24 GASEOUS IONS A N D THEIR REACTIONS GASEOUS IONS AND THEIR REACTIONS BY H. S . W. MASSEY Department of Physics, University College, London Received 25th Januury, 1952 The first part is concerned with the nature of gaseous ions. Information available from experiments on the formation of clusters by alkali metal ions is discussed. Clusters are formed not only with polar molecules but also rare gas atoms. The recent work on the molecular ions of the rare gases is also described. Some special features of negative atomic and molecular ions are summarized and attention is drawn to the importance of ions existing in metastable states. The second part is concerned with the rates of reactions in which ions are involved. These are classified under five headings : reactions leading to production of positive ions, formation of negative ions, change in the nature of the ions, detachment of electrons from negative ions and recombination. The different processes which can occur in these various categories are listed and some indication of the factors which determine their rates is given. The behaviour of ions in a condensed medium is very complicated and it is natural to turn towards gaseous ions in the hope that the phenomena concerned will be so much simpler that a start may be made in understanding them.This is only partly true for even the behaviour of ions in gases is often unexpectedly complicated as will be shown below. In this paper it will only be possible to give a very cursory account of certain selected aspects of gaseous ionics.The first part will be concerned with the nature of ions in gases and the second with the rates of reactions in which ions are concerned.H . S . W. MASSEY 25 ion, positive or negative, does not remain long in its atomic form if it is moving in a gas at ordinary pressures which has not been very specially purified. This is mainly because the charge on the ion leads to a considerable attraction between the ion and a polar molecule such as a water molecule, which is normally present in appreciable concentrations in an impure gas. The failure to realize the im- portance of cluster formation has vitiated many experiments designed to in- vestigate the properties of atomic ions. In the years just before the war some progress was made towards the establishment of quantitative methods of studying cluster formation by positive ions and post-war developments have shown that atomic ions may even combine readily with atoms, usually regarded as chemically inert, to form quite stable molecular ions.We shall begin by summarizing the information which has been obtained about the formation of complex positive ions. 1.1. Polar cluster formation by alkali metal ions.-One of the most effective ways of studying the nature of a gaseous ion is by measurement of its mobility in the gas concerned. A technique for carrying out such measurements under carefully controlled conditions of gas purity has been developed by Tyndall and Powell.1 By taking very special precautions they were able to measure the mobilities of the alkali metal ions in rare gases of such purity that no cluster formation occurred during the passage of the ions through the experimental chamber.Munson and Tyndall2 were then able to investigate the effect on the mobility of the addition of small but measurable quantities of water vapour to the rare gas. The mobility was found to be very much reduced by an amount which was independent of the concentration of water vapour down to very low concentrations (to partial pressures as low as 4 x 10-4 mm). Thus the mobilities of Li+, Na+, Kf, Rb+ and Csf ions in pure helium are 25-6, 24.2, 22.9, 21-4 and 19.6 cm?/V sec respectively whereas in helium containing a small amount of water the corresponding values are 11.70, 11.1 5, 11.85, 12.8, and 13.4 crn?/V sec. Similar results are obtained for the other rare gases. As the reduc- tion is independent of the water vapour concentration it follows that the size of the cluster is also independent of this concentration.It is possible by using Langevin’s theory 3 of the mobility of the ions to place an upper limit to the masses of the clustered ions and hence to the number of clustered molecules. This limit comes out to be about 6 for LiT, Na+ and K-+ ions. If an estimate can be made of the effective radius of a cluster the number of attached molecules can be determined more definitely. In this way it is found that the number of attached molecules is about 4 for Li+ and this is in agreement with predictions made by Bernal and Fowler 4 using their theory of the structure of liquid water. On the other hand it seems quite certain that Csf ions attach several molecules whereas according to.Berna1 and Fowler, they should not.A remarkable feature of the results is the rapidity of the association reaction. There is no evidence in these experiments of the presence of any ions intermediate between the unclustered and fully clustered varieties. The only reasonable ex- planation of this is that the rate determining process is the first attachment. Once this has occurred the full cluster builds up very rapidly. This is consistent with the requirement that the first attachment can only take place in a three-body collision. When the frequency of such collisions is examined it is seen, however, that even the first attachment takes place very much more rapidly than would be expected.Thus the estimated probability of an ion making a three-body collision while passing through the experimental chamber is only about 2 x 10-2 when there is 1 % water present. Nevertheless observable cluster formation is found in xenon when there is only 0.005 % of water present. The reason for the initial attachment taking place so much more rapidly than anticipated is still not clear and remains an important subject for further investigation. 1. THE NATURE OF GASEOUS IONS.-It has long been known that an atomic The reduced mobility must clearly be due to cluster formation.26 GASEOUS IONS AND THEIR REACTIONS 1.2. Association of alkali metal ions with inert gas atoms.-In 1939 Munson and Hoselitz,s who were studying the mobility of Lit ions in xenon, found evidence for the existence of ions with smaller mobility than the atomic ions which would not be eliminated even with the most careful purification of the xenon.This suggested that the heavier ion might be a molecular ion of the type LiXef. To investigate the matter further the mobility of Lif ions in helium at liquid hydrogen temperature was measured. In this case polar impurities must certainly have been frozen out and yet again it was found that an ion of smaller mobility was present. This could only have been LiHe+. From the proportion of clustered ions, their mobility and its variation with temperature it was possible to estimate the number of atoms attached in a cluster and also the dissociation energy. It was found that at least one and probably two atoms of Kr and Xe may attach to Li+ ions at room temperatures, the dissociation energy of the cluster being about 0.3 eV for Kr and 0.4 eV for Xe.At room temperature there is very little attachment of He atoms but at least one such atom is attached at liquid hydrogen temperatures, the dissociation energy being about 0.07 eV. This is rather smaller than that calculated by Meyerott 8 using quantum theory. 1.3. Molecular ions of the rare gases.-The existence of stable He2+ molecules has been known for some time and it was further known from the intensity of emission of helium band spectra that there must be a considerable concentration of such ions in the positive column of a glow discharge in helium. Despite this it was not considered at all likely that if positive ions were withdrawn from such a source they would be mainly He2+ and not He+.Thus Tyndall and Powell6 used a helium discharge as a source of the He+ ions for their experiments on the mobility of these ions in their helium. They obtained the value 20 cm2/V sec for this mobility. A little later Massey and Mohr 7 calculated the mobility using the quantum theory of collisions and allowing for the resonant charge transfer process He-+ + He 3 He + He+. (1.1) Their result, 11 cm2/V sec, was much smaller than the observed value. In 1946 Meyerott 8 suggested that the observed value might actually be that for Hezf and this has since been confirmed by Hornbeck’s recent measurements.9 He finds a mobility of 10.8 cm2/V sec for He+ and 19 cm2/V sec for He2+. The recent history of this matter is even more remarkable.In 1949 Biondi and Brown 10 applied a new microwave technique to investigate the rate of loss of electrons in a helium afterglow. At low pressures (< 20 mm Hg) the main loss is due to diffusion and from the measurements the mobility of the positive ions could be determined. It was found to be 12 cm2/V sec which we now know indicates that the ions were He+. At higher pressures (> 20 mm Hg) recombina- tion becomes the most important process of electron loss. Under these conditions Biondi and Brown measured the recombination coefficient for the electrons and found the large value 2 x 10-8 cm3/sec. To explain this large coefficient Bates 11 suggested that the recombination process is one of dissociative recombination to He2+, viz.(1 .2) He2-t + e -+ He’ + He” in which the energy released by the recombination is used in dissociating the mole- cule. This explanation has been confirmed by a remarkable experiment suggested by Holstein and carried out by Brown.12 The recombination coefficient in helium afterglow containing a small amount of argon was observed and found to be too small for measurement whereas in pure helium it was at least 104 times larger. Measurement of the mobility of the ions in the mixed helium-argon afterglow showed that they were A+ and the low recombination coefficient can be ascribedH. S . W. MASSEY 27 to the absence of molecular ions. is due to reactions of the kind The large proportion of ions present as A+ (1.3) where He’ denotes a metastable or other excited helium atom.It appears that under the low pressure conditions in Biondi and Brown’s first experiments the proportion of He2+ is small but it builds up rapidly as the pressure increases. This would be expected as the He2+ ions must be formed by some secondary process the probability of which will increase with the pressure. Bates 11 made an estimate of the rate of: production of He2f ions by three-body collisions : He‘ + A +He + A+ + e, He+ 4- He + He --f He2+ + He, and found it to be of the correct order of magnitude to explain Biondi and Brown’s results. The absence of molecular ions in the helium-argon mixture experiments suggests that HeA+ molecules are either unstable or very weakly bound. On the other hand studies of recombination and diffusion of ions in neon and argon 13 show that Ne2+ and A2+ ions are quite stable and play a vital role in determining the rate of recombination just as in helium.The much greater stability of the homonuclear molecular ions is understand- able in terms of the quantum mechanics. The resonance degeneracy due to the identity of the HeHe+ and He+He, for example, increases the strength of the bond in the molecule. 1.4. Analysis of ionic constitution in a plasma.-In view of the somewhat un- expected nature of the positive ions formed in simple gases it is important to have available a convenient technique for determining the ionic constitution of a plasma. Boyd 14 has developed a velocity analyzer for this purpose which operates on the same principle as the linear accelerator.It has the great advantage of being a very compact instrument so that it may be inserted in a discharge plasma without appreciably disturbing the discharge and can be used to explore the variation in ionic constitution at different points in the plasma. With this instrument Boyd 15 was able to show that He2+ ions are the most abundant species in a glow discharge in helium even at quite a low pressure (0-006 mm Hg, with 100 mA discharge current). A large range of possibilities await the use of this instrument for the analysis of discharge plasmas. 1.5. Negative ions.-l.5.1. Atomic ions.-Although all elements possess stable positive atomic ions this is by no means true for negative atomic ions. Thus no rare gases form negative ions nor does nitrogen. The most stable nega- tive atomic ions are those of the halogen atoms.Thus the electron affinity of fluorine is 4.13 eV which is actually greater than the ionization energy of caesium. The electron affinities of other important atoms are H (0.747 eV), 0 (2.2), C1 (3.1), Br (3.6) and l(3-2). Another important aspect of negative ions, as distinct from neutral atoms and positive ions, is that the number of stable excited states of negative ions is very limited. It seems that 0-- possesses one stable excited state with very small binding energy but H- does not.16 Hasted 17 has recently produced evidence derived from a study of the rates of detachment of electrons from negative ions on collision with rare gas atoms, that not only 0- but also F- and C1- possess one stable excited state of low binding energy. This supports the conclusions arrived at by Bates 18 for 0- and F- from an empirical study based on extrapolation of the properties of neutral atoms and positive ions.In the gaseous phase no doubly charged negative ions such as 0 2 - are stable. Thus the energy of 0-- is about 6.5 eV greater than that of 0-. It may seem re- markable that doubly charged negative ions are certainly stable in electrolytes. The reason for this is cluster formation with polar solvent molecules. These molecules enclose the ion in an electrical double layer. Owing to the presence of (1 -4)28 GASEOUS IONS AND THEIR REACTIONS this layer the energy required to remove an electron from the ion is greater than it would otherwise be. This means that the electron affinity is effectively increased and this increase is large enough to make clustered 0-- ions quite stable in an aqueous solution.It follows also that the electron affinity of an atom such as C1 is much greater in solution than in the gaseous phase. Negative ions naturally form clusters when present in a gas containing a polar impurity just as do positive ions. Just as in electrolytes the presence of the cluster tends to increase the stability of the ion. 1.5.2. Molecular negative ions. 19-The diatomic molecules of most of the elements which form stable negative atomic ions, also form stable negative ions. Thus Fz-, C12-, Br2-, 12- and 0 2 - are certainly stable. In this connection it is of interest to note that the alkali superoxides such as KO2 are polar compounds K+02-.The electron affinity of 0 2 has been deduced 20 as 0-7 eV from a study of the energy relations in cyclic processes involving these superoxides. Although H2- is stable as a molecule it is unstable towards the dissociation into H2 and an electron. H2 has a negative electron affinity. The resonance degeneracy in homonuclear diatomic negative ions is a stabiliz- ing factor as with positive ions but it is not sufficiently effective to render stable such ions as Hez-. Certain molecules such as OH which are isoelectronic with halogen atoms form quite stable negative ions. 1.6, Ions in metastable states.-It is important to remember that many ions possess low lying metastable excited states of quite long lifetime. As ions are likely to be formed in these excited states with quite high probability they may play an important part in determining the rates of reactions in which the ions are involved.In the same way, for negative ions which possess a stable excited state this state is metastable and excited ions may persist for times greater than that spent by the ion in an experi- mental apparatus. A different kind of ionic metastability has been observed by Hippel and Condon 21 in the course of mass spectrograph studies of the products of dissoci- ation of certain hydrocarbon molecules by electron impact. Certain ions such as C4H10+ and C3H5+ break up while passing through the spectrograph showing that they are only metastable towards dissociation. Effects of this sort would be expected for complex ions as it is necessary that the surplus energy should con- centrate on a particular degree of freedom before dissociation can occur.As the energy may be unduly dispersed among many degrees of freedom owing to the complexity of the system, the time before chance leads to a sufficient concentration in the dissociation mode may be quite long. Thus the electron affinity of OH is 2.1 eV. Some examples are given for positive ions in table I. TABLE 1 .-METASTABLE STATES OF CERTAIN POSITlVE IONS ion metastable excitation life-times states energy (eV) (set) - 0' 2D 3.3 *P 5.0 0.2 N+ IS 4.1 0.9 ID 1.9 300.0 2. REACTIONS INVOLVING IoNs.-We may classify the reactions which can occur in which ions are involved under the following headings : (a) reactions leading to production of positive ions, (b) reactions leading to formation of negative ions, ( c ) reactions leading to change in the nature of the ions, ( d ) reactions leading to detachment of electrons from negative ions, (e) recombination processes.H .S . W. MASSEY 29 Under these headings a great number of processes are included and it will be quite impossible to do much more than list the most important of them and give some guide as to the factors which determine their rates. In most instances it will be convenient to specify the rate in terms of an effective cross-section Q such that the chance of a collision leading to the reaction concerned in which one of the reactant atoms or molecules travels a small distance d through a gas containing N of the other reactant molecules CM-3 is Ned.2.1 Reactions leading to production of positive ions.-Typical reactions of this kind are : A + e --f A+ + e + c ( a l ) ionization by electron impact (02) polar dissociation (a3) photoionization (a4) ionization by positive ion impact (a5) ionization by neutral atom impact (a6) ionization by metastable or excited atoms (a7) associative ionization. AB f c --f A -t B- 4- D A + Lv --f A- 1- c A + B --f A+ -I- Bf t e A f B --f A+ 4- B -l- e A + B’ --f A ‘ + B 4- e A $- B’+AB+ + e Ionization by electron impact is an important process. The cross section rises from zero for electrons with energies EO just sufficient to produce ionization to a maximum of the order of the gas kinetic cross-section of the atom at an energy between 2 and 4Eo after which it falls off gradually. In general the velocity variation of the cross section is similar to that for ( a l ) but the maximum is of the order 10-3 to 10-4 times as large. It has been observed in 0 2 , NO, CO and Br2.22 The size and frequency variation of the photo-ionization cross-section varies from atom to atom in a rather irregular way.For many atoms such as 0 and A it may be of the order 10-17 cm2 for frequencies near the threshold 23 whereas for Na and K 24 it is several orders of magnitude smaller. Processes (a4) and (a5) both involve ionization arising from transfer of energy from relative translation of two systems of atomic dimensions to electronic excita- tion energy. In such cases the cross-section is very small if the relative velocity z’ of the colliding systems is small compared with the orbital velocity u of the electrons concerned in the transition. This is because, under these circumstances the collision takes place so gradually that it is effectively adiabatic.When ZJ > u the cross-section is very similar to that for ionization by electrons of the same velocity. It follows that, unless very energetic ions and atoms are present the contribution to the ionization arising from processes (a4) and (as) is negligible. Process (a6) is distinguished from (a4) and (a5) in that the energy necessary for ionization is not provided from that of relative translation but from the excitation energy of one of the colliding systems. The factors which exclude (a4) and (a5) as important sources of ionization do not apply and the cross-section for (a6) may be as large as gas kinetic or even greater.The process (1.3) is an important example. It is of course necessary that the excitation energy of B exceed the ionization energy of A. Otherwise some energy must be supplied from relative translation and the same limitation would apply as to (a4) and (a5). Process (a7) is a variant of (a6) in which the atomic products combine to form a molecular ion. If the process is exothermic the size of the cross-section does not depend markedly on the relative velocity v of the colliding systems but it is sensitive to the relative positions of the potential energy curves for the molecules AB’ and AB+. It can be quite large but it is difficult to predict whether in any particular case it will be large or small.An example is provided by the production of He2’ ions by the process inverse to (1.2). The inverse process to (a7) is one of the most important sources of electron recombination. The process (a2) is more important as a source of negative ions.30 GASEOUS IONS A N D T H E I R REAC'TIONS 2.2. Reactions leading to formation of negative ions.-Typical reactions of this kind are : A -1- c -+ A- -j- hv AB -t ~9 --f A -1- B' AB + e -+ A+ + B- -1 c (h 1 ) radiative attachment (h2) d issocia tive at tachnien t (03) polar dissociation A -i- B -f- c --f A- -j- B A .!. c + c -+A- -t e } (65) three-body attachment. These processes are distinguished by the way in which the energy released on attachment is disposed of. The cross-section for this process is always very small, of order 10- 22 cm*, and is rarely important except under conditions of very low pressurc, (h3) has already been considered as it is identical with (a2).The cross-section for (62) behaves quite differently. The process is essentially a resonance one in which the electron energy must be nearly equal to the energy difference between the ground level of AB and that which corresponds to a " vertical " transition to a potential energy curve of AB-. The cross-section has a sharp maximum of order 10-19 to 10-20 cm2 at a particular electron energy and is negligible for energies greater or smaller than this by a few electron volts. It has been observed with 0 2 , CO, NO, 12 and Br2 and other molecules.2~ In (64) the surplus energy is first transferred to excite vibration of the AB- molecule.The vibrationally excited molecule will dissociate by the reverse pro- cess to that which leads to its formation unless the excitation energy is further transferred either to a second molecule C on collision or is radiated. The possi- bility of a process of this kind depends on a coincidental intersection of a potential energy curve of AB- with that of AB at a point near the normal separation of the atoms A, B in the neutral molecule. It seems likely that production of 0 2 - ions from thermal electrons in 0 2 occurs in this way 26 but some doubt has recently been thrown on the validity of these results.27 In (65) the surplus energy is taken away by a third body, eithcr a neutral atom or an electron. These processes occur at rates greater than that of radiation attach- ment only if the pressure exceeds one atmosphere or the electron concentration is greater than 1018 cm3.2.3. Reactions leading to changes in tkc nature (1-f the ions.-Ty pica1 reactions In (61) it is emitted as radiation. In (b2) and (63) the surpliis energy is used in dissociating a molecule. charge transfer dissociation by electron i rnpac t dissociation by molecular impact three-body association cluster formation. The charge transfer process ( ~ 1 ) is similar to (a4) and (a5) in that it involves exchange of energy between relative translation and electronic excitation. The process is nearly adiabatic when the velocity of relative motion is much less than aAE/h, where AE is the magnitude of the energy transferred from or to relative translation, h is Planck's constant and a is a length of the order of gas kinetic diameters.The cross-section rises to a flat maximum at a velocity comparableH . S . W. MASSEY 31 with aAE/h and then falls off rather more rapidly than for ionization collisions such as (a4) and (05). In general the most probable charge transfer processes, when the ion energies do not exceed a few eV, will be those for which AE is smallest. It is important in reckoning AE for a particular process to remember that the initial ions A+ as well as the final atom A and ion B+ may be in excited states (see 1.6). As an indication of orders of magnitude the cross-section for charge transfer between two atoms whose masses are of order 10 times that of a hydrogen atom will be negligible if the energy of relative motion is much less than 500AE2 eV, where AEis measured in eV.Dissociation by electron impact (c2) is a process closely similar to ionization by electron impact ( a l ) . In each case part of the kinetic energy of the electron is transferred to the atom or molecule to excite it to an upper state. If this state of AB+ is an unstable one dissociation follows. The cross-section will behave in much the same way as for the process (01). Dissociation by atom impact (c3) will be restricted in the same way as processes (a4), (a5) and (cl) if it proceeds via electronic excitation. It is possible, however, to cause dissociation by transfer of energy to molecular vibration. Whether this will give rise to much larger cross-sections is still very uncertain.Three-body association as in (c4) is exactly similar to the corresponding process with neutral atoms and molecules which plays such an important role in chemical reactions in the gas phase. For information about such processes the reader must refer to some such book as The Theory of Rate Processes by Eyring and Kimball. Once a sufficiently complex ion has been built up further association may take place without direct intervention of a third body. This is because the activated complex which is formed has a long lifetime and may be stabilized before it dissoci- ates even if the collision frequency is very small. 2.4. Reactions leading to detachnient of electrons from negative ions.-Typical reactions of this kind are : A- + hv+A f e A- f B’ --f A f B + e A- 4- e -+ A + e + e A- f B -+ A + e -k B A + B + A B + e (dS) associative detachment.(dl) photodetachment (d2) detachment by excited atoms (d3) detachment by electron impact (d4) detachment by atom impact Since these processes involve the removal of a bound electron most of them are analogous to processes which lead to positive ion production. Thus (dl), (d2), (d3) and (d4) are respectively analogous to (a3), b6), (01) and (d), and the remarks made in $ 2.1 about the latter are applicable to the corresponding negative ion reactions. It is important to remember, however, that electron affini- ties of atoms are usually much smaller than ionization energies so that a process such as ( d l ) will occur with quanta of much lower frequency than will (a3). Also the cross-section for (d4) will become negligible only for energies of relative motion much smaller than for (a5).No analogue of (dS) appears in 0 2.1. This is because the dissociation energy of a molecule AB is often comparable with or larger than the electron affinity of A or B while that of a molecule ABf is usually much smaller than the ionization energy of A or B. The rate of a process such as (dS) is likely to depend on the relative position of the potential energy curves of the AB- and AB molecules and at present there is little information about even the order of magnitude of the cross-section for any particular case.32 GASEOUS IONS AND THEIR REACTIONS 2.5. Recombination reactions.-Typical reactions of this kind are : A+ + e -+A + hv ABf + e -+A + B A+ + e + B -+A + B (el) radiative eIectron recombination (e2) dissociative recombination (e3) three-body electron recombination (4 mutual neutralization A-+B+->AB+liv (e4) radiative ionic recombination A- + B+ -+ A' + B" A- + B+ + C + A + B + C 1 (e6) three-body ionic recombination.+ A B + C I It is usual to give the rate of recombination in terms of the recombination co- efficient a rather than a cross-section Q r . If 1; is the mean relative velocity of the colliding ions IX = P e r . The first three reactions involve recombination between electrons and ions and as they involve electron capture they have analogues among the processes leading to negative ion formation. Thus (el), (e2) and (el) are respectively analogous to (bl), (b2) and (b5), but the presence of the Coulomb force between the interacting ions and electrons leads to some modification of the considerations applying to the negative ion formation reactions. The coefficient for radiative recombination is of order 10-12 cm3 sec-1 for electrons and ions at ordinary temperatures.Although the great number of states into which the electron may be captured raises the cross-section above that for radiative attachment by a factor of order 100, radiative recombination is still a very slow process.28 The importance of dissociative recombination in deter- mining the rate of loss of electrons in afterglows has already been referred to in S 1.3. Observed recombination coefficients in these cases show that the dissoci- ative recombination proceeds between lo4 and 105 times faster than radiative recombination.Three-body electronic recombination is only important at very high pressures owing to the difficulty of transferring energy from an electron to an atom or molecule. To give a coefficient comparable with that for dissociative recom- bination the pressure would need to be greater than 1000 atm. The three reactions (e4), (e5) and (e6) all involve recombination of positive ions with negative ions instead of electrons. (e4) may be dismissed as unim- portant in almost all circumstances. Mutual neutralization (e5) has been discussed theoretically by Bates and Massey29 who show that the coefficient for ions of thermal energy probably varies widely with the states of excitation of the resultant neutral atoms or mole- cules, but may be quite large, of order 10-8 cm3 sec-1.Three-body ionic recombination (e6) is much more important than for the corresponding process with electrons. It has been discussed theoretically in a classical paper by Thomson.30 The coefficient for simple ions at ordinary tem- peratures increases at a rate which is initially proportional to the pressure but saturates at a pressure of about 1000 mm Hg at a value of order 10-6 mm. At greater pressures the coefficient decreases inversely at the pressure. This decrease is not allowed for in Thomson's theory but was explained by Langevin.31 Experi- ments by Sayers32 and by Marshall, Luhr and Gardner33 have confirmed the validity of the theory. 3. CONCLUDING REMARKS.-AlthOUgh a good start has been made towards understanding the factors which determine the rates of reactions involving ions and estimates of varying accuracy may be made about the rates in particular cases, much still remains to be done before reliable values can be given for all the reactions which may be important in any particular set of phenomenaH .S . W. MASSEY 33 General reference : Massey and Burhop, Electronic and Ioiric Impact Phenomena (Oxford, 1952). 1 Tyndall and Powell, see Tyndall, Mobility ofPositive IOJZS in Gases (Cambridge, 1938). 2 Munson and Tyndall, Proc. Roy. SOC. A , 1939, 172,28. 3 Langevin, Ann. Chem. Phys., 1903, 28, 289. 4 Bernal and Fowler, J . Chem. Physics, 1933, 1, 515. 5 Munson and Hoselitz, Proc. Roy. SOC. A , 1939, 172, 43. 6 Tyndall and Powell, Proc. Roy. SOC. A , 1931, 134, 125. 7 Massey and Mohr, Proc. Roy. SOC. A, 1934, 144, 188. 8 Meyerott, Physic. Rev., 1946, 70, 671. 5, Hornbeck, Physic. Rev., 1951, 84, 615. 10 Biondi and Brown, Physic. Rev., 1949, 75, 1700. 11 Bates, Physic. Rev., 1950, 77, 718 and 78, 492. 12 Biondi, Physic. Rev., 1951, 83, 1078. 13 Biondi and Brown, Physic. Rev., 1949, 76, 1697 ; Redfield and Holt, Physic. Rev., 14 Boyd, Nature, 1950, 165, 142. 15 Boyd, Proc. Physic. SOC. A , 1950, 63, 543. 16 Massey, Negative Ions (Cambridge, 1950), 2nd ed., p. 58. 17 Hasted, Proc. Roy. SOC. A (in course of publication). 18 Bates, Proc. Roy. Irish Acad., 1947, 51, 151. 19 Massey, Negative Ions (cambridge, 1950), 2nd ed., chap. 2. 20 Kazarnovski, Cornpt. rend. U.R.S.S., 1948, 59, 67 ; Uri and Evans, Trans. Faraday 21 Hippel and Condon, Physic. Rev., 1945, 68, 54; Hippel, Physic. Rev., 1947,71, 594. 22 Massey, Negative Ions (Cambridge, 1950), 2nd ed., p. 46. 23 Seaton, Proc. Roy. Sac. A , 1951, 208,408. 24 Ditchburn and Jutsum, Nature, 1950, 165, 723 ; Ditchburn, Tunstead and Yates. 25 Massey, Negative Ions (Cambridge, 1950), 2nd edn., p. 58. 26 Bloch and Bradbury, Physic. Rev., 1935,48, 689. 27 Biondi, Physic. Rev., 1951, 84, 1072. 28 Bates, Buckingharn, Massey and Unwin, Proc. Roy. SOC. A , 1939, 170, 322. 29 Bates and Massey, Phil. Trans., 1943, 239, 269. 30 Thomson, Phil. Mag., 1924, 47, 337. 31 Langevin, Ann. Chem. Phys., 1903, 28, 289, 433. 32 Sayers, Proc. Roy. SOC. A , 1938, 169, 83. 33 Marshall, Luhr and Gardner, Physic. Rev., 1938, 33, 75. 1951, 82, 874; Hornbeck, Physic. Rev., 1951, 84, 615. SOC., 1949, 45, 217. Proc. Roy. SOC. A , 1943, 181, 386.