76 IONS OF ALKALINE EARTHS THE IONS PRODUCED BY TRACES OF ALKALINEEARTHS IN HYDROGEN FLAMES BY T. M. SUGDEN AND R. C. WHEELER Dept. of Physical Chemistry, University of Cambridge Received 27th January, 1955 The concentration of free electrons produced when traces of the alkaline earth metals were added as salts to various hydrogen -1- air flames has been studied by a resonant cavity method, operating at a wavelength of about 10cm. It has been studied as a function of amount of added metal and of the temperature of the burned gases. Pre- liminary and extensive calibrations were carried out with alkali metals. In particular, comparison of the number of free electrons produced by addition of the same amounts of lithium and of sodium enabled estimates to be made of the concentration of hydroxyl radicals in the various flame gas systems used, by taking into account the known relative stabilities of sodium and lithium hydroxides. This has enabled the concentration of negative hydroxyl ions produced to be calculated.The alkaline earths show a much more complicated variation of electron concentration with amount of metal added, and this has been interpreted in terms of the formation of both positive and negative ions containing one atom of metal each. Analysis of the results suggests that the positive ions are mainly of the type (BaOH)+, and that these are produced in equilibrium amounts. A discussion of the stability of radical-ions of this type is given. The negative ions are considered to arise by combination of hydroxyl ions with molecules of the diatomicT .M . SUGDEN AND R . C. WHEELER 77 oxides. Such ions are shown to be reasonably stable, but the results indicate that they cannot be formed in amounts corresponding with thermal equilibrium. The kinetics of their formation are discussed, and found to be consistent with the observations. A large amount of previous work has shown that when alkali metals are present in flame gases a t high temperature (- 2000" K), the ionization which occurs is explicable on the basis of equilibrium between the metal, its positive ion, and free electrons, provided that reasonable account is taken of the side reactions involving the free hydroxyl radicals of the flame gases to give the hydroxide of the metal and negative hydroxyl ions, also in equilibrium amounts.1 The most obvious expression of this equilibrium is the dependence of the concentration of electrons on the total concentration of metal present (free or combined as hydroxide), which is expressed by over wide ranges of concentration wherc the proportion of free metal ionized is small.KX is a constant for a given flame, and [Ao] the concentration in the flame gases of the total alkali metal present (free or combined). Work on the alkaline earth elements has shown that this simple law is not obeyed,2 and that for very small amounts of metal prescnt in thc flame gases, the electron concentra- tion rather follows a law [el2 == KA+[Ao] Throughout this paper A will be used to represent an alkali mctal, and B an alkaline earth. In the last expression b and c are constant for a given flame, and [Bo] is the total concentration of alkaline earth (free or combined, expressed in terms of atoms or compounds with one atom of alkaline earth).The purpose of the work to be described is the determination of these parameters b and c for various conditions of gas temperature and composition, and to see whether they can be interpreted on an equilibrium basis, and if so, what ions take part with electrons in this equilibrium. It is already known that when alkaline earths are present in the hot gases from flames containing hydrogen and oxygen, the great majority of the metal is prescnt in the form of the diatomic oxide B 0 . 3 ~ 4 In the ranges of temperature and concentration of alkaline earth uscd here, appreciable dimer- ization of this oxide does not occur, so that compounds and ions containing only one atom of R need be taken into account.EXPERIMENTAL The ionization has been studied by measurement of the concentration of free electrons using the resonant cavity method described in the previous paper,s and used previously in work of similar type.6.7 Metered streams of hydrogen and air were mixed, sometimes diluted with excess nitrogen, and burned in a M&ker type of burner of nickel. The metals were added as fine sprays of solutions of salts from an atomizer, which had been calibrated for delivery into the flame gas supply to the flame. This burner, about 2 cm in diameter, was surroundcd by another similar one, supplied with a gas mixture of the same com- position, but without added salt, giving a total diameter of about 4cni.This outer flame shielded the salt-bearing inner gases from cntrainment of outside air, which causes aftcr-burning with the excess hydrogen, and introduccs marked inhomogeneity of tem- perature near the boundaries. Somewhat hydrogen-rich mixturcs were used, since these gave a more clearly defined central column of gas of fairly uniform temperature. The temperatures were measured by the method of sodium D-line reversa1,g which has proved very satisfactory for work of this type, and a series of flames chosen in which the tem- perature of the central column of gases did not vary by more than 9: 10°C over the region used for measurement of electron concentration, i.e. about 12 cm of height. The surface of the burner formed part of the lower face of a cylindrical resonant cavity tuned to resonate in the T E o , ~ , ~ mode at a wavelength of about 10cm.The burned gases from the flame escaped through a hole in the upper end of the cavity, rather larger in diameter than the column of hot gases. This hole was electrically sealed to prevent78 IONS OF ALKALINE EARTHS escape of microwave radiation by a very coarse mesh of about ten strands of stout gauge platinum wire. The burner and exit-hole were offset from the axis of the cavity so that the cross-section of the conducting central column of gas was in a region of more nearly uniform electric field than if it had been concentric with the cavity. The cones of primary combustion (about 3 mm high) were inside the cavity, but being near the end, in a region of low electric field, any ionization in them, which would almost certainly not be thermally equilibrated, had little eifect.This method, which was chosen as the most convenient in operation, gave the same results as when the flame was placed a little below the cavity, with the burned gases entering via a gauze similar to the exit onc. The cavity was excited through an iris aperture by a CV36 klystron, from which it was almost isolated by a large wedge attenuator to reduce coupling. The microwave power transmitted was rectified by a silicon crystal, similarly isolated from the cavity by an attenuator. Measurements of Q, which is decrcased by the losses due to conduction by free electrons, being rather tedious to carry out in large numbers, the transmission of the cavity at fixed frequency was measured when the central column of gases was made conducting by addition of salts, and compared with that of a “ clean ” flame, which was practically non-conducting.This effect was calibrated by using sodium salts in the atomizer, where the proportionality between the square of the electron concentration and that of the sodium added is well established.1 The whole cavity was water-cooled. Fluctuations in the behaviour of the apparatus were eliminated by frequent checks against sodium. An absolute check on the reliability of the system was obtained for sodium by measuring the Q of the cavity, and comparing the concentration of electrons thus measured with the theoretical value (that derived on a basis of calculations of thermodynamic cquilibrium at the measured temperature).As described in the previous paper,s the electrical con- ductivity a is given by where &o and Ql are the Q’s of the cavity in the absence and presence of conducting flame respectively, OJ = 27r (frequency of radiation), and g is a numerical factor relating to the size of the cavity, the size of the column of conducting gases, and its position inside the cavity. This factor is readily calculated. The electrical conductivity is related to the number n of electrons per cm3 and hence to their partial pressure in atmospheres [E], if thermally equilibrated, by ne2 wl where e and m are the electronic charge and mass respectively, and wl is the frequency of collision of an electron with molecules of gas.Using a value 9 of w1 of 8.8 x 1010 sec-1, a value of [E] of 4.4 x 10-8 atm was found in a particular case of sodium added to a hydrogen + air flamc, comparing with a theoretical value for thermal ionization of thc sodium added of 5.9 x 10-8 atm for [el. This supposed only the simple ionization Na + Na+ + E (see below). This agreement is more than satisfactory, in view of the many measurements and assumptions involved, and may involve some cancellation of errors. It is certainly good enough to validate the method as giving a reasonable measure of the absolute concentration of free electrons. Relative measurements of this con- centration under various conditions of flame and added metal are accurate to within f 5 % with respect to each other. The method was capable of dealing with electron concentrations down 108 electrons per cm3 ([E] - 3 x 10-11 atm).(J = -- __- m fd + w12’ RESULTS HYDROXYL CONCENTRATIONS FROM COMPARISON OF LITHIUM AND SODIUM Since it was suspccted that the presence of hydroxyl might affect the ionization of the alkaline earths (as later it will be seen is very probably the case), a short study of the conccntration of free hydroxyl radicals in the flame gases was made by comparing the ionization from lithium and sodium. It appcars that while sodium exists almost entirely as free atoms in the flame gascs from hydrogen -t air flames, lithium is prcscnt to a very large extent as the hydroxide LiOH, in amounts 1 given by the equilibrium LiOH+LiSOH. The ionization of an alkali metal added to a flame is given by an equation due to Saha,loT.M. SUGDEN AND R. C . WHEELER 79 where V is the ionization potential in eV, T is the absolute temperature in OK, and K is the equilibrium constant of the ionization A + A+ + e in atm. The ionization given by the same total concentrations of lithium and sodium added to a flame may be expressed by a modified equation of this type where 4Li = [LiOH]/[Li], the corresponding quantity for sodium being approximately zero, on account of the instability of NaOH. If the equilibrium constant of LiOH + Li + OH is K’, then + ~ i = [OH]/K’. Measurements of the relative electron concentrations for the two metals leads to a value for $ ~ i , and it has been found that K’ is satisfactorily represented 1,11 by K‘= 7.6 x 10s exp (-- 102,0001RT) atm, so that values of [OH] Q) > .- a- Molarity of solution FIG.1.--The variation of electron concentration with total metal added, plotted as [el2 against molarity of solution in the atomizer. Sodium calibration added to show different dilution law for alkaline carths. Flame-gas temperature 2010” K. may be derived. The rcsults are shown in table 1, where they are compared with calculated values. The calculated values were obtained from the equilibrium com- position of the burned gas at the measured sodium D-line reversal temperature, using the data of Lewis and von Elbe 12 for the equilibrium constant of the reaction H20 + OH + 4H2. This gas consists largely of H20, unreacted H2 and N2, with up to about 0.05 % of OH and H, whose concentrations are buffered by the major constituents.The agreement TABLE RESULTS OF HYDROXYL AND HYDROXYL ION TESTS temp. of flame gases C K) k i 21 80 8.7 4.0 x 10-4 5.6 x 10-4 1.2 2109 9.3 2.1 Y Y 3-4 9 , 1.1 2063 14.6 1.7 ,) 2.1 3, 1.3 2010 15.3 9.6 x 10-5 1.2 9, 1.2 1965 18.2 6.3 y y 7.3 x 10-5 1.2 1907 27 3.4 9 , 3-7 $ 9 1.2 1855 31 2.3 9, 2-1 Y9 1.380 IONS OF ALKALINE EARTHS is seen to be good, and it is not unlikely that the experimental values are better than the calculated ones. These hydroxyl radicals are capable of reacting with electrons to give hydroxyl ions, OH- 6 OH + E, and if the equilibrium constant of this reaction is K", then it is given by in atm. This equation is a slightly modified form of the Saha equation to take account of the different statistical weights of the ion and the uncharged molecule.It assumes that the interatomic distance and the frequency of vibration are the same in the hydroxyl radicals and ions, which is not likely to be greatly in error, and in any case has little effect on the value of K". Thus 4' = [OH]/K" = [OH-J/[c] may be calculated if K" is known. d 1907OK /_i_O_ 2 BOOK 0 . 5 [SroJ x IO'atrn FIG. 2.-Plots of the function [Sro]/[c]2 against [Sro] for three temperatures. K" has been calculated from the last equation at the various temperatures used with a value 13 of E, the electron affinity of OH of 2.7 eV (62 kcal). The derived values of +' are given in the last column of table 1, and are seen to be very nearly constant. If the revised value of E = 2.82 eV given by Page14 is used, these values are about doubled, but the constancy is little affected.ELECTRON CONCENTRATIONS FOR ALKALINE EARTHS The electron concentrations for the alkaline earths, calcium, strontium and barium, are com- pared with that for sodium for various amounts of the metals added to a givcn flame in fig. 1. The plots are of relative [€I2 against the concentration of the salt solution in the atomizer (molarities). The chlorides were generally used, but the results were independent of the anion, so that the solution is merely a convenient vehicle for conveying the metal into the flame. It will be seen that the electron con- centration rises much less rapidly than the linear (calibration) result for sodium. Other alkali metals give straight lines like that for sodium.Similar results have been obtained for all the flames used, the error becoming rather large, however, for calcium in thc cooler flames, which gives a very small number of electrons. Wheeler 7 has shown that linear plots can be obtaincd in terms of a relation [el2 = b[Bo]/(l 3- ~[Bo]) by plotting [Bo]/[c]~ against [Bo] with interccpt 1/b on the ordinatc and slope clb. Such plots are shown for three flames in fig. 2. [Bo], the total concentration of alkaline earth B, is obtained from the molarity of the salt solution by calibration of the atomiser (a 1-M solution gave [Bo]==3.5 x 10 - 5 atm). The partial prcssure of electrons [el is obtained from the effects on the transmission of the cavity at resonance as described in outline above. Fig. 2 shows good straight lines, provided that [Bo] does not rise above 10-6 atm (003 M solutions).With barium and strontium at least, [Bo] does not rise above the vapour pressure of the oxides BaO and SrO, as quoted by Claassen and Veenemans,ls so that solid oxide is most unlikely to be present. The cooler flames (< 2000" K) should permit the prescnce of a little solid CaO for the higher levels of [Bo] used, but there was no cvidence of this in the gases insideT. M. SUGDEN AND R , C . WHEELER 81 the cavity in the form of continuous radiation. It can be seen that at very low [Bo], the above equation reduces to [el2 = b[Bo], resembling the expression for alkali metals. Hence the values of b obtained for the various flames may be compared with the cor- responding values of the proportionality constant for sodium, and this is shown plotted against 1/T in fig.3. These parameters plotted in fig. 3 are very closely related to the I / T ( " K ) 16* FIG. 3.--Plots of log b against 1/T for the alkaline earths, with sodium plot added for comparison. equilibrium constants for ionization to positive ions and electrons, and are in fact these equilibrium constants if there are no side equilibria arising from, e.g., the presence of hydroxyl radicals in the gases. They will be examined from this point of view in the next section. The parameters c for the alkaline earths in the various flames are similarly plotted against 1/T in fig. 4. They show little significant variation with temperature, and unlike b, vary in the anomalous order Ba, Ca, Sr. This also will be commented on in the discussion.---------.- 7--- V 0 0- 0 - I / T ( W ~ la4 FIG, 4.-Plots of log c against 1/T. DISCUSSION If the variation of ionization with amount of alkaline earth depends only on an equilibrium B + a-1- -1 E, where B represents a molecule of any substance con- taining only one atom of the alkaline earth B, and if the ionization is sinall com- pared with the total B present ([Bo]), then the situation is the same as with the alkali metals, and a dilution law [el2 E DO] is obtained. This does not coincide with the expcrimental results, which give a less rapid variation of [el with [Bo],82 IONS OF ALKALINE EARTHS and an attempt will be made to explain the observed variation by considering other ionic equilibria which may occw in this case.One way in which the observed results can be explained is to suppose that a negative ion B-, containing one atom of B, can be made. Then putting B + Bi- I- E ; K$ = [B'][€]/[B], [E] -k [B-1 = [B'] (charge balance), [B] - LBO] (small ionization), B - B + E ; KB = [B][E]/[B-], the following equation may be deduced which is of the observed form, with b = K&, and c = l/KB. The formation of hydroxyl ions in equilibrium amount does not affect the form of the dependence. Another explanation of a low rate of variation of [el is to suppose that extensive dimerimtion to unionized moleculcs of type B2 occurs, but the prcssures of alkaline earth available are considered to be too low for this at these temperatures, and in any case this leads to a prediction that [Bo]/[E]~ against [el2 will bc linear, which is not the case.This hypothesis of a positive ion B+ and a negative ion B- will therefore be adopted for the present. The possibilities for the ion Bi- arc the singly ionized metal BI, the ionized oxide (BO)f, and the ionized hydroxide radical (BOH)+. The last two will be essentially electrovaleiit compounds made up of B2+, and 0-, OH- respectively, with highly distorted (polarized) ions. The ion (BOH)+ has constituent ions with a closed shell (inert gas) type of structure, and in this resembles the alkali hydroxides AOH and the alkaline earth oxides BO. The experimental parameters b are the same as the equilibrium constant KB for the ionization to give the positive ion, and hence the corresponding " ioniza- tion potential " may be deduced from them in two ways, using the Saha equation.Firstly, the variation of loglo b with l/Tshould give a straight line of slope -5050 V (second law method), and secondly, the absolute value of b at a given temperature may be used to obtain a valuc of V (third law method). These values, obtained from the results shown in fig. 3, are given in table 2, together with the values for sodium, and the known first ionization potentials of the atoms. Good agrcement TABLE 2.-IONIZATION POTENTIALS first i.p. from i.p. from absolute &%I (eV) 2000' K (eV) slope of fig. 3 value of fig. 3 at metal Na 5.12 5.1 5.1 ca 609 4.16 5-19 Sr 5-65 3.96 4.97 Ba 5.19 3.57 4-75 betwecn thc various methods applies for sodium, but not for the others. The formation of hydroxyl ions has little effect on the results for sodium because 4' is independent of temperature for the flamcs used, and because it is quite small (about 1).The implication of the lack of agreement between the last two columns for the alkaline earths is that the neutral molecule on which the positive ion is based is not the compound of B which is dominant in the flame gases4.e. it is not the oxide BO, which is known to make up well over 90 % of the total B present. Thus thc ion (BO)-l- is ruled out. The positive ion must therefore bc derived from a neutral constituent which is present in different amounts at differcnt temperatures. The free atoms B form such a constituent, but table 2 shows that the observed ionization potentialsT . M . SUGDEN AND R . C .WHEELER 83 are much too low compared with the known ones. Thus the atomic ion Bf may be eliminated as well. The neutral hydroxide radicals BOH will be unstable with respect to the oxides BO, and will be rather like the unstable halide radicals, such as BaF, with which they correspond in electronic structure. The spectra of these radicals have recently been identified in flames of this type 4 and resemble those of the halides.16 These spectra also indicate that BOH is a very minor constituent compared with BO. The ion (BOH)+ may, however, be relatively stable on account of its closed shell electrovalent structure (i.e. the molecules BOH will have low ionization potentials). The ionic equilibria governing it may be set up as follows : with charge balance ignoring the other types of positive ion already rejected, and mass balance [E] + [OH-] = [(BOH)+I, D o 1 = LBO], ignoring neutral constituents other than oxide.This system of equations leads to Kl W2Q"ol +Y1 + $9 ' [€I2 = which is of the same form as the observations when c[Bo] << 1. The parameter b is then K1[H20]/4'(1 + $'). For the flames used the variation of [H20] with temperature is negligible, as is that of 4' (cf. table 1). Hence the temperature coefficient of b should be the same as that of K1. Assuming this to be so, a value of the heat of formation of (BOH)+ from B2+ and OH- may be worked out by combining the results with standard thermodynamic data. This is set out in table 3 . TABLE 3.-REACTION SCHEME FOR HEAT OF FORMATION OF BOH+ AH0 (kcal) reaction Ca Sr Ba BO + HzO --> BOH+ + OH- 96 91 80 B + O +BO -103 -111 -126 B2++ 2~ + B -414 - 384 -349 20H -+ 0 + H20 - 19 - 19 - 19 20H- + 2 0 H + 2 ~ 124 124 124 B2+ + OH- 3 BOH+ - 316 -299 -290 reference present work Brewer 17 Znt.Cuit. Tables 18 Dwyer and Oldenberg 19 Smith and Sugden 13 TABLE 4.-HEATS OF FORMATION FROM IONS (kcal/mole) ht. of ht. of ht. of formation ht. of formation from ions charge on from ions charge on each ion each ion substance formation per unit substance formation per unit substance KOH 125 125 CaOH 316 153 CaO RbOH 123 123 SrOH 299 150 SrO CsOH 120 120 BaOH 290 145 BaO hr. of ht. of formation formation per unit from ions charge on each ion 685 171 663 165 64 1 161 The final figures from table 3 are compared in table 4 with the heats of formation of alkali hydroxides AOH from A+ and OH-, and with those of the alkaline earth oxides from B2+ and 02-. The last column of each set of three gives the energy involved for each pair of unit charges on the two ions, assuming all the molecules to be essentially electrovalent.It will be seen that the values deduced for the84 IONS OF ALKALINE EARTHS radical-ion lie very reasonably between those for the alkali hydroxide and those for the alkaline earth oxide. The steady increase in the heat per pair of unit charges in the series AOH --f (BOH)+ -+ BO is consistent with steady shortening of the interionic distance. The variation of b with temperature is thus consistent with the presence of these ions. The absolute level of b must also be consistent if this is the true explanation.K1 is given in statistical terms by where the q's are the appropriate partition functions, and AH^ is the heat of reaction at absolute zero. The q factor has been evaluated using either known interatomic distances and frequencies of vibration, or reasonable calculated ones. For calcium with AH0 = 96 kcal, a value of K1 = 9 x 1011 is obtained (the q factor is about 3). At 2000" K the components of the burned gas gave [HzO] - 0.3 atm, and $ r = 1.2 (table 1). This data yields a calculated b of 1.4 x 10-11 atm, com- paring with the measured value of 4.5 x 10-12 atm. This three-fold difference is by no means unreasonable in view of the possible errors in AH^, and the assumptions made. There is also some doubt about the statistical weight of the ground electronic state of the oxide.This has been taken as a singlet, but if it were a triplet the agreement would be rather improved. Similar results obtain for strontium and barium. There is thus a very strong case for considering that the ion B+ is in fact of type (BOH)+. Further, the existence of this kind of ion at low concentrations of alkaline earth is quite independent of whatever complications may arise at higher concentrations, i.e. it is not necessarily tied to the formation of ions of type B-. It may readily be equilibrated in the time available by the following scheme of actual processes B + H20 + BO + Hz B + OH +BO + H BO + H + (BOH)+ + E E + H20 + OH- + H. No ternary collisions are involved in any of these. The first two pairs involve heats of reaction of about 20 kcal, and will have low energies of activation.The third pair is 30-50 kcal endothermic in the forward direction, with a back reaction likely to have zero energy of activation. The last reaction is about 50 kcal endothermic in the forward reaction, and again thc energy of activation will not be much greater than this. None of the energies involved is sufficiently high to prevent enough effective collisions for the system to come near equilibrium. The parameter c of the results is much more difficult to deal with. It is approximately independent of tempesature, and decreases in the anomalous order Ba, Ca, Sr. This anomalous order in the alkaline earths has been com- mented on already by Drummond and Barrow20 in connection with some pro- perties of the oxides BO, and there is little doubt that the oxides are important here.There are two negative ions worthy of consideration, viz., the oxide ion (BO)-, and an ion made by attachment of OH- to BO with formula (0BOH)--, and with electrovalent structures B+02- and 02-BZfOH- respectively. The former may be introduced in the equilibrium which leads to c = 1/(1 4- $')K3. Now $ r varies hardly at all with temperature, so the implication of the near constancy of c is that the reaction which K3 describes must have a very small heat change. This is impossible if (B0)- is stable. In the same way, if the other negative ion is used, BO- F+ BO + E ; K3 = [BO][C]/[BO-], (0BOH)- + BO + OH-; K4 = [BO][OH-]/[(OBOH)-]T. M. SUGDEN AND R . C. WHEELER 85 leads to a value of c = $'/(1 + 4')&, and the same objection applies.Hence neither of these two ions is feasible on an equilibrium basis. This conclusion warrants further examination on the basis of stability. The ion (B0)-, which would be electrovalent, would be derived from B+ in a 2 s state, which is a larger ion than that of the singlet state of B2f. Similarly the 0 2 - ion is certainly larger than the 0- ion. Hence (B0)- will be less stable than (BO)+, which has already been rejected as a likely positive ion. The other negative ion, however, is, like (BOH)+, made up of closed shell ions 02-B2+0H-, which will tend to lend it stability. In this connection, Wheeler 2 has found strong evidence of specific interactions in flame gases between the positive ions of alkali metals and molecules of alkaline earth oxides, which are readily explicable by the presence of compound ions of the same type, viz.B2+02-A+. Calculations using the methods of Rittner 21 for one of these, (SrONa)+, lead to a heat of formation from SrO and Na+ of 125 f 20 kcal. This is sufficient to make this compound ion stable with respect to its dissociation products under flame gas conditions. The ion (0BOH)- should have about the same stability with respect to BO and OH-, and thus should appear in our experiments. Further, fragments such as Ba20+ have been observed mass-spectrographically by Aldrich.22 A difficulty arises, however, in the formation of this negative ion from BO and OH- on account of the few collisions between them in the time available, particularly since these may need to be three-body collisions to remove the heat of formation released.The only other ways in which it can be formed involve either the simultaneous production of a positive ion from the flame gases by, e.g., BO + H20 + (0BOH)- + H+, which requires too much energy, or by processes involving collision between two molecules each containing an atom of B, e.g., BO + BOH + (0BOH)- + Bf, which are far too infrequent. The time allowable for a position near equilibrium to be reached is of the order of 10 msec, from leaving the burner, during which the average molecule makes about 107 collisions with other molecules, and an electron about 109 collisions with molecules. The fraction of OH- ions is of the order of 10-7 of the total gases, so that a BO molecule will only collide with one or two OH- ions in the time available.The possibility of equilibrium being established is thus very remote, and large departures from it might be expected. The reactions BO + H20 + (BOH)+ + OH- OH- + OH + E will be reasonably well equilibrated by the reactions quoted previously, which fulfil the necessary collisional conditions, If to this is added d[(OBOH)-Ifdt = k[BO][OH-], where k is essentially the collision frequency (possibly including the concentrations of third bodies), then for the very early stages of the production of the complex negative ion, where its decomposition can be ignored, it may be shown that the concentration of electrons is given by This is of the observed form with c = k$'t/(l + 4') On the basis of bimolecular collisions at 2000" K, k has a value of 5 x 10-10 molecule-1 cm+3 sec-1, assuming a collision diameter of 3 A, which becomes 2 x 109 in atm-1 sec-1.For t = 10-2 sec, therefore, kt$'/(l + 4') - 107 atm-1, which is the same order of magnitude86 IONS OF ALKALINE EARTHS as the coefficients c observed. This will vary very little with temperature. Three- body collisions will be about 1000 times as infrequent as two-body ones, but on the other hand, the collision diameter chosen for a two-body collision between an ion and a large dipole is probably considerably too small. The absolute magnitude and small variation of c with temperature is thus reasonably explained. As has already been pointed out, the order Ba, Ca, Sr is characteristic of many of the properties of the oxides BO of the alkaline earths, and the result obtained here, which is really a measure of the collisional cross-section of the oxides, is in line with this. CONCLUSION The complicated ionization, as evidenced by the variation of electron con- centration with amount of alkaline earth present in hydrogen + air flames, is in strong contrast with the simple case of alkali metal elements.Positive ions are produced, in equilibrium with electrons and hydroxyl ions, and considerations of the amounts of ionization, and their variation with temperature, indicate strongly that these are the hydroxide radical-ions (BaOH)+, (SrOH)+, (CaOH)+. These are thermodynamically probable bodies, the results indicating that they fit well in a series of essentially electrovalent molecules such as CsOH, (BaOH)+, BaO.A full account of the results can be given if, in addition, negative ions containing one atom of alkaline earth are produced, and it is shown that combination of alkaline earth oxide molecules with hydroxyl ions to give, e.g., (0BaOH)- is feasible. The results are, however, inconsistent with thermal equilibrium of these, and it is shown that the time available in the flame system is insufficient for this equilibrium to be brought about by collisions of, in this case, BaO and OH-. Simple kinetic calculations show that the degree of combination which could take place is consistent with the observed results. Although the method used is somewhat indirect, it is difficult to explain the results in any other way, and there are good thermodynamic reasons why the interpretation adopted should be the correct one. Thanks are due to the Imperial Oil Company of Canada for the award of a scholarship to one of us (R. C . W.). 1 Smith and Sugden, Proc. Roy. SOC. A, 1953, 219, 204. 2 Wheeler, Diss. (Cambridge, 1954). 3 Huldt and Lagerqvist, Ark. Fys., 1950, 2, 333. 4 James and Sugden, Nature, 1955,75, 333. 5 Sugden, this Discussion. 7 Sugden and Thrush, Nature, 1951, 168, 703. 8 Gaydon and Wolfhard, Flames, their Structure, Radiation and Temperature (Chap- 9 Belcher and Sugden, Proc. Roy. SOC. A, 1950,201,480. 10 Saha, Phil. Mag., 1920, 40,472. 11 James and Sugden, Proc. Roy. SOC. A, 1955,227, 312. 12 Lewis and von Elbe, Combustion, Flames and Explosions of Gases (Academic Press, 13 Smith and Sugden, Proc. Roy. SOC. A , 1952,211, 31. 14 Page, this Discussion. 15 Claassen and Veenemans, 2. Physik, 1933, 80, 342. 16 Pearse and Gaydon, The Identification of Molecular Spectra (Chapman and Hall, 17Brewer, Chem. Rev., 1953, 52, 1. 18 Int. Crit. Tables (McGraw-Hill, New York, 1929). 19 Dwyer and Oldenberg, J. Chem. Physics, 1944, 12, 351. 20 Drummond and Barrow, Trans. Faraday SOC., 1951, 47, 1275. 21 Rittner, J. Chem. Physics, 1951, 19, 1030. 22 Aldrich, J. Appl. Physics, 195 1 , 22, 1 168. 6 Adler, J. Appl. Physics, 1949, 20, 1125. man and Hall, 1953). Inc., New York, 1951), appendix A. London, 1950).