A Determination of Free Energy Changes from a Gas Phase Study of Equilibria

O equilíbrio de reacões íon-molécula de agregação (“clus ter ing”) en tre íons (C2H2)m e moléculas N2 em fase gasosa foi estudado por técnica de espectrometria de massa de alta pressão, em misturas N2-C2H2 irradiadas por partículas α. Valores de energia livre de agregação, ∆Gn-1, n, foram determinados para reações (C2H2)m(n-1)N2 + N2 (C2H2)m+nN2, para diferentes valores de m e n. Para m=2, i.e., para (C2H2)2, os valores encontrados para ∆Gn-1, n, quando T = 129 K, foram 0.87± 0.20 kcal/mol para (n-1, n) = (2,3) e 0.88± 0.20 kcal/mol para (n-1, n) = (3,4). Para m = 3 (“íon-nucleador” (C2H2)3), as variações de energia livre encontradas foram 0.91± 0.30 kcal/mol para (n-1, n) = (2,3); 0.73± 0.30 kcal/mol para (n-1,) = (3,4); 0.65± 0.30 kcal/mol para (n-1 ,n) = (4,5); e 0.58± 0.30 para (n-1, n) = (5,6).


In tro duc tion
The at mo sphere of Ti tan is mainly com posed 1,2 of nitro gen, with a few per cent of meth ane, and acet y lene as one of its mi nor com po nents.In pre vi ous stud ies 3,4 we re ported the thermochemical data re gard ing the clus ter ing of N 2 /CH 4 on dif fer ent core ions of in ter est in un der stand ing Ti tan's chem is try.Pure N 2 and CH 4 , as well as N 2 -CH 4 mix tures were used to ob tain the data.In the pres ent work, we have car ried out stud ies on N 2 -C 2 H 2 mix tures at high pres sures (1-20 Torr).As in pre vi ous stud ies, the main purpose was to ob tain thermochemical data on clus ter ing ion-molecule re ac tions per ti nent to the ion chem is try of Titan's at mo sphere.In for ma tion of this type is fun da men tal to an un der stand ing of the com plex chem is try as so ci ated with plan e tary at mo spheres for the fol low ing rea sons, among oth ers: (1) ions rep re sent ef fi cient nu cle at ing agents, re sult ing in the for ma tion of large clus ter buildup and even tu ally drop let for ma tion; (2) clus ter ing mod i fies the chem is try as so ci ated with ion neu tral iza tion be cause the lig ands can act both as heat "sinks" for en ergy re leased in the neu tral iza tion as well as near est-neighbor part ners in chem i cal re ac tions; (3) plan e tary at mo spheres con tain both po lar and non-polar com po nents, which com pete both as lig ands and as can di dates for the core ions within clus ters, there fore dic tat ing the ter mi nal ion chem is try.This over all com pe ti tion is ul ti mately con trolled by the thermochemistry and ki net ics as so ci ated with each in divid ual clus ter ing and as so ci a tion re ac tion ex pected to occur in any given at mo sphere be cause of its com po si tion, par ti cle den sity, tem per a ture, pro file, etc.
The clus ter ing of N 2 on the clus ter ions (C 2 H 2 ) m + was in ves ti gated.Re ac tion-free en ergy changes, ∆G 0 n-1, n corre spond ing to: were de ter mined at one tem per a ture, with N 2 act ing as a third-body.Very lit tle data re gard ing clus ter ing with acet y lene ions have been re ported to date.The for ma tion of acet y lene clus ter ions, such as An ef fi cient charge trans fer mech a nism from N i + ( i = 1-2) ions as sures 5,6 the for ma tion of C 2 H 2 + ions.This can be un der stood on the ba sis of the fol low ing con sid er ations: • In mass spec tra ob tained in ni tro gen and in acet y lene, re spec tively, with high en ergy al pha-particles, the pri mary ions N 2 + and C 2 H 2 + are dom i nant (ap prox i mately 80% in each case) 7 .As the frac tion of acet y lene in the N 2 -C 2 H 2 mix ture is ≤ 2% in the pres ent ex per i ment, the ex pected dom i nant pri mary ion is N 2 + , fol lowed by N + ; • The first ion iza tion en ergy (IE) of C 2 H 2 , to form (C 2 H 2 ) + , is only 11.394 eV 8,9  ).• Finally, it is eas ily ver i fied that un der the pres ent exper i men tal con di tions, the for ma tion of N 3 + and N 4 + by the ter nary re ac tions: is ex pected to be in sig nif i cant in com par i son to the bi molec u lar trans fer charge from N 2 + and N + to C 2H2.The ex -pected pri mary ion in the α-par ti cle radiolysis of ni tro gen con tain ing trace amounts of acet y lene, such as in the present ex per i ment, is thus es sen tially C 2H2 + , which fol lows the re ac tion: This is con sis tent with the ob ser va tion of Lind and Bard well 10 , who have shown that ir ra di a tion of N 2 -C 2 H 2 mix tures by α-par ti cles from ra don does not lead to the syn the sis of ni tro gen com pounds, the fi nal prod uct be ing the same as that which is formed in the ab sence of ni tro gen.Nev er the less, they ob served that the en ergy ab sorbed by the ni tro gen con trib uted to the poly mer iza tion of C 2H2 to form the solid cuprene, [(C 2H2)m].Once formed, C 2H2 + can re act with C 2H2 to give 5 C 4H4 + *, an ex cited com plex, which in turn will be ei ther sta bi lized by col li sion with a third body (N 2 ) at higher pres sures, or dis so ci ated into the con den sa tion ions C 4H3 + and C 4H2 + : The for ma tion of C 4H4 + (or (C 2H2)2 + ) via chan nel (2) can be rep re sented by the three-body ion-molecule as so ci ation re ac tion where k stands for the ef fec tive re ac tion con stant.These ions can then un dergo sub se quent clus ter ing reac tions with C 2H2 or N 2. In the pres ent study only re ac tions cor re spond ing to equi lib rium (1) were in ves ti gated.
Fig ure 1.The sche matic of the ap pa ra tus: C-cryostat; Ca-calorific con duc tor sur rounded by heat ers for tem per a ture reg u la tion; E-extraction hole; G-glass; Gi-gas in let; L 1-liq uid N 2 in let; L 2-liq uid N2 or He in let; P-polarization elec trode for ex trac tion hole; P 1, P2-pumps; Q 1-quadrupole mass fil ter for ion anal y sis; Q 2 quadrupole mass fil ter for neu tral gas anal y sis; RC-reaction cham ber; IC-ionization cham ber; S-alpha sources; T-temperature probe.

Ex per i men tal
The mea sure ments were per formed with the High-Pressure Mass Spec trom e ter at the Université de Paris-Sud/LPGP, where ion iza tion is ini ti ated by alpha-particle bom bard ment.The ex per i men tal sys tem is the same as pre vi ously de scribed 4,11 .Fig ure 1 il lus trates the over all ge om e try of the mass spec trom e ter sam pling system.Ions are gen er ated in a field-free stain less steel source, by 5.4 Mev α-par ti cles from three en closed 241 Am (  40 µCi cm -2 ) ra dio ac tive sources fixed on the source walls.Ions exit the source through a 50 µm di am e ter hole into a low pres sure ( P ≤ 10 -5 Torr) anal y sis cham ber.These ions are ac cel er ated and fo cused by elec tro static lenses, mass an alyzed by a quadrupole mass fil ter, and de tected by a 17-dynode elec tron mul ti plier.The high est mass to charge ra tio (mass/z) value stud ied was 246.Since it is known 12 that the trans mis sion in a quadrupole de creases as the value of the ion mass in creases, cor rec tions were ap plied for varia tions in the mass spec trom e ter trans mis sion with re spect to the se lected mass.The neu tral gas is pumped by a 600 l/s cryo genic pump which main tains the pres sure in side the mass spec trom e ter at val ues less than 10 -5 Torr.The re action cham ber is pumped by a 140 l/s turbomolecular pump, yield ing a back ground pres sure on the or der of 10 -7 -10 -8 Torr.A sec ond quadrupole mass spec trom e ter, Q 2, downstream from the ion-extraction hole was used as a neu tral gas analyser, permiting con tin u ous mon i tor ing of the partial pres sures of the mi nor ity gases.In or der to re duce wa ter im pu ri ties, the gases flowed through a cold trap at 77 K before be ing in tro duced into the re ac tion cham ber.
The gases were sup plied by L'Air Liquide and were used as pur chased.A N 2 -C 2 H 2 (98:2) mix ture, which accord ing to the sup plier con tained < 3 ppm O 2 , < 2 ppm H2O, < 2 ppm CO, < 1 ppm CO 2, and 1 ppm PH 3, was used as the ini tial mix ture.Pure N 2 (< 0.1 ppm and < 1 ppm H 2O) was added to the N 2 -C 2 H 2 mix ture to change the con cen tration of acet y lene.Ni tro gen (N 2 ) was used both as the bath and the ligand gas, and acet y lene (C 2 H 2 ) was 0.05 to 2% of the to tal N 2-C 2H2 gas mix ture.Ex per i ments were performed un der a to tal pres sure rang ing from 5 to 50 Torr, and at tem per a ture val ues of 129, 132 and 273 ± 2 K.The tem per a ture was mea sured us ing a di ode, in serted di rectly in the re ac tion cham ber (see Fig. 1), close to the sam ple region, and cal i brated # at am bi ent and liq uid ni tro gen temper a tures.In this range, de vi a tion from lin ear ity can be con sid ered neg li gi ble, and so I∝V is as sumed.A com bi nation of tech ni cal dif fi cul ties, re lated to the si mul ta neous con trol of tem per a ture and mix ture com po si tion, pre vented us from ob tain ing enough data at dif fer ent tem per a tures to de ter mine enthalpy changes.Ion iza tion at the source results in rapid pri mary ion-neutral re ac tions that gen er ate C 2 H 2 + .Clus tering re ac tions be tween C 2 H 2 + , C 2 H 2 , and N 2 then take place, re sult ing in the equi lib rium (1).Un der the con di tions of the pres ent study, the clus ter ing neu trals (ligands) and the third body nec es sary for collisional sta bi li zation of the in ter me di ate com plex are the same (N 2 ).Equi lib rium con stants K n-1, n are cal cu lated as usual where [ I + .(n-1) L] and ( I + .nL ) cor re spond, re spec tively, to the mea sured ion in ten si ties of the re ac tant and prod uct ions of the stud ied equi lib rium (1), and P L is the pres sure of the ligand L in at mo spheres.Free en ergy changes ∆G 0 n-1, n , were ob tained from the ther mo dy namic re la tion ∆G 0 n-1, n = -RT ln K n-1, n , con nect ing the equi lib rium con stant K n-1, n and the free en ergy change ∆G 0 n-1, n ; R is the per fect gas con stant.Equi lib rium con di tions are dis cussed in Refs. 4 and 11.Fur ther more, as will be shown in the next sec tions, the equi lib rium con stants were ver i fied to be in de pend ent of the ligand (N 2) pres sure be tween 10 and 50 Torr, as well as of the C 2H2 par tial pres sure.
The es ti mated er rors as so ci ated with the equi lib rium con stant mea sure ments were 10-20% for m = 2, and 20-30% for m = 3.These er rors are mainly re lated to noise, which of ten ap peared dur ing the peak in ten sity mea surements at low tem per a tures (in gen eral be low 150 K), and for which no ex pla na tion could be found in our ex per i ment.As a con se quence, a rel a tively large dis per sion of the points was ob served in the equi lib rium con stant plots.Never the less, the un cer tain ties in ∆G 0 n-1, n are of ten re ported to be in the range of± 0.2-0.5 kcal/mol, and the pres ent re sults lie within this range.

Re sults
Fig ure 2 pres ents the mass spec tra of a N 2-C 2H2 mixture for P(C 2H2) = 3 mTorr and two dif fer ent ni tro gen pressures (5 and 30 Torr, re spec tively) at a tem per a ture of 132 K.At the lower N 2 pres sure, the most ob vi ous fea ture is the group ing of the mass pat tern into subpatterns which re peat them selves with a pe ri od ic ity of 26 mass units.We can reason ably as cribe these peaks to (C 2H2)m + ions, with m = 2 to 10 (the peak at m = 1, C 2H2 + , i.e. , cor re spond ing to mass/z = 26, was ob served only at higher tem per a tures, e.g. at 273 # Although the accuracy inferred from the calibration curve is higher than 2 K, the ability to state that the temperature in the source is defined within this value comes from our previous measurements, followed by a comparison with the results r eported by other authors (see "Comment on the Errors" at the end).However, as regards the free energy uncertainty, the errors associated with the equilibrium constants predominate over those of the temperature.K).At higher N 2 pres sures, the shift ing of these peaks to higher mass val ues is ob vi ous.Low in ten sity peak groups at in ter me di ary mass val ues also showed an in crease in their in ten si ties as the ni tro gen pres sure was in creased.A pro posed scheme show ing the for ma tion of [(C 2 H 2 ) m (N 2 ) n ] + clus ters from the pri mary ion C 2 H 2 + is given in Fig. 3, where we have also in cluded ex change reac tions of N 2 for C 2 H 2 .Given the greater well depth for C 2 H 2 as a ligand (see next para graph), this exo ther mic displace ment seems to be an es sen tial fea ture of the sche matic of the clus ter for ma tion, as ob served in other com pos ite clus ter sys tems 13,14 .
Al though (C 2 H 2 ) m + ions were clearly pre dom i nant at the lower N 2 pres sures, as shown in Fig. 2, at tempts to inves ti gate the equi lib rium un der the ex per i men tal con di tions used in our ex per i ment were not succesful.The ligand (C 2 H 2 ) pres sure in ves tigated ranged from 5 to ap prox i mately 260 mtorr.For P(N 2 ) = 10 Torr, it was ob served that at the low est C 2 H 2 pres sures (be tween 5 and 40 mTorr, ap prox i mately) the ra tio between the prod uct and the re ac tant ion in ten si ties, tended to in crease slightly with pres sure, but not di rectly pro por tional to pres sure as required un der equi lib rium con di tions ( I m+ 1 /I m = KP L ).Above 40 mTorr, the ra tio tended to ward a con stant value.The rea son for this is not clear.The re sults sug gest that at 132 K, lower C 2 H 2 pres sures might be one of the nec es sary con di tions to achieve equi lib rium for the above re ac tions.We also see that in both spec tra of Fig. 2, at 5 and 30 Torr, a se ries of clus ters start ing at mass/z = 66 (which pos si bly cor re sponds to [X(C 2 H 2 ) r (N 2 ) s ] + , X be ing a un known compound), prob a bly formed in the dis charge from im pu ri ties or from the gases un der study.Nev er the less, this se ries is out of the scope of the pres ent study.+ N 2. Equi lib rium con stants K 2 2,3 and K 2 3,4 vs. acet y lene pres sure, for P(N 2) = 10 and 20 Torr at T = 129 K.The equi lib rium con stant is given as K m n-1, n , where the su per script m stands for the num ber of acet y lene mol e cules in the re ac tant and in the prod uct ion.
Fig ure 4 shows the equi lib rium con stants K m n-1, n ( m = 2; n = 3-4) for re ac tion (1) ver sus the par tial pres sure of acet y lene (5-260 mTorr), for two dif fer ent val ues of the nitro gen pres sure (10 and 20 Torr).The val ues of K 2 n-1, n remain con stant as a func tion of the acet y lene pres sure over the en tire range stud ied, for both val ues of the ni tro gen pres sure.This re sult is con sis tent with the at tain ment of equi lib rium in the re ac tion cham ber.
The same checks were made for the K 3 n-1, n ( m = 3; n = 2-6) con stants, shown in Fig. 5. Ex cept for K 3 1,2 and K 3 5,6 , they can be con sid ered in de pend ent of the C 2 H 2 par tial pres sure within the pres sure range 5 to 400 mTorr, for a N 2 pres sure of 20 Torr.How ever, the re sults for K 3 5,6 sug gest a ten dency to wards a con stant value for acet y lene pres sures  The sig nals given cor re spond to the for ward re ac tions.higher than ap prox i mately 200 mTorr.We there fore assume the equi lib rium for pres sures above 200 mTorr.For prac ti cal rea sons, the study of the K 3 n-1, n de pend ence on the ligand pres sure N 2 (Fig. 6) was done at a con stant ra tio of P(C 2 H 2 )/ P(N 2 ) = 2 10 -2 (the avail able ini tial mix ture).In view of their ob served in de pend ence (again, only K 3 1,2 , not shown, is not found in equi lib rium con di tions) as a func tion of the C 2 H 2 con cen tra tion, this should not af fect our conclu sions re gard ing equi lib rium.Both sets of mea surements, vary ing ei ther N 2 or C 2 H 2 , show the same trend, i.e. , the K m n-1, n ( m = 3; n =3-6) are in de pend ent of the par tial pres sures of N 2 and C 2 H 2 within the ex per i men tal ac cu racy of ± 30-40% for the equi lib rium con stants.
The de ter mi na tions in ferred from the ex per i men tal results are sum ma rized in Ta ble 1, where the log of the equilib rium con stants for re ac tion (1), as well as the free en ergy changes for the cor re spond ing for ward re ac tions are shown.

Dis cus sion
McCrumb et al. 5 have in ves ti gated re ac tion (5).At 2.8 Torr and 300 K, the sta bi li za tion of C 4 H 4 + * (chan nel 2) was dom i nant, chan nels (3) and (4) be ing un im por tant in their ex per i ment.The for ma tion of (C 2 H 2 ) 2 + was also in ves tigated by Rakshit and Warneck 15 , us ing CO 2 as a third body.They also stud ied the for ma tion of the clus ters (C 2 H 2 ) 3 + and C 2 H 2 + .CO 2 , as well as the as so ci a tion of C 2 H 2 with C 4 H 2 + and C 4 H 3 + , also with CO 2 as a third body.The measured re ac tion con stants for all these clus ter ing re ac tions where C 2 H 2 was the ligand mol e cule were very high, whether in N 2 or CO 2 , and on the or der of 10 -26 -10 -27 cm 6 s -1 .How ever, for the clus ter ing of CO 2 with C 2 H 2 + , they found a much lower value for the cor re spond ing re action con stant, k ≤ 4 10 -30 cm 6 s -1 .In other words, the clus tering of C 2 H 2 with C 2 H 2 + leads to the for ma tion of (C 2 H 2 ) n + clus ters at least 10 4 times faster than the as so ci a tion of CO 2 with C 2 H 2 + .As a gen eral trend, it is ob served that N 2 displays a slower re ac tion con stant than CO 2 as re gards its clus ter ing on the same ion.More over N 2 is ob served to be less ef fi cient than CO 2 as a third body.For ex am ple, in the case of the for ma tion of (C 2 H 2 ) 2 + , the lit er a ture gives k = 1.6 10 -26 cm 6 s -1 and 0.6 10 -26 cm 6 s -1 for CO 2 and N 2 , respec tively 5,15 .This prob a bly re flects the lower num ber of de grees of free dom in N 2 16 .The rel a tive re ac tiv ity of the lig ands CO 2 , N 2 , C 2 H 2 is thus seen to in crease in the or der N 2 < CO 2 < C 2 H 2 .This is quite rea son able in terms of the ba sic ity of these lig ands, which is a func tion of their polarizability, α ( α(N 2 ) = 1.76 Å 3 , α(CO 2 ) = 2.59 Å 3 and α(C 2 H 2 ) = 3.33 Å 3 ).The greater sta bil ity of the C 2 H 2 .C 2 H 2 + com plex, rel a tive to C 2 H 2 .CO 2 and C 2 H 2 .N 2 also fol lows from this or der of ba sic ity, and is stressed by our fail ure to ob serve equi lib ria once the (C 2 H 2 ) m + complexes are formed.
There fore, it is plau si ble to ex pect that in or der to have re ac tion rates on the same or der as those lead ing to the forma tion of (C 2H2)m + clus ters, the par tial pres sure ra tio P(N 2)/ P(C 2H2) must be at least 10 4 .This is con sis tent with the spec tra shown in Fig. 2 for P(N 2)/ P(C 2H2) ~10 3 , where (C 2H2)m + clus ters are pre dom i nant; how ever, when the pres sure ra tio is in creased to 10 4 , [(C 2H2)m(N 2)n] + clus ters are clearly ob served.
It should be re mem bered that the spec tra shown in Fig. 2 were ob tained at a dif fer ent tem per a ture than that used by Rakshit (132 K in this work and 300 K for Rakshit with CO 2).The much lower tem per a ture in our work should favor clus ter ing re ac tions by in creas ing the cor re spond ing equi lib rium con stants.
Studies in volv ing com pos ite clus ters have been reported in the lit er a ture (see for ex., Refs.13 and 14).In these stud ies, the lig ands un der in ves ti ga tion were po lar (HCN, H 2O, NH 3, H 2S), thus in volv ing ligand-ligand bonds stron ger than those in the pres ent case where the ligands are non-polar.Ni tro gen and acet y lene clus ters are much more frag ile, rais ing the ques tions as to whether changes in the ni tro gen pres sure also af fect the acet y lene equi lib rium.Even though the es ti mated val ues of enthalpy changes are con sis tent with the ex pected numbers (see be low), we be lieve that fur ther in ves ti ga tion is needed in or der to clar ify this point.
The tem per a ture de pend ence of the equi lib rium constants was not in ves ti gated in the pres ent study, and so enthalpy changes, ∆H 0 n-1, n , could not be de ter mined.However, an es ti ma tion of ∆H 0 n-1, n can be made if we at trib ute the es ti mated val ues for the cor re spond ing en tropy changes, ∆S 0 n-1, n .If we es ti mate ∆S 0 n-1, n as -20± 3 cal/mol K, a range in which most of the val ues de ter mined for cluster ions of the X + (N 2 ) n -type fall 14,17,18 , then ∆H 0 n-1, n can be es ti mated from the ther mo dy namic re la tion ln K = ∆S 0 /R -∆H 0 /RT , which con nects the equi lib rium con stant K and the en tropy and enthalpy changes.This yields enthalpy changes in the range of -3.4 to -3.1 ± 0.4 kcal/mol, which are roughly the same as those found for other clus ter ing reac tions with ni tro gen for the same num ber of clus tered mol e cules.These es ti mates are merely spec u la tive and are to be used with cau tion.
To ex plain the pos si ble for ma tion of or ganic-nitrogen mol e cules in the at mo sphere of Ti tan, Ca pone et al. 19 pro -posed a mech a nism in volv ing ex change re ac tions be tween N 2 , CH 4 and C 2 H 2 in HCNH + .(L) n clus ters ( L = ligand).Later, HCNH + .(N 2 ) n , as well as C p H q + .(N 2 ) n and C p H q + .CH 4 for ma tion in the al pha-particle radiolysis of N 2 -CH 4 mix tures was ob served at Orsay by these authors 3,4 .Hiraoka and Kebarle 21 stud ied C p H q + .(CH 4 ) n = 1-4 .Ta ble 2 shows the es ti mated ∆G 0 val ues cor re spond ing to the for ma tion of these ions at 129 K (the same as in Ta ble 1).This tem per a ture is close to that of the re gion of max imum cos mic ray-activated chem is try in the at mo sphere of Ti tan, es ti mated 1,19 as 150-160 K.The com par i son of the sta bil i ties found for these clus ters and those of the acet ylene-nitrogen clus ters in ves ti gated in the pres ent study show that clus ters with the same num ber of clus tered mol ecules around the core ion pres ent com pa ra ble ∆G 0 .If present in the at mo sphere of Ti tan they could prob a bly all in ter act by ex change re ac tions, ul ti mately lead ing to the for ma tion of [(C 2 H 2 ) m (N 2 ) n ] + .

Com ments on the er rors
In de ter min ing the enthalpy and en tropy changes in some of our pre vi ous work, the tem per a ture ranges for the dif fer ent re ac tions stud ied were rel a tively small.This is a com mon fea ture among pre vi ous stud ies involv ing ion clus ter ing with N 2 re ported by sev eral lab ora to ries.In our ear lier stud ies on the O 2 + (N 2 ) n and NO + (N 2 ) n 11 , and HCNH + (N 2 ) n 3 clus ters, small ranges of T were also used.Later, good agree ment was obtained by Hiraoka and Nakajima 18 be tween their thermochemical data and our data for O 2 +(N 2 ) 2 ; good agree ment was also found be tween the the o ret i cal results ob tained by Ha and Nguyen 20 and our ex per i men -tal de ter mi na tions for ∆H 0 re gard ing HCNH + (N 2)n.How ever, the ab so lute val ues of our equi lib rium constants were much larger than those mea sured by Hiraoka and Nakajima, re sult ing in smaller val ues for ∆G 0 .This was par tic u larly true for the larger clus ters (n 1), where the ∆S 0 val ues did not lie within the expected range (20 ± 3 cal/mol.K), but rather were lower.Since then, how ever, in or der to avoid collisional induced dis so ci a tion when sam pling the frag ile clus ters, more pre cau tions have been taken 4 re gard ing the magni tude of the ra tio be tween the prod uct and re ac tant ions I + nL and I + ( n-1) L. The re sults re cently ob tained 4 for the clus ter ing of CH 5 + and C 2H5 + with CH 4 pro vide a ba sis for com par i son with the mea sure ments of K made by Hiraoka and Kebarle 21 .The equi lib rium con stants (and there fore of ∆G 0 ) for these as so ci a tion re ac tions are in very good agree ment.Fur ther more, the cor respond ing ∆S 0 val ues also are within the ex pected range men tioned above.

#
Since no protonation is involved in the formation of the clusters, we will not consider structural formula or charge localization, even though the first clustering step starts with the primary reactant ion C 2H2+; i.e. , C 2H2+.(C 2H2)m\_1 .(N2)n = [(C 2H2)m(N 2)n] + .

Fig ure 2 .
Fig ure 2. The mass spec tra (sig nal in ten sity S in ar bi trary units) of a N2-C 2H2 mix ture for P(C 2H2) = 3 mTorr and T = 132 K.The spec tra show the ef fect of ni tro gen pres sure vari a tion for P(N 2) = 5 and 30 Torr.Mixed clus ters with N 2 and C 2H2 lig ands are clearly more abundant at the higher ni tro gen pres sure.

Fig ure 3 .Fig ure 4 .
Fig ure 3. A sche matic show ing the for ma tion of [(C 2H2)m(N 2)n] + clus ters from the pri mary ion C 2H2 + in a N 2-C 2H2 mix ture ( A = C 2H2 and N = N 2).The com plete set of re ac tions starts with re ac tion 1, (C 2H2)m + .(n-1)N 2 + 2N 2 (C 2H2)m + nN2 for each com bi na tion of the vari ables m = 1-9 and n = 1-6 (ranges seen in the spec trum of Fig. 2).For the sake of sim plic ity, only part of the scheme is shown in the fig ure.