THE DETERMINATION OF THE ELECTRON AFFINITY OF THE HYDROXYL RADICAL BY MICROWAVE MEASUREMENTS ON FLAMES BY F. M PAGE Dept. of Physical Chemistry, Free School Lane, Cambridge Received 28th January, 1955 An improved method of measuring the direct attenuation of centimetric radio waves has been used to obtain the concentrations of free electrons resulting from ionization of sodium in hot flame gases. By studying the variation of electron concentration with the calculated concentration of hydroxyl radicals in isothermal sets of such gases, resulting from burning different mixtures, the equilibrium constant of the reaction OH- % OH + e is determined. From this the electron affinity of the hydroxyl radical is deduced to be 65 f 1 kcal. This value is discussed in relation to other measurements in flames and to previous estimates.The idea of using the secondary zone of a flame as a high temperature bath in which to study the equilibria between atoms, molecules, ions and electrons was used by Rolla and Piccardi 1 and developed by Sugden and his co-workers. The method is neat and convenient, but suffers from the disadvantage that the flame gases may affect the equilibria being investigated. Further studies have shown that the effects of the flame gases are principally due to hydroxyl, and that if due allowance is made for these effects, experiment and theory can be brought into agreement.aS3 A great drawback to the early attempts to exploit this field was the lack of control of the flame variables of temperature and composition, and the inaccuracy of the techniques for measuring the concentration of electrons.The development of microwave techniques greatly facilitated the work, since measurements are specific to the electron, except where heavy ions exceed the electrons in concentration by several powers of ten, which is not likely to be realized in practice. The ways in which these difficulties have been brought under control has been set out in an earlier paper in this Discussion.4 EXPERIMENTAL The measurement which is required is that of the number of electrons per cm3 in the flame gases. This is made by determining the attenuation per centimetre of K-band radiation when traversing the gases. This attenuation can be related, by electromagnetic theory quoted by Sugden,4 to the number of electrons per cm3. Early measurements using this technique measured directly the attenuation produced by a flame burning in a gap in a waveguide system.In an attempt to achieve greater sensitivity and stability, a double beam system has been set up. It is illustrated schematically in fig. 1. This apparatus was capable of giving measurements of the attenuation of the flame reproducible to 0.005 db between 0.10 and 4.00 db. The crystal outputs were balanced when only one flame was attenuating, and this attenuation, which was entirely due to the presence of alkali metal in the flame, was then replaced by stopping the supply of alkali metal, and adjusting the calibrated resistive attenuator until balance was again reached. The earliest work on equilibria in flames suffered from the disadvantage that it was necessary to alter the temperature of the flame whenever the composition was altered.A number of flames were therefore chosen, such that a set of flames, all at the same temperature, was available in which the burned composition was different in each flame. These flames, produced by burning carefully metered mixtures of oxygen, nitrogen, and hydrogen, were all sheathed by nitrogen, as it has been found that such sheathed flames a788 ELECTRON AFFINITY OF HYDROXYL have a fairly uniform temperature cross-section.2 The gases were burnt on a flat Mkker type burner, 6 cm by 1 cm, the burner top being formed from Kanthal AD heat-resistant alloy. After preliminary experiments to map the temperature-composition contours, sets of four flames were chosen at 100" intervals from 1800°K to 2600°K.These chosen flames were set up, and their temperatures measured by the sodium D-line reversal method, the compositions being adjusted slightly where necessary until the measured reversal temperatures were within 5" of the desired temperature. This represented the limit of the method, and of the calibrated pyrometer on which the method is ultimately based. The temperatures were measured at the level of the waveguide system, that is, about 3 cm above the primary cones. Alkali metal was added to the flame as a salt spray from an atomizer containing a solution of the alkali metal chloride. I SoUARE-WAVE MODULATOR I U POWER ZIx f FLAMES ATTENUATORS CALIBRATED RESISTIVE AT TENU ATOR a+- + t L CRYSTALS f BALANCING RESISTIVE ATTENUATOR 1 PUSH-PULL Po FIG.1. Besides the temperature, the other important flame parameter is the thickness. This was measured at the level of the centre of the waveguide system, by a screw caliper, carrying on each limb a piece of platinum wire. The caliper was closed until the tips of the pieces of wire just glowed. Various other methods have been tried in these laboratories, but none were appreciably better than this simple device, RESULTS Let us consider the equilibria consequent upon the introduction of an easily ionizable metal into a flame. It is known that electrons are produced, some of which form hydroxyl ions, and that the metal hydroxide may be stable. M t s M + + c , OH- % OH + E, MOH % M + OH, All concentration terms are expressed in atm.Introducing equations for conservation of metal, and for charge balance, we have [XI = [MI + [M+] + [MOH], where [XI is the total M introduced into the system, [M+] = [el + [OH-]. Solving these equations by inserting the equilibrium constants, we obtain kI2(1 + [OHI/K2)(1 3- [OH]/&) + KikI(1 + [OH]/K2). KiFI The second term on the right-hand side arises from the finite amount of M+ formed, and may usually be ignored, while for sodium, and to a lesser degree, potassium, the term (1 -I- [OH]/&) may be put equal to unity since NaOH is relatively unstable, and may be neglected.5 Therefore, for the special case of sodium at the temperatures used in these experiments, we may write ~1INaI = [EIW + [OHIIKZ).F. M. PAGE 89 Inserting the attenuation per cni (p), which is proportional to the partial pressure of electrons (p = k[e]), or K1"aI = ( P 2 / W ( 1 + [OHI/K2, 1/82 = (l/K~kWal) + ([oHl/&k2[Nal&).A plot of 1/82 against [OH] should therefore yield a straight line, the ratio of whose slope to intercept is the value of K2, the equilibrium constant of the reaction OH- + OH + e. A typical set of results is given in table 1. The partial pressures of [OH] were cal- culated from the partial pressures of hydrogen and oxygen in the pre-burned gas mixture, and the thermodynamic data given in Lewis and von Elbe.6 TABLE 1 H;h comNPpsitio~z atF$;04 a g . thickness cm dbrcm 1/82 reversal temp. ("K) flame 2000A 62 27 11 4.6 -349 1.45 -241 17.2 1995 2000B 48 41 11 5.7 -313 1.15 -216 21.4 2000 2000C 41 48 11 6.8 -203 0.96 -209 23.2 1995 2000D 33 56 11 9.3 -187 0.95 -193 27.8 2000 Two similar sets of results, obtained at 2200" K, are shown in fig.2, where lip2 is plotted as a function of [OH]. It will be seen that the points do lie on straight lines, whose slope and intercept, though different for the two lines, do bear the same ratio to each other, as required by theory. These slopes and intercepts are given in table 2. 2200°K,NNaCI Two Atomizers 2200°K, N/2 NaHC030ne Atomizer 10 $2 5 I [OH]X 10' atrn /$HI x lo4 atm FIG. 2. Equilibrium constants were measured by this method at 100" intervals from 1900" K to 2200" K. Below this range, the ionization of sodium was insufficient to give a reason- able level of attenuation, The full set of results is given in table 2.TABLE 2 temp. (OK) slope intercept KZ Wm) 1900 1-02 x 105 12.2 1.4 x 10-5 2000 a 2.0 x 105 6.9 3.3 x 10-5 4-5 x 105 16.4 3.6 x 10-5 1.1 x 105 8.6 8.0 x 10-5 8 2200 c( 1.6 x 104 2.4 1.5 x 10-4 P 3.0 x 104 4.1 1.4 x 10-4 2100 The suffices a, /3 refer to experiments with differing values of Kl[Na], either due to a different atomizer, or to a different strength of salt solution in the atomizer.90 ELECTRON AFFINITY OF HYDROXYL At temperatures above this range, it was not possible to obtain a sufficient variation of composition, and an alternative method was adopted, in which, by comparing flames at different temperatures, the various constants of proportionality, the atomizer delivery, and the ionization of the alkali metal could still be eliminated, though their temperature coefficients had to be taken into account.We may write the equation developed in the previous section in the form Ki"a1 = (P2/k2>(1 + EoWK2). The temperature dependent terms in K1, i.e. the thermal ionization constant of sodium, may be estimated from the Saha equation for the ionization of alkali metals ; 7 the con- stant of proportionality between the attenuation, and the partial pressure of electrons (k) also depends on the temperature, and over a wide range of temperature, the change in the burnt gas volume, and the finite ionization of the sodium may also be significant. TABLE 3 temp. ("K) 2300 2400 2500 2600 K2 x lO4(atm) 2.95 5.8 11.1 14.1 All these temperature effects can be calculated readily, and combined into a correction factor with which the observations at high temperatures may be brought into comparison with those at a reference temperature-in the present case 2200" K.When this is done, we may write (1 + [OHI/K2)t = (1 3- [OHlIluz>o(Po/Pt>2f(T> wheref(T) is the correction factor, and the suffix 0 refers to 2200" K and t to the higher temperature. The factor (1 + [OH]/K& is that at 2200" K, and was obtained from the results of the previous section. All the data are available to calculate the values of K2 at the higher temperatures, that is up to 2600"K, from a knowledge of the easily measured attenuations PO and fit. Finally we may consider the possibility of a finite degree of ionization. In the derivation of the equation relating the attenuation to the amount of alkali metal in the flame, the term arising from the ionized alkali metal [M+] was ig- nored. At high temperatures, and with the more readily ionizable alkali metals, this is not valid.Indeed at 2600" K even sodium is 2 % ionized when a N solution is sprayed into the flame, and a more dilute solution of caesium will be almost completely ionized. Under these conditions of com- plete ionization, we may neglect the term arising from the un-ionized metal, while retaining that arising from the ion. The relation then becomes P I = I~l(1 -I- [OH]/&). This can be used to evaluate K2 if the atomizer delivery, and the constant of proportionality (k) are known, or else it can be combined with the expression for the attenuation due to sodium, where the fraction of metal ionized may be neglected, and either the constant of proportionality, or the ionization constants of the alkali metals and the atomizer delivery may be eliminated.If one assumes that the latter two quantities are known accurately, then a value for K2 is obtained (1.3 x 10-3 atm) which is in fair agreement with the otherF . M . PAGE 91 values obtained at this temperature. The importance of this method lies in the support that it gives to the theory behind the previous methods, rather than its value as a separate determination. The various values of K2 obtained during this work are plotted logarithmically as a function of 1/T in fig. 3, and the graph has a slope which corresponds to an electron affinity of 66.1 kcal, or 2.86 eV, in excellent agreement with the mean of the values (2.87 eV) obtained from the separate measurements by applying the Saha equation in the form loglo K2 = (- 5050 V/T) + loglo T - 5.6.The values thus obtained are included with other similar values in table 4. The concord of the values for the electron affinity determined by methods depending on both the second and third laws of thermodynamics is itself strong support for the values so obtained. DISCUSSION The value of the electron affinity of the hydroxyl radical that has been obtained experimentally in this work is in good agreement with other estimates that have been published, based on similar experiments,zS 3 but since these estimates have been criticized recently 8 in comparison with the lower values suggested by theoretical arguments, it is necessary to consider all the methods by which the experimental values have been obtained.These methods are, including the three described above : (a) from the isothermal variation of composition, (b) from the comparison of flames at different temperatures, (c) from the complete ionization of caesium, (d) from the number of heavy ions in a flame. Smith and Sugden 2 studied the dielectric constant of a flame at frequencies about 100 Mcls and deduced the relative numbers of electrons and heavy ions in the flame. From the principle of electrical neutrality, they were able to separate these into potassium and hydroxyl ions, and give two values for the equilibrium constant K2, viz., 4.2 x 10-5 atm at 2050" K and 1.2 x 10-4 atm at 2170" K. (e) From the absolute level of the attenuation of a flame.The same workers 3 showed that though the relative attenuations of sodium and potassium were correct, yet they were both low in comparison with the pre- dictions of the Saha equation, and this was ascribed to the formation of hydroxyl ions, by the same argument as used in the present work. They deduced values for K2 from three flames : 7 x 10-5 atni at 2145" K, 1.2 x 10-4 ,, 2245"K, 3 x 10-4 ,, 2260°K. This method could be applied to the results used in methods (a), (6) and (c), but some additional values were given by the earlier workers in a private com- munication, which it is preferable to consider : temp. ("K) 2060 2097 2137 2195 2243 2291 2291 2257 K2 x lO4(atm) 0.28 0.58 1.0 0.9 1.2 1.7 3.4 2.3 These results were obtained from flames in decreasing order of fuel to air ratios.James and Sugden 9 studied the intensity of the resonance radiation emitted by a flame containing alkali metal, and were able to estimate the value of K2 from the decrease in the intensity of the radiation from caesium with dilution, due to a finite degree of ionization. The value given was 1.2 x 10-4 atm at 2167" K. (g) From the effect of other electron acceptors on the attenuation of (f) From the emission of resonance radiation by a flame. a flame.92 ELECTRON AFFINITY OF HYDROXYL The addition of about 0.1 % of a halogen to a flame containing alkali metal produces a measurable reduction in the attenuation and a theoretical analysis of this reduction, assuming that halogen acid, alkali halide and halide ions are formed, in addition to the hydroxide ions and alkali hydroxide postulated in this paper, and that all are at equilibrium, leads to the expression : [(Po/P)~ - 11(1/[YI) = 1/K4’ + I/&‘ + [Yl/K4’Ks’, where K4’ = K4(1 + e)(l + +), Ks’ = K5(1 + e)(l + +’), [Y] = total concentration of halogen, 8 = [halogen acid]/[halogen atom], fi = [OH]/&, $’ = lOHIK2, K4 = [Hal][metal]/[alkali halide], K5 = [Hal][electron]/[halide ion], halogen, respectively.halogens respectively, can be obtained from the experimental data.10 PO, p = attenuation in the absence and presence of added The values of K4/ and K5’, which come from the effects of alkali halide and Taking the ratio of these effects to eliminate 8, Ks’lK4’ = (Ks/K4)(1 -k $’)/(I -k $1, or 1 + $’ = 1 + [OH]/& = (1 + $)(Ks’K4’1K4‘Ks).The mean value of K2 obtained from the preliminary results on the effect of chlorine, bromine, and iodine on sodium, potassium, rubidium and caesium at a temperature of 2243” K, and using the values of 1 + 4 given by Smith and Sugden (1.0, 1.2, 1.7 and 3.5 for the flame used for Na, K, Rb and Cs respectively) was 2 3 x lO-4atm. (h) From the halogen effect in isothermal sets of flames. It is necessary, when evaluating K2 by method ( g ) , to calculate the equilibrium constants K4 and Ks. The isothermal sets of flames used in the experimental part of this paper enable this calculation to be avoided. The argument used follows that of the previous method in that the halogen acid effect (0) is eliminated by taking the ratio of the salt and ion effects.The attenuation in the absence of halogen is given by the equation derived earlier, which is, using the $-notation : KlEXI = EE12(1 + +)(I + +’I, or 1!P2 = (UK1[XIk2)(1 + +)(l + $0 Combining this with the expression for R, the ratio of the halogen effects, we obtain RIP2 = (Ks/KiK4k2~Xl)(1 + +‘Y. That is, a plot of the square root of R/P2 against [OH] should yield a straight line, from whose slope and intercept the value of K2 can be deduced in the same way as was done in the first method described. This method has been used to determine the value of K2 from a study of the effects of chlorine on the attenuation produced by caesium, and gave a value of 3.1 x lO-5atm at 2000”K, and 1.3 x lO-4atm at 2200°K. The results at 2000” K are illustrated in fig. 4. The extrapolation required is a long one to be made on only three points, but is a fairly easy one to make.These estimates of the electron affinity of the hydroxyl have been quoted at some length since in most cases the estimate was incidental to the main interest of the work from which the data were taken, or else the estimate was assumed andF . M. PAGE 93 the data used to calculate other functions, whose numerical values, determined by other methods, have been used in the present calculations. It is necessary, in order to assess the weight to be attached assumptions on which the various methods are based, how far these assumptions are valid, and how far the different assumptions made in the different methods support each other by the concord of the results. Although the majority of the methods given depend upon the measurement of the attenuation of microwave radiation by the flame, it is significant that an entirely different method (f) gives a result which corresponds closely with the remainder.The attenuation methods all depend on the proportionality of the observed attenuation and the concentration of electrons, but it has been demonstrated many times that under conditions where the only variable is the normality of the salt solution in the atomizer, the attenuation is proportional to the square root of this normality as predicted by Ostwald’s dilution law for small degrees of dissociation. Furthermore, Belcher and Sugden 11 showed that the variation of the attenuation with frequency is entirely compatible with the assumption, to the experimental data, to consider the I 5 I @H) 1oSatm FIG. 4.3 while in a paper by Andrews, Axford and Sugden,l2 the number of electrons in a transient flame was measured by the attenuation, and shown to be the same as the number derived from measurements of the d.c. conductivity. Only in two methods (c), (e) is any assumption made about the exact value of the constant of proportionality; in all others it is enough that such a proportionality exists. Method (d), not being an attenuation method, does not make this assumption, though it does make a comparable appeal to electromagnetic theory. In methods (c) and (e) also, the magnitude of the ionization constant of the alkali metal is obtained from Saha’s equation, while in method (b) this equation is used, though only to obtain the temperature variation of the ionization constant. The thickness of the flame is concerned in all methods except (f) and (g). The possibility that indrawn air may affect the composition, the temperature, or the temperature distribution cannot be important in the regions of the flame where measurements were made; method (f) was used with a flame sheathed by a second flame, a technique used by Sugden and Wheeler in their resonant cavity method,l3 which has produced numerical results for the alkali metals in close agreement with those from the direct attenuation methods.Methods (a), (b), (c), (d), (h) all used a nitrogen sheath to protect the flame, while methods (e) and (8) used an unsheathed flame, though one in which the temperature cross-section was fairly uniform.Finally, sodium was the substrate in methods (a), (b), (c) and ( g ) , potassium in methods (d), (e) and ( g ) , rubidium only in method (g), and caesium in methods The measurement of the temperature of the flame is fundamental to all the methods, and the sodium line reversal method has been used throughout the ( 4 7 (f>7 (9) and (h).94 ELECTRON AFFINITY OF HYDROXYL work. This method is the most appropriate one for the study of equilibria in which atoms of alkali metal are involved. It has been found that similar flames, set up by different workers at different times, gave closely similar results, suggesting that the figures obtained have a real significance, and that the temperatures quoted in this paper form a coherent set.Furthermore, the temperature is involved in the estimation of other equilibrium constants used in methods (b), (e) and (g), and these methods give values in agreement with the remainder. All methods use the values of the hydroxyl concentration in the burned gases at the measured temperature obtained by calculation from the thermodynamic data given ia Lewis and voii Elbe.6 The use of these calculated values is probably satisfactory, since in almost every case the flames were well removed from stoichiometry. The vexed question of whether or not the assumption of thermo- dynamic equilibrium is valid cannot be answered simply. The hot gases of the secondary zone of the flame have a few milliseconds in which to reach equilibrium before reaching the measuring zone, but the possibility that this is insufficient cannot be overlooked.In any case, the flame is not an isolated system, and though the term “ equilibrium constant ” has been loosely used in this paper, it is more proper to consider the flame as a steady state, in which the appropriate concentration products may approach the values of the true equilibrium constants fairly closely. No evidence has yet been found that would suggest unquestionably that any appreciable degree of disequilibrium existed, while the coherence of the results obtained by the various methods is evidence that the assumption of equilibrium is at least a good approximation. In addition, the study of the halogens referred to under method (g), has led to preliminary values for the electron affinities of chlorine, bromine and iodine which agree with the values obtained by completely different methods to within a few kilocalories.These results depend on a much more complicated system of equilibria than do the results for hydroxyl, and yet there is no evidence for any significant deviation from the expected results, due to disequilibrium. Although the criticisms based on the fact that all the methods described use flames to reach the ternperaturcs required apply to all methods, and there must be some doubt about thc hydroxyl concentration, the temperature, and disequi- librium, yet the fact that eight different and distinct methods yield coherent results, and these results cover a range of 700 deg., and as mentioned, other quantities can be evaluated on the basis of these results, which are in good agreement with the accepted values, is strong indication that the experimental value given to the electron affinity is correct.It may be said in passing that the question of whether it is hydroxyl which is in fact responsible for the observed effects has not been answered. No other possible entity has been considered, but such an entity must vary with the flame composition in the same way as does hydroxyl. The flames do contain large quantities of N2, H2 and H20, but these have negligible electron affinities, while of the minor constituents, the hydrogen atom concentra- tion is of the order of that of hydroxyl (lO-4atm) and the oxygen atom con- centration is several powers of ten lower. Neither of these minor constituents can therefore contribute appreciably to the removal of electrons.It has been claimed throughout this paper that the various methods give results that are in good agreement. How good this agreement is, may be judged from table 4, where the electron affinities are calculated from the equilibrium constants by Saha’s equation, and are collected together. Since there appears little doubt that the experimental value is correct, it is now necessary to examine the evidence for the indirect estimates, which lead to a value of about 50 kcal. These methods are : lattice energy calculations, argu- ments based on an analogy with the oxygen atom, and certain extrapolations based on spectra. Of these, the lattice energy calculations are by far the most important, and lead to two very different values, depending on whether or not the dipole moment of the hydroxyl radical is taken into account.F .M . PAGE 95 The arguments by analogy are based on the fact that the oxygen atom and the hydroxyl radical have very nearly the same ionization potential, and that therefore it is reasonable to expect that they would also have thc same electron affinity. Tf this was so, the electron afinity of hydroxyl would be about 53 kcal. However, as James and Sugden 9 mcntion, Mulliken has pointed out that thc valence statc of thc oxygen atom is different in the free atom and in thc hydroxyl radical, and the addition of an electron to thc latter will completc an inert gas shell. An application of bond theory suggests that this will lead to thc electron affinity of the hydroxyl radi- a l bcing about 15 kcal higher than that of the oxygen atom, i.e.about 68 kcal. The methods which arc based on a spectral correlation of the measured clectron affinitics of thc halogcns with the so-called electron-transfer spectra of thc alkali halides, followed by an interpolation to determine the electron affinities of the hydroxyl, and other radicals, are of extremely doubtful value.14 They suggcst a valuc of about 83 kcal which, un- expectedly, is very close to the un- corrected lattice encrgy valuc given by Goubcau.ls This author actually obtained a valuc of 78 kcal, but thc higher figure follows from the use of thc later value of the heat of formation of hydroxyl obtained by Dwyer and Oldenburg.16 Goubeau and Klemm 17 corrected the earlier electron affinity by assuming that the TABLE 4 temp.(OK) 1900 2000 2100 2200 2300 2400 2500 2600 2600 2050 2170 2145 2245 2260 2060 2097 21 37 2195 2243 229 1 229 1 2257 21 67 2243 2000 2200 K2 (atm x 105) 1.4 3.4 8.0 14 29.5 58 110 140 130 4-2 12 7 12 30 2.8 5.8 10 9 12 17 34 23 12 23 13 3.1 VeV 2.80 2.82 2-83 2.88 2.88 2.89 2.89 2.98 3.00 2.86 2.86 2.92 2.99 2.82 2.95 2.88 2-85 2-96 2.98 2.98 2.84 2.87 2-86 2.85 2.85 2.88 The mean value of all detcrminations is 2.87 eV, or 66.2 kcal, with a probable error of the mean of 0.3 kcal. The value derived from a plot of loglo KZ as a function of 1/7 is 69.8 kcal. This must be reduced by about 6 kcal to give the value at 0" K. hydroxyl radical had a dipole moment of 2 D, and from this they estimated that the true valuc of the electron affinity should be somc 29 kcal lowcr, that is, 53 kcal, which is the same as the value deduced, incorrectly, from an analogy with the oxygen atom.While the lattice-encrgy calculations of thesc authors is probably the best so far, the figures thus derived may be in considerable error, since they are obtained as the difference of two large quantities, and furthermore, the dipole correction, which amounts to ovcr one-third of the wholc, may wcll be grcatly in error, and it cannot be said that the value is in any way in disagreement with the value of about 65 kcal which follows from the correct argument by analogy. From this cursory survey, it is apparent that the various indircct estimates arc compatible with any value of the electron affinity bclwcen 45 and 85 kcal, but that the value of 65 kcal can bc supported well, probably better than most.The discrepancy which it has been claimed in a recent review 8 existed betwccll the indircct estimates and thc valuc obtained from a study of flames is sccn to bc illusory, and the two methods are in good accord. Considerable wcight must be attached to the practical determinations outlined in this paper, and the value of the electron affinity of the hydroxyl radical at absolutc zero is put, after con- sidcring all the dcterrninations and cqtirnates, at the mean of the expcrimental96 THEORY OF MOLECULAR OSCILLATOR determinations from the Saha equation (66kcal) and by graphical methods (70 kcal at 2000" K which becomes 64 kcal at 0" K), that is, at 65 kcal i 1 kcal, or 2-82 eV. The author would like to express his indebtedness to his many colleagues, in particular Dr. T. M. Sugden, for continued advice, guidance, and encourage- ment during the progress of this work. 1 RoIla and Piccardi, Atti accad. Lincei, 1925, 2, VI, 29. 2 Smith and Sugden, Proc. Roy. SOC. A, 1952,211, 31. 3 Smith and Sugden, Proc. Roy. SOC. A, 1952, 211, 58. 4 Sugden, this Discussion. 5 Sugden and Smith, Proc. Roy. Soc. A, 1953, 219, 204. 6Lewis and von Elbe, Combustion, Flames and Explosions of Gases (Cambridge 7 Saha, Phil. Mag., 1920, 40, 472. 8 Pritchard, Chem. Rev., 1953, 52, 529. 9 James and Sugden, Proc. Roy. SOC. A , 1955 (in press). 10 Sugden, 5th Int. Symp. on Combustion (Pittsburgh, 1954, in press). 11 Belcher and Sugden, Proc. Roy. SOC. A , 1950, 201,480. 12 Andrews, Axford and Sugden, Trans. Faraday Soc., 1948, 44,427. 13 Sugden and Wheeler, this Discussion. 14 Rabinowitch, Rev. Mod. Physics, 1942, 14, 112. 15 Goubeau, 2. physik. Chem. B, 1936, 34,432. 16 Dwyer and Oldenburg, J. Chem. Physics, 1944, 12, 357. 17 Goubeau and Klemm, 2. physik. Chem, B, 1937,36, 362. University Press, 1938).