it plays a considerable partin the N,V shift to longer wave-lengths. Froin a theoretical point of viewanother effect is also expected to play a contributory part. This effect iscalled ‘‘ hyperconjugation ” and is due to a delocalisation of the electronsin thc CH, groups.That is, it results from the inadequacy of our traditionalboiid diagrams to represent the whereabouts of electrons. It would raisethe ground state and, by itself, lower (increase the term value of) the excitedstate. The inductive and hyperconjugation effects work in the samedirection on the ground level, but in opposite directions on the upper level.The observed decreases of excited level term values then prove the importance11 Proc. Roy. Soc., 1940, -4, 174, 207.l2 R. S. Mulliken, Rev. Mod. Physics, 1942, 14, 265.REP.-VOL. SLIV. 34 GENERAL AND PHYSICAL CHEMISTRY.of the effect of charge transfer on the excited state. There is little doubtthat this effect of hyperconjugation must occur : the only question is thequantitative one of how important it is relative to the charge transfereffect." Mulliken suggests that the red shift in the N,V transition may beentirely explained by hyperconjugation ; but as shown above, this does notaeem likely in view of his own agreement that charge transfer is largelyresponsible for the ground state raising.? In other cases (see discussionbelow on cyclic diems) i t seems clear that the effects of hyperconjugationhave been over-estimated.I n the effect of alkylation on systems largerthan the ethylene molecule, it is probable that hyperconjugation becomesmore important, relative to the inductive effect, than in ethylene; for, asW. C. Price and A. D. Walsh l4 have stressed, the inductive effect is shortrange, and therefore such a property as the activation of the p-position intoluene must be explained as due to hyperconjugation. Similarly, themarked lowering of r1 ionisation potential (9-24 to 8.92 v.) in toluenerelative to benzene must be explained as to a considerable extent due tohyperconjugation since the electron ionised previously spent only a part ofits time in the neighbourhood of the alkyl groups.The smaller value of theionisation potential lowering (0.32 v.) relative to the ethylene-propylenechange (0-80v.) agrees with the importance of a short-range effect in thelatter case. We shall return to these points in our discussion below of thespectra of the alkylbenzenes.These explanations of the ionisation potential decreases and AT, V redshifts are satisfyingly general, as indeed they must be since red shifts occuron methyl substitution of all types of chromophore. Exceptions do, how-ever, occur : for example, a-methylstyrene shows a violet shift of certainbands relatively to styrene,15 as does the monomethyl derivative of trans-stilbene relatively to its parent.16 These exceptions are probably due tosteric interference, on methyl substitution, with the co-planarity needed formaximum conjugation effects.That 1 : 4 steric interference with co-planarity may be considerable is shown by the propeller shape of 1 : 3 : 5-triphenylbenzene l7 and the probable lack of co-planarity in diphenyl itself.1813 A. D. IValsh, Faraday Society Symposium on The Labile Molecule, Sept., 1947.14 Proc.Roy. SOC., 1947, A , 191, 2 2 .16 G. N. Lewis and M. Calvin, Chem. Reuiews, 1939, 25, 273.17 L. Pauling, " Nature of the Chemical Bond," Cornell, 1940, 2nd ed., p. 219.18 (Migs) M. M. Jamison, (Miss) M. S. Lesslie, and E. E. Turner, Ann. Reports, 1946,43, 161. * The ideas of charge transfer and hyperconjugation are not entirely distinct. &IsPrice has shown [ref. (9), p. 2621, hyperconjugation has implicit in it the idea of cliurgetransfer in the ionised or excited state.Price 9 has developed a somewhat different approach to the simple idea of chargetransfer. Although some charge transfer occurs in the ground state, a much greatercharge transfer is supposed to take place in the excited or ionised state as a result ofalkyl substitution.The effect is to bring about relative stabilisation of the upperstates, thereby reducing excitation and ionisation energies.t He suggests that about 0.14 V. of the 0.80 V. decrease in 77-1 ionisation potential,in passing from ethylene to propylene, is attributable to hyperconjugation.l5 A. D. Walsh, ibid., p. 32WALSH: F'AR ULTRA-VIOLET SPECTRA AND RELATED TOPICS. 35Overlapping the long wave-length side of the first N,V absorption, allunsaturated hydrocarbons show a broad band of very low intensity whichappears as a " step-out " in the absorption curve. In the olefins the bandis structureless (or, as in ethylene, has only diffuse structure) but in thecyclic dienes and in benzene it reveals a sharp vibrational structure whichresembles that found in the first Rydberg tran~iti0n.l~ In view of this andof the very low intensity, E.P. Carr l9 has suggested that in all unsaturatedhydrocarbons the " step-out " represents a transition to a triplet analogueof the lowest Rydberg excited level. In ethylene itself, the 0 , O band appearsto be a t 2070 A.The singlet-triplet transition of the ground state probably occurs a tmuch longer wave-lengths. Phosphorescence requires a long-lived excitedstate. Since triplet-singlet transitions are well known to be of lowprobability, and since the ground states of most molecules are singlets, it isnatural to identify the upper, phosphorescent, state as (often) triplet. Bystudying the phosphorescence of organic molecules dissolved in rigid solvents,G. N.Lewis and M. Kasha 2o have succeeded in determining the heights ofthese triplet states for many organic molecules. trans-Dichloro-, -dibromo-,and -di-iodo-ethylene all give nearly identical heights of 74 kcals. Jf thisis near to the value for ethylene itself, a weak transition should occur aroundConsiderable progress has therefore been made in determining theprobable heights of the various possible excited electronic states of theethylene molecule. R. S. Mulliken and C. C. J. Roothaan21 have given atheoretical discussion of the twisting frequency and the barrier height forfree rotation in each of'the various electronic states of the ethylene moleculeand also for the lowest state of the ionised molecule. They conclude thathyperconjugation tends to make the 90" twisted form of the molecule morestable than it would otherwise be.Triple-bond Molecules.-The vacuum ultra-violet spectra of acetylene,methylacetylene, hydrogen cyanide, the cyanogen halides, diacetylene, anddimethyldiacetylene have been reported.22 The first, x-l, ionisationpotential of methylacetylene is 11-30 v.as compared with 11.41 v. foracetylene. That the reduction (0.11 v.) is very much smaller than forpropylene relatively to ethylene (0.80 v.) is a significant fact for theories ofalkylation red shifts. It cannot be explained by larger size of the chromo-phore as with toluene-benzene. It is probably due in part to the inductiveeffect being less with a triple than with a double bond. This is under-standable [cf.ref (5); p. 591 in general terms from the interpretation interms of hybridisation given above of the inductive efTect. It affectsdirectly the c bond of the C=C. Since this is sp-sp its electrons are much3900 A.In Chem. Reviews, 1947, 41, 293.so Ibid., p. 401; J. Anher. Chem. SOC., 1944, 66, 2100; 1945, 67, 994; M. Kasha,Chem. Reviews, 1947, 41, 401.21 Ibid., p. 219.22 W. C. Prim and A. D. Walsh, Trans. E'araday Xoc.. 1945, 41. 38136 GENERAL ANL) PHYSICAL CHKiMISTRY.more tightly bound than those in an sp2-sp2 bond. The repulsion betweenthese electrons and the outlying T; electrons is therefore smadl relatively toethylene. A slight change in thc CJ bond is not likely therefore to producemuch change in binding of the x electrons in C r C .As regards the hyper-conjugation effect, it is often supposed that this, so far from being lessimportant with methylacetylene than with propylene, is particularlyimportant with the former molecule. Such a supposition has it's difficulties,because the spectroscopic effects produced by conjugating a C5ZC withanother unsaturated group are Eess, not more, than those produced witlhC=C instead of C-C. Thus the 1790 A. peak in benzene (see below) isshifted to 1910 A. in phenylacetylene but to 1950 A . in styrene; while the2000 A . region of benzene moves to 2390-2200 A . in phenylacetylene*and2400-2300 A. in styrene. The conjugating power is reduced as we passfrom C=C to C-C, the reduction being a natural consequence of the tighterbinding in CCC cxpected theoretically and found experimentally.On theother hand, in CH,-C--C)- tlhe conjugation is in two planes, so that the C-Cbond is likely to be shortened more than the C-C in CH >C=c<, ofherthings being equal. This means that the x-type overlap, which is theessential phenomenon of all conjugation, will be more efficient across C-Cadjacent to C-C than adjacent to C=C, other things being equal. Buteven in diacetylene, where also the conjugation is two-dimensional, the firstionisation potential only drops from 11-41 in acetylene to 10.79 V. indiacetylene (i.e., by0.62 v.) as against a drop of 0 . 8 0 ~ . for propylene-ethylene.A belief that CH, conjugates more with CEZC than with C=C is thereforenot without its difficulties.A further argument against increased importanceof hyperconjugation in methylacetylene,23 zliz., that the C-C bond shows Eessand not more resistance to twisting than in ethane, is not valid, as has beenpointed out elsewhere; but there seems to be no chemical evidence insupport of the H atoins of CH, in methylacetylene having ail acidic functionand that of -CECH having an acidity less than in acetylene, as is required ifhyperconjugation structures such as H C:H2=C=CH are supposed veryimportant. The main evidence for great importance of hyperconjugation inmethylacetylene lies in the well-known marked shortening of the C -C bond.But i t should be remembered that this shortening and strengthening isattributable in part to the acetylenic, sp, nature of one of the carbon valenciesinvolved.* The shortening and strengtheningis marked and abrupt as we pass from H-C= t o H-CG, in the series CH,,C,H,, C',H2, in which there is no question of conjugation : it may be eveninore marked in passing from CH3--C'= to CH3-C= for the same reason.I n so far as the shortening of Cj-C! in methylacetylene is, however, attributablet o hyperconjugation, one needs to distinguish between the total hyper-Refs.13 and 26 explain this.23 J. D. Dunitz and J. M. Robertson, J . , 1947, 1152.24 J. Amer. Chem. SOC., 1939, 61, 927.2 5 V. Henri Memorial 1-01., Desoer, Liege, 1947.* L. Pauling, H. I). Springall, and K. J. Palmer 21 recognised this effect, but it mayhave a greater importance than they gave it.See also C. A. CouIson.2conjugation effect (which is important for the bond shortening) and thehyperconjugation-effect per x electron (which is important for the ionisation-potential changes) : in this way i t may be possible to reconcile smallionisation changes with a fairly large total effect. Obviously, too, thestabilities of the resulting ions, as well as one molecule with another, need tobe compared for a full discussion of the ionisation-potential change^.^Hutndiene, Hexatriene, a d Derivatives.-The far ultra-violet spectra ofbutadiene, isoprene, 97-clirnethylbutadiene, and chloroprene have heendescribed by W. C. Price and A. D. Wa1sh.l' The same authors 28 have HI)studied the spectra of hexatriene and divinylscetylene. H. Rastron, R.t4.Davis, and L. W. Butz 29 hac*e reported the spectra of alkyl and otherderivatives of divinylacetylene in the region 2300-2900 A .At room temperature butadiene gas appears to be mainly s-trans, i.e., tohave a trans-arrangement of the double bonds about the conventional singlebond ; but the spectroscopic evidence 2'7 30 shows the existence also ofappreciable amounts of the s-cis-form . Similarly, the spectroscopic evidenceindicates the existence of various forms of hexatriene.28 It is now reasonablycertain that the s-trans-form of butadiene is the lower-energy is0rner,~l9 32 sothat the proportion of s-cis increases with temperature.Price and Walsh28 showed that a graph of first ionisation potentialagainst frequency of the niaximum of the first N,V transition was linear forethylene, s-trans-butadiene, and hexatriene.This linear graph (Fig. 1) isalso quite well fitted by cyclopentadiene and cylohexadiene, furan, andpyrrole (see below). Isoprene, chloroprene, and $y-dimethylbutadiene donot lie far 08 it. One would expect therefore that i t would also be fitted bys-cis-butadiene. The first ionisation potential of s-cis-butadiene has beendetermined as 8.75 v . ~ O From Fig. 1 we should therefore expect themaximum of the N,Vl transition for s-cis-butadiene to lie a t about 44,500ein.-l or around 2250 A., i.e., slightly to long wave-lengths of the N,V1transition for s-trmts-butadiene (2200-2000 -4.). Direct observation ofS , V , for s-cis-butadiene a t room temperature is difficult because it isexpected to be a rather weak transition l2 and the much greater strengthof the s-trans-N,F", transition will tend to conceal i t : but i t is significant>that the weak absorption of butadiene gas around 2400-2200 a.is foundto be strongly temperature dependent ,33 increasing with temperature as i twould if i t were due to s-cis- present with the s-trans-form.The linearity of the ionisation potential--AT, Vl frequency graph with itsregular movement of the X, T', transition by about 1.2 v. to long wave-lengths2 6 -1. D. Walsh, J . , in the press.2 s Ibid., 1946, A , 185, 182.29 ,I. Anzer. Cheni. Soc., 1943, 65, 973.:'" T. 31. Sugden arid -4. I). Wal~li, l ' m n s . Fumcl(~!j Svc., 1945, 41, 76.2 i Proc. Roy. Soc., 1940, A , 174, 210.J.C. Aston, G. QZBSZ, H. 117. Woolley, and F. G. Hrickwedde, J . Chem. Plrysic.~,1946, 14, 67.32 A. D. Walsh, Nature, 1940, 157, 768.33 €3. 8. Rasmrissen, 1). I). Tunnicliff, and IC. I:. Brattitin. .7. C ' h P w . l'h+vics, 1943, 9,43238 GENERAL AND PHYSICAL CHEMISTRY.for every 1 v. drop in ionisation potential, is a significant empirical fact stillto receive a theoretical explanation.Cyclic Dienes.-W. C. Price and A. D. Walsh 34 have described the vacuumultra-violet spectra of cyclopentadiene, cyclohexadiene, thiophen, pyrrole,and furan. G. Milazzo has photographed, under high dispersion, the spectraoutside the vacuum region of p y r r ~ l e , ~ ~ N-de~teropyrrole,~~ N-methyl-pyrrole,36 and thi~phen.~' An important point is the appearance withN-methylpyrrole of a region (2600-2250 A , ) with no apparent analogue inthe spectrum of pyrrole.It is probably consequent upon the lone pair I$Bu tad i e n e (s -trans)&-Dimethyl -butadieneHexatriene\ First ionization potentia/s plottedagainst N-+ 5 transitions.I I I6L7 000 50,000 40,000 340N-+& Y rnax., cm.-l.FIG. I .9electrons in N-methylpyrrole being less tightly bound than in pyrrole(because of the electron-releasing properties of the methyl group) and soapproaching in strength of binding the CC x electrons with which nearlycomplete (" homocyclic ") conjugation therefore occurs : in that case thenew region is probably analogous to the 2600 A. region of benzene. Thio-phen 37 also shows regions of absorption probably closely analogous to thoseof benzene and appears to furnish, like N-methylpyrrole, a case of nearlyh oniocyclic conjugation.In dimethylfulvene, which has five equivalent x electrons in a ring ands4 Proc.Roy. SOC., 1941, A , 179, 301.35 Rend. Accad. Itul., 1942, 4, 87.37 Communication presented a t XIth International Congress of Chemistry, London,36 Gazzetta, 1944, 74, 152.1947WALSH : FAR UTATRA-VIOTdET SPECTRA ANT) RELATED TOPICS. 39one in a side chain, the first absorption region has moved right up to 3700 A.,38resulting in visible colour. Other absorption regions occur a t 2600 A.,382 1 0 0 ~ . , ~ * and a peak (probably Rydberg in character) a t 1 8 0 0 ~ . 3 ~ Thelongest-wave absorption is considerably weaker than the following absorptionas with all the cyclic dienes.cycZoPentadiene and cyclohexadiene show markedly lower first ionisationpotentials (8.62 and 8.4 v., respectively) and N , V , transitions a t markedlylonger wave-lengths than s-trans-butadiene.Since s-cis-butadiene alsoshows a markedly lower x-l ionisation potential and an N , V , transitionprobably at longer wave-lengths than in the s-trans-form, these characteristicsare evidently largely a property of the cis-arrangement of the double bondsrather than due to hyperconjugation via the CH, groups of cyclopentadieneand cyclohexadiene. The latter effect doubtless plays a part, but i t appearsless than was earlier th0ught.m Table I lists the probable N , Vl, N , V2, andN , V3 locations for the cyclic and open-chain hydrocarbon dienes. WhenPrice and Walsh wrote their paper in 1940 27 the N , V 2 and N , V3 transitionswere thought to lie together, but Mulliken l2 later showed that thesetransitions should be separated.TABLE I.First T-I I.P.Molecule.N,V, (A.). N , V , (A.). N,V3 (A.). (volts).s-trans-Butadiene . . . . . . 2200-2000 ? ? 9-07s-cis-Butadiene ......... 240CL-2200 1880 ? 1760-1650 ? 8.75cycZoPentadiene . . . . . . . . . 2400-2200 1980-1850 1660-1450 8-62cycloHexadiene . . . . . . . . . 2600-2400 2070-1 900 ? 8.4(max. 2320)(max. 2480)R. S. Mulliken40 discussed the “abnormality” of the cyclic dienehydrocarbons relative to s-trans-butadiene. Sugden and Walsh 3O showedthat the abnormality lay rather in the N,Vl location for s-cis-butadiene ifthis was supposed to occur a t the same wave-lengths as for s-trans.Theabove deduction that it probably lies a t bnger wave-lengths clarifies thispoint and gives to the N,Vl column of Table I the smooth order of theionisation potential column.Benzene and its Derivatives.-Price and Walsh 14 have published newspectrograms of the far ultra-violet spectrum of benzene. It is now wellknown that benzene exhibits absorption around 2600 A., rather strongerabsorption around ZOOOA., and a much stronger peak of absorption a t1790 A. The upper level a t 2600 A. is established as lBZzL [see ref. (3)’j andthat at 2000 A. is probably lBItt. The absorption a t 1 7 9 0 ~ . certainlyinvolves a Rydberg transition,14 for it has a sharp vibrational patternidentical with that accompanying other members of a Rydberg series lyingto shorter wave-lengths.The 1790 A . absorption probably also represents atransition to the lEl,l upper level. It has been suggested4l9 l4 that tjhe4 8 Quoted by R. S. Mulliken and C. A. Rieke, Rep. Prog. Physics, 1941, 8, 259.39 A. D. Walsh, unpublished spectrograms.4 1 G. Norclheim, H. Sponer, and E. Teller, ibid., 1940, 8, 455.*O J . Chem. Physics, 1939, 7, 339continuous background of the region is due to CH bond dissociation resnltingfrom transfer of energy by internal collision from the excited TC electron to aCH bond electron. T’ransition to each of the three states lB,,,, I B l u , and lEl,Lrepresents absorption that is X,V1 in type.42 It is noteworthy, however,that if benzene fits the linear graph of Fig. 1 it is the 2 0 0 0 ~ .region thatcorresponds to the N , V , transition of hexatriene, butadiene, etc. Similarly,with thiophen, which, we have seen, probably represents a case of nearlybenzene-like conjugation, i t is the 2200-2000 A. region that apparentlycorresponds to the N , V , transition of the other dienes and trienes.Lewis and Kasha 2o find a triplet state of benzene 85 kcals. above theground state. This fits with the earlier report by A. L. Sklar 43 of absorptionaround 3 4 0 0 ~ . (corresponding to -85 kcals.) so weak that it only showswith 20 em. of liquid benzene. Experimentally, it is difficult to be sure ofthe validity of such a report since very slight traces of impurity (e.g.,anthracene) would give rise to appreciable absorption around 3400 A .in such a long column of liquid; but the work of Lewis and Kasha nowprovides important corroboration.Sklar has interpreted the transition aslAl, --+ 3-E17,.43The far ultra-violet spectra of many derivatives of benzene have beenreported.14> 15, 44 A significant empirical fact is that with increasingconjugation between the side chain and the ring the 2000 A. transition ofbenzene moves much further to longer wave-lengths than does the 2 6 0 0 ~ .or the 1790 A. transition. In this respect the 2000 A. transition again showsgreater similarity to the N,V1 regions of open-chain dienes and trienes thando the 2600 A. and 1790 A. regions.The 2600 A. region in benzene represents absorption “ forbidden ” by thesymmetry.It would not occur if vibrations did not take place to destroythe symmetry. I n simple benzene derivatives the destruction of‘ thesix-fold symmetry means an intensification of the transition and importantchanges in vibrational structure. The very complete analysis of thevibrational structure in the benzene transition (explaining practically all thestrong bands, more than seventy in number) has made i t profitable to studyin detail the analogous region for benzene derivatives. Much careful studyhas been devoted to this : of monosubstituted benzenes, chloroben~ene,~~fluorobenzene,46 toluene,47, 48 phenol,49 aniline,50 and pyridine 51 have allbeen recently studied. The spectra can be interpreted4’ as due to acombination of the transition forbidden for the benzene structure (butappearing because of the occurrence of suitable vibrations) and of a transition4 2 R.S. Mulliken, J . Ghern. Physics, 1939, 7, 20, 353.4 4 A. D. Walsh, Trans. Faraday SOC., 1946, 42, 62.4 z H. Sponer and S. H. Wollman, J . Ghem. Physics, 1941, 9, S16.4(i S. H. Wollman, ibid., 1946, 14, 123.4i H. Sponer, ibid., 1942, 10, 672.4 8 N. Ginsburg, W. W. Robertson, and F. A. Matsen, ibid., 1946, 14, 51 1.49 F. A. Matsen, N. Ginsburg, and JV. W. Robertson, ibid., p. 511.43 Ibid., 1937, 5, 669.X. Ginsburg and F. A. Matsen, ibid., 1945, 13, 167.H. Sponer and H. Stucklen, ibid., p. 167allowed by the lowered symmetry caused by the migration of e1ect)rons to orfrom the side chain. The perturbation of the hexagonal benzene electronicsymmetry is the greater the greater the difference in clectroiiegativitybetween H and the atom or group that replaces it.Thus fluorobenzeneshows a greater change from benzene than does chlorobenzene. The nearultra-violet spectra of disubstituted benzenes have also been 52 ashave the spectra of certain trisubstituted benzenes in the vapour state,namely, the three trichlorobenzenes and 1 : 3 : 5-trimethylbenzene.%, j q 9 55A. L. Sklar 5G and K. P. Herzfeld 57 have discussed the intensities andwave-length shift,s of these various substituted benzenes relatively to benzeneitself in terms of energy changes consequent upon the migration of chargefrom the side chain into the benzene ring.F.A. Matsen, W. W. Robertson, and R. L. Chuoke 58 have comparedthe near ultra-violet spectra of toluene, ethylbenzene, isopropylbenzene,and tert.-butylbenzene. They find that the bands representing the transitionallowed by the lo$ered symmetry due to migration of electrons into the ringbecome stronger and shift to long wave-lengths as one passes from tert.-butyl- to isopropyl-benzene to ethylbenzene to toluene. They ascribe thisresult to increase of hyperconjugation between the side chain and the ring,as the side chain changes from tert.-butyl to . . , methyl; this effectswamping the inductive effect which should cause greater wave-length andintensity increases as one passes in the reverse direction. The hyper-conjugation must do this by tending to lower the excited state, since,according to Price,g the first x-l ionisation potential decreases as one passesfrom toluene to ethylbenzene to isopropylbenzene to tert.-butylbenzene. Theexplanation fits with the point made above that, with a large conjugatedsystem such as a benzene ring, the hyperconjugation effect should assume agreater importance relative to the inductive effect than in simple olefins.Experiments on chlorination and broniination 595 6o have similarly shown areactivity of the benzene ring in the order methyl > ethyl > isopropyl >tek-butyl.The same order is found in carcinogenic activity.61 That thehyperconjugation effect should decrease in the order inethyl . . . tert.-butylis understandable as follows.In CH,- the carbon valencies towards H haveconsiderable p character and therefore tend to give x-type overlap with a 2pvalency on the adjacent carbon atom : hence the fundamental reason for thehyperconjugation. Changing the H atoms for CH, groups has the effect l3 ofevoking more s character in the carbon valencies towards CH,; i.e., therewill be less x-type overlap between the CC bonds of tert.-butyl and anadjacent C=C than between the CH bonds of CH, and an adjacent C=C.j2 H. Sponer, Rev. Mod. Phywk.s, 1942, 14, 124..,.I H. Sponer, Cheni. Reviews, 1'347, 41, 281..A 13. Sponer and &I. H. Hall, V. Henri Meinorid Vol., Uesoer, LiGpe, 1947.jb J. ( ' h e m . I'?i~~sks, 1939, 7, 984.6i Cheni. Reviews, 1947, 41, 233. j8 l b i d . , p. 473.jY P.B. D. de la Mare and P. W. Robertson, J . , 1943, 279.uo E. Berliner and F. J. Bondhus, J . Anier. C'henL, ~YOC., 1946, 68, -73%.H. Sponer and M. J. Stallcup, ibid.-4. hllman, Conipt. r e d . , 1047, 225, 738,n 42 GENERAL AND PHYSICAL CHEMISTRY.J. R. Platt and H. B. Klevens 62 have measured the absoluteintensities of absorption (in n-heptane solution) of the 2000 A. and1790 A. regions in benzene and of the analogous regions in toluene, ethyl-benzene, and the three xylenes. Passage from benzene to tolueneconsiderably increases the intensity of the " 1790 A." and " 2000 A." regions.At the same time a shift to the red of these regions occurs greater than withthe " 2600 A." bands. Similar changes occur on passing from toluene to thexylenes.Since theoretical reasoning shows that the intensity of the" 2600 A." bands should be proportional to the intensity of the N , V transitionsa t shorter wave-lengths and inversely proportional to the square of theseparation of the 2 6 0 0 ~ . bands from those a t shorter wave-lengths, thesefactors alone should cause an increase of intensity in the toluene 2600 A.bands by a factor of about 1.5. The experimental increase is by a factorof 2-0. This suggests that breakdown of selection rules due to loweredsymmetry or charge migration may not be the most important factors indetermining the intensity of the 2600 A. bands ; and illustrates the danger ofexplaining effects in one band system without taking into account whathappens in all the other band systems.J.R. Platt, H. B. Klevens, and G. W. Schaeffer 83 have studied the absorp-tion of borazole (I). This molecule is interesting because it has an obvioussimilarity of structure to benzene. Indeed it has been called " the inorganicbenzene ". That considerable delocalisation of the N lone-pairelectrons occurs is shown by the BN distance, which at 1.44 A.in trismethylaminoborine. The absorption reveals (a) four\ N / ~ ~ diffuse bands starting a t 1995 A. which appear to be analogousto the 2000 A. bands of benzene, but of intensity about 10times smaller; ( b ) a strong continuum, like the 1 7 9 0 ~ .benzene peak, with a maximum a t 1720 A. or somewhat below. No bandsanalogous to the benzene 2600 A. system, however, were found, though theywould have been seen if their intensities had been only one-twentieth ofthose of the benzene bands.It seems to the Reporter that this absence ofan analogue of the benzene 2600 A. region is to be linked with its absence inpyrrole. I n both molecules not all the x electrons are equivalent : in pyrrolethe N lone pair and the C=C x orbitals have different binding energies, andin borazole the atomic orbitals contributed by the B and N atoms to themolecular x orbitals are not equal in binding energy. When, in benzene orN-methylpyrrole or thiophen, the participating atomic orbitals are made ofequal or approximately equal binding energy, the 2600 A. region appears.Halogeno-ethyZenes.-The vacuum ultra-violet spectra of the halogeno-ethylenes have been examined in detaiL6* They exhibit much sharpvibrational structure and bands which fit well into Rydberg series.The x-lionisation potentials are all less than in ethylene. It is difficult to explainthis except as due to conjugation of the C=C n electrons with the p x electronsHHN/ B \vH is considerably shorter than the single-bond distance (1.62 A.)HBH (I.)62 Chem. Reviews, 1947, 41, 301.64 A. D. Walsh, Trans. Faraday SOC., 1945, 41, 35.63 J . Chem. Physics, 1947, 15, 598WALSH : FAR ULTRA-VTOLET SPECTRA AND RELATED TOPICS. 43on the C1 atoms.6 This is important because there has been a tendency insome quarters to cite as evidence for the conjugation effect only such factsas the well-known shortening and strengthening of the CCI bonds relative toCC1 in the alkyl chlorides.This is hardly sound 65 because CH bonds showa similar shortening and strengthening in passing from alkyl-H to vinyl-H.In the latter bonds the effect can be explained in terms of the enhanced scharacter of the carbon valency towards H.13 It is all the greater when theC is part of a triple bond. That in the CCI bonds an additional effect ispresent, however, is shown by Table I1 which has been compiled byJ. Duchesne.66 Whereas for CH the change in force constant is only 15%TABLE 11.Bond BondCH adjacent force Bond CC1 adjacent force Bondto : constant. length. to : copstant. length.Single bond (CH,) 5.07 1.094 Single bond (CH,Cl) 3-30 1.77Double bond (C,H,) 5-4 1 48 Double bond (C,Cl,) 3.44 1-73Triple bond (HCN) 5.7 1.06 Triple bond (ClCN) 4-31 1.67in passing from top to bottom of the table and 3% in bond length, for CClthe corresponding figures are 30% and 6%.The argument from ultra-violet spectra is therefore corroborated. A further argument is as follows.The dipole moment (p) of propylene (0.35 D.) gives a rough measure of themoment to be expected on changing an sp3 C valency (as in C2H6) for sp2(as in C2H,). Now the difference of p(vinyl-Cl) (1-44 D.) and p(Et-CI)(2.05 D.) is considerably greater than 0.35 D. Since on changing from Et-Clto vinyl-C1, we should not expect a greater reduction in p by the hybridisationeffect than the value of 11 in propylene, there must be a second importanteffect a t work.*The spectroscopic evidence for conjugation between the C=C and C1 TCelectrons lies in part in the lowered ionisation potentials, and in part in thelong wave-length shifts suffered by the N , V transition in the chloro-ethylenes.One might explain these effects in terms of repulsion betweenthe C=C x and C1 p x electrons, but the thought content of this explanation isbasically only a different way of expressing that involved in the molecularorbital Ianguage of conjugation-for the node in the highest normallyoccupied x orbital of the conjugated system on the latter explanation is thetranslation of the repulsion on the former. An interesting, but somewhat(i6 A. D. Walsh, Trans. Paraday SOC., 1947, 43, 60.6 6 Private communication. 6 7 Trans. Paraday SOC., 1944, 40, 537.* The strength of bonds to such groups as vinyl or phenyl relative to methyl is areflection of their higher electronegativity.A. Burawoy 6 7 was one of the first todiscuss the reason for this raised electronegativity. He argued that replacement of uelectrons by n electrons meant a change from strongly bound to weakly bound electrons,with consequent decreased electron density at the carbon atom. It therefore permittedan increased hold by the carbon atom on the electrons of the other linkages. There isno doubt that, in general terms, this explanation is essentially correct : the discussionin ref. (13) puts the same thought content in different (qiiantum mechanical), butequivalent, languagepuzzling,64 point is that cis-dichloroethylene appears to have a lower dionisation potential but a shorter wave-length N , V transition tham the tmns-isomer.Carbonyl Compounds.-The far ultra-violet spectra of acetaldehyde,6Racraldehyde, crotonaldehyde and mesityl oxide, 69 benzaldehyde and furfur-aldehyde,44 and glyoxal 70 have all been recently reported.Broadly speaking,the observations fit well into the theoretical pictiire drawn by H. L. McMurrJ-and It. S. M ~ l l i k e n . ~ ~ Glyoxal, like bntadiene, appears to prefer to existin the s-trans-forni. 'Chis fits with recent work on the emission spectrum of'glyoxal in the near ultra-violet.72M. Lawson and A. R. F. 1)uncan 73 have obtained the spectrum of'deuteroacetorie and compared it with that of' acetone. In the spectra ofacetone and other carbonyl compounds, there occurs a vibrational frequencyca.1200 cm.-l which has been attributed in the past to a valence vibration ofthe C=O bond. No frequency of this magnitude, however, occurs in thespectrum of deuteroacetone around 1 9 5 0 ~ . A new explanation for thefrequency in acetone in this region must therefore be found : Lawson andDuncan suggest hydrogen bending in the methyl groups. The 1200 cm.-lfrequency in other carbonyl transitions of a t least such cases as formaldehydemust still be ascribed to the C=O valence vibration since no alkyl groups arepresent.It. S. Holdsworth and Duncan 74 have carried out intensity measurementson the absorption regions around 1950 and 1650 A. in aliphatic ketones.The intensity of the transition around 1950 A.decreases when the hydrogenatoms in acetone are replaced by methyl groups, whereas that of theabsorption around 16.50 A. increases. Whatever the explanation of theseeffects, they are probably to be linked with significant intensity differencesbetween acetaldehyde and acraldehyde F9 : in acetaldehyde the 1800 A . band(corresponding to the ketonic 1950 A. absorption) is weaker than the band at1 6 5 0 ~ . , but in acraldehyde the longer wave-length band (at 1750 A.) ismuch stronger than that at 1650 A. In acetone the 1950 A. are very muchstronger than the 1650 A.I. I. Rusoff, J. R. Platt, H. B. Klevens, and G. 0. Burr 75 have measuredthe absorption of various fatty acids in varions solvents as far as 1700 A.H. L. McMurry 76 has given a theoretical discussion of the spectra of saturatedcnrboxylic acids, esters, and salts,The first ionisation potentials of a considerable number of carbonylcompounds are now known or may be estimated with reasonable probability.These ionisation potentials refer to the removal of a lone pair electron frointhe oxygen atom of the >CEO group. The fact that thev lie below the396 8 A.D. Walsh, Proc.. Roy. SOC., 1946, A , 185, 176.(LB Idem, i b i d . , 1943, 41, 495.i l Proc. Nat. d m d . Sci., 1940, 26, 312; H. L. McMurry. J . Chen,. Physics, 1041, 9,i 2 A. G . Gaydon, Trans. Faraday SOC.. 1947, 43, 36.i 3 J. Chent, Physics, 1944, 12, 329.P 5 J . Amer. Chem. Roc.., 1943, 67, 673.i o Idem, ibid., 1946, 42, 62, 60.231, 241.i 4 Chena.Reviewd, 1947, 41, 311.7 G J . Chew. Ph!pic.v, 1942, 10, 655WALSH : VAR ULI'RA-VIOLET SPECTRA AN 1) REr,ATEU TOPIC'S. 45value estimated theoretically by Mulliken i i is explained by him, antigenerally accepted, as due to accumulation of negative charga on the oxygenatom, i.e., to the C-0 polaxity of the carbonyl bond. Consequently, byarranging carbonyl compounds in decreasing order of lone-pair ionisationpotential, it is possible to determine the order of increasing carbonyl bondpolarity.7s3 79 This is important because it is notoriously difficult to separatemolecular dipole moments into bond moments. An obvious prerequisitefor this technique is that a molecule shall be ~ ~ 1 1 represented by a boncldiagram.'I'hc establishrnciit in this ivay of a probable order of carbonyl boldpolarity has brought to light important correlations.As the bond polarityincreases, so the bond length increases, the bond stretching-force constantdecreases, and the bond energy decreases. In other words, as the bondpolarity increases, so the bond weakens.If wethink of any bond A B as containing two electrons in an orbital formed bythe overlap of two atomic wave functions {ha and +f;, then it is natural towrite the bonding wave function as a#.\ -+ b$,;. Remembering that the totnlprobability of finding one of the electrons of this orbital somewhere in spaceis just 1, we must " normalise " the wave function by writing (athi +b$I,)/da2 -k 2abS + b2 where X = J#Ll$udr over all space. Now the squaresof the coefficients of and $u give the probabilities of finding an electronaround the respective nuclei A and B ; consequently it is natural 80 to take theproduct of the coefficients of and #B as a measure of the probability offinding the electron in the shared region of the bond.Intuition tells us thatfor a strong bond the electrons must be shqred, i.e., spend most of theirtime between thc nuclei. The product Y = ab/(u2 4- 2abS $- b2) maytherefore be taken as a measure of tjhe strength of the bond. Nowd+ 6-One may ask why shouW increasing polarity weaken the bond?and, finding the masimuni of this function as a / b varies, w e can readilyshow that it occurs when a / b = 1. The maximum bond strength thusoccurs when a = b, i.e., when the bond is non-polar, and falls off as polaritydevelops-in agreement with the experimental fact.Put into ordinarywords, this calculation simply expresses the fact that as polarity increasesthe-bonding orbital comes to lie more and more on the side of the moreclectronegative atom that is remote from thc bond; and, in so far as i tdocs lic outsidc thc bond, obviously its bonding fuiiction is lost (Figs. 2and 3).This is not the inaiii fact or a t work, howcvc~, iii (.awing bond wnkcningwith increase of bond polarity. The calculation neglects any interactioiibetween the bonding electrons and neighbouring electrons. Yet it is justi i J . Chem. Phys.ics, 1933, 3, 664.i a A. D. Walsh, Trans. Faraday SOC., 3946, 42, 56.78 ldenr, ibid., 1947, 43, 158. C. A. Coulson, Proc.Roy. Soc., 1939, A , 169, 41346 GENERAL AND PHYSICAL CHEMISTRY.this interaction that causes change in binding of the lone-pair electrons asthe polarity changes. As the polarity increases the lone-pair electronsbecome subject to an increasing repulsion. At the same time the bondingelectrons become subject to an equal and opposite repulsion. The availablefigures 79 for the ionisation potentials of the bonding electrons bear this out.Now the more tightly bound are bonding electrons in a spectroscopic sense thegreater the contribution of their orbital to the bond in a chemical sense.81This is a general rule which can be made the basis of a useful definition ofbond order.82 The weakened binding of the bonding electrons as polarityincreases therefore means a weakened bond strength.Portion o f orbital/ost fur bond~ngFIG. 2.FIG. 3.Polar bonding orbital. Non-polar b o d i n g orbital.The binding of the bond electrons in a carbonyl bond also decreases asthe bond polarity increases for another reason. Increase of the polarity isdue fundamentally to the influence of other groups in the molecule in reducingthe effective electronegativity of the carbon atom towards the oxygen (thatof the oxygen atom being constant). Now reduction in carbon atomelectronegativity means a direct reduction in binding of the bond electrons,apart from the indirect reduction through the ensuing polarity : it is ageneral rule that, even in non-polar bonds, reduction in electronegativity ofthe atoms at either end of the bond means a reduction in bond strength.Thus the Si-Si bond is weaker than the C-C, and the S-S than the 0-0, andthe 1-1 than the Br-Br than the Cl-Cl.\V. Gordy 83 has recently stressedthis point. There are thus three reasons for the weakening of bond strengthwith polarity increase, which may be symbolised as on p. 47.The way in which changing carbon atom electronegativity works inchanging bond strength may be translated into an alternative language ofchanging hybridisation of ~a1encies.l~ This causes a direct change of 0bond strength and, via a repulsion of G and x electrons, also a change in xbond strength. By such a translation it should be possible to relate thebond strength changes to changes in magnitude of, say, CH bendingfrequencies in CHO of the various aldehydes.81 R.S . Mulliken, Physical Rev., 1934, 46, 551; J . Chenz. Physics, 1939, 7 , 121;82 A. D. Walsh, Trans. Paraday SOC., 1946, 42, 779.83 J . Chem. Physics, 1946, 14, 305, but see A. I). Walsh, ibid., 1947, 15, 688, for 8K . Fajans, ibid., 1942, 10, 760.qualificationWALYH : FAR ULTRA-VIOLET SPECTRA AND RELATED TOPICS. 47The weakening of bond strength with increasing polarity is almostcertainly of general application, a t least provided effects (1) and (2) workin the same direction. The idea is not entirely new, F. Arndt andB. Eistert 84 having put forward a similar idea on quite different grounds.Electrons in neighbouring bonds may play a similar part to the oxygenlone-pair electrons in carbonyl compounds in bringing about effect (3).Sometimes, of course, effect (1) may work in the opposite direction to effects(2) and (3).The introduction of hydroxyl into ethane to give CH,*CH,*OHmust increase the effective electronegativity of the carbon atom to whichi t is attached, but yet introduce polarity into the previously non-polar C-Cbond. In this case there is slight evidence that the polarity effect is thegreater.Z6 I n passing from (C-H)C21L, to (C-H)L$2112, however, we increasebinding of bond --+ Weakening of bond . ( 1 )electronsDirect reduction oflteduction of effective C ,xDirect reduction of bond 7 strength . . . * (2)‘xIncrease of polarity\ atom electronegativityIncrease of repulsiveinteraction with otherelectrons .1 Reduction in binding ofbond electronsIJ.W-eakening of bondstrength .. . - (3)the effective electronegativity of the carbon valency towards H,13 so at thesame time increasing the C-H polarity; and yet the C-H bond strengthdefinitely increases, showing that here effect (1) is more important than theeffects (2) + (3). Obviously there is need for further work to relate thevarious effects quantitatively to known parameters. In a series such asMe-Cl, Pri-C1, Bnt-Cl effects (1) and (2)-(3) work in the same direction as incarbonyl compounds and therefore predict unambiguously a weakening inthat order. [In this particular series, reduction of hyperconjugation acrossthe C-C1 bond as we pass from Me to tert.-butyl will be a small, additional,effect reinforcing the polarity weakening.]I n using the bond strength-polarity relation it is thus necessary to askfirst whether effects (1) and (2)-(3) reinforce each other. Secondly, it mustbe remembered that bond strength changes do not necessarily paralleldissociation energy changes : the latter involve the energies of the dissociationproducts, as well as of the original bond.* Thirdly, the relation applies to** Ber., 1941, 74, 423, especially pp. 442 ff. and 452.* For some discussion of the distinction of bond energies from dissociation energies,R - 61see L. H. Long and R. G. W. Norrish 8 5 and refs. (26) and (65).Proc. Roy. SOC., 1946, A , 187, 3374 8 GENEBAL AND PHYSICAL CHEMISTRY.bonds that are covalent in character : we cannot use it to predict that thedistance between the ions A and B- in an ionic lattice involving a largenumber of ions will be greater than the distance A-B in an isolated covalentmolecule-in fact the reverse is probably true.a6 Fourthly, the relationapplies to a particular bond modified only by the neighbours to which it isattached. It cannot be applied simply to compare a bond between nucleiA-B with one between nuclei C--B-for other effects [as well as effect (1)above opposing (2) + (3)] may well be very important. It thus has adifferent experimental basis from V. Schomaker and D. P. Stevenson'srule,87 which predicts a bond shortening with increase of bond polarity andis supported with comparisons solely of a bond A-B with C-B or C-D.Finally, we may note that it has become common to describe a polarbond (AB) as a resonance hybrid of an ionic and a covaleiit cxtreme ; and todeduce that its stability is greater than that of either extreme. This isincontrovertible, so long as i t is realised to refer to a resonancc hybrid ofA-B and AIB-, not in their normal conditions, but stretched or compressedto make their internuclear distances equal (at say, a distance 2). *4notherbond AB, of greater polarity, could also be described as a resonance hybridof A-R and A .B- ; Ijut these forms are not the same as before, having nowan internuclear distance that is the same for each but now equal to y. Theresonance energy for the more polar bond may be said to be greater, but thatbondisnot necessarilythe more stable-it alldependson therelative magnitudesof the resonance energies and the energies required to compress and extendA-B and A ' B- from x to y. In other words, the concept of a bond resonatingbetween a covalent and an ionic extreme does not necessarily help us tocompare the strengths of two bonds differing only in polarity-the extremesto which the bonds are related differ in tjhe two cases. The concept thereforedoes not imply-as has sometimes been supposed-that the more polar a bondthe stronger is its bond energy.Miscellaneous.-R. J. Thompson and A. B. F. Duncanss have madeabsolute intensity measurements on the absorption regions (at 52,500,66,000, and 77,000 cm.-l) of ammonia.W. C. Price s9 has photographed the vacuum ultra-violet spectra ofhydrogen selenide, hydrogen telluride, and the corresponding deuteriumcompounds. The spectra show we1 1-developed Rydberg series correspondingto excitation of one of the non-bonding electrons on the Se or Te atom.Roughly, the ionisation limits lie at 9.7 v. (H,Se) and 9.1 v. (H,Te).A review and discussion of the absorption spectra of certain gases inrelation to atmospheric physics and chemistry has been given byPrice has also photographed the absorption spectrum of diboranc dolvn t oZOO0 A . ~ ~ Other work by the same author has now finally established thatthe diborane molecule has a " bridge " rather than an ethaiie-like86 H. Bassett, Quart. Reviews, 1947, 1, 347.J . Amer. Chem. SOC., 1941, 63, 37.Private communication.J . Chenz, Physics, 1946, 14, 573.8o RepD. Prog. Physics, 1942-1943, 9, 10.91 J . Chem. Physics, 1947, 41, 207WALYH : YAK ULTRA-VIOLET SPECTItA AND liEI,ATEI> TOY1C;S. 4!)1%. S. Nulliken 92 has given an authoritative discussion of what this means iiiteriiis of molecular orbitals. From the point of view of the chemist, thec1 C1 c1simplest and most easily understood reprtwntation 93 is probably in t criiis ofco-ordinate links from B--H bonds to vacant boron orbitals, as (11), analogousto the formula (111) usually written for Al,Cl,. A. B. Burg 94 has shownthat the behaviour of diborane towards bases does not particularly accordwith the earlier suggestion 95 of a ‘‘ protonated double BB bond ”.A. D. W.,J. N. AGAR.A, D. WALSH.92 ( ‘ l i p t i ? . Reuiews, 1947, 41, 507; seo A. J. E. IVelr11, .Jm. Repork, 1945, 42, 67,93 A. I). Walsh, J . , 1947, S!).R4 J . L 4 ~ i t ~ r . Ohewk. Xoc., 1947, 69, 747.95 K . 8. Pitzer. ihid.. 1945, 67, 11%;.review of earlier work