A determination of free energy changes from a gas phase study of equilibria [(C2H2)m(N2)n-1]+ + N2 = [(C2H2)m(N2)n]+

Abstracts

Gas phase equilibria of ion-molecule clustering reactions between (C2H2)m+ ions and N2 were investigated by high-pressure mass spectrometry in N2-C2H2 mixtures irradiated by a-particles. Free energy values of clustering, DG0n-1, n, were obtained for reactions (C2H2)m+.(n-1)N2 + N2 <img border=0 width=32 height=32 src="../../../../../../img/revistas/jbchs/v8n3/a12img01.gif">(C2H2)m+.nN2, for different values of m and n. For m = 2, i.e., for the "core ion" (C2H2)2+, the values found for DG0n-1, n at T = 129 K are 0.87 ± 0.20 kcal/mol for (n-1, n) = (2,3) and 0.88 ± 0.20 kcal/mol for (n-1, n) = (3,4). For m = 3 ("core ion" (C2H2)3+), the free energy changes were found to be 0.91 ± 0.30 kcal/mol for (n-1, n) = (2,3), 0.73 ± 0.30 kcal/mol for (n-1, n) = (3,4); 0.65 ± 0.30 kcal/mol for (n-1, n) = (4,5), and 0.58 ± 0.30 for (n-1, n) = (5,6).

ion-molecule reactions; mass spectrometry; Titan atmosphere

O equilíbrio de reacões íon-molécula de agregação ("clustering") entre 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 a. Valores de energia livre de agregação, DG0n-1, n, foram determinados para reações (C2H2)m+(n-1)N2 + N2 <img border=0 width=32 height=32 src="../../../../../../img/revistas/jbchs/v8n3/a12img01.gif">(C2H2)m+nN2, para diferentes valores de m e n. Para m=2, i.e., para (C2H2)2+, os valores encontrados para DG0n-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 æ 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).

Article

A determination of free energy changes from a gas phase study of equilibria [(C₂H₂)_m(N₂)_n-1]⁺ + N₂ = [(C₂H₂)_m(N₂)_n]⁺

Carlos V. Speller*^a and Marc Fitaire^b

^a Divisão de Plasmas/LABMAT, Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina, 88040-900 Florianópolis - SC, Brazil

^bLaboratoire de Physique des Plasmas^#, Université de Paris-Sud, 91405 Orsay Cedex, France

Received: May 7, 1996; October 29, 1996

O equilíbrio de reacões íon-molécula de agregação ("clustering") entre 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 a. Valores de energia livre de agregação, DG⁰_{n-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 DG⁰_{n-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 æ 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).

Gas phase equilibria of ion-molecule clustering reactions between (C₂H₂)_m⁺ ions and N₂ were investigated by high-pressure mass spectrometry in N₂-C₂H₂ mixtures irradiated by a-particles. Free energy values of clustering, DG⁰_{n-1, n}, were obtained for reactions (C₂H₂)_m⁺.(n-1)N₂ + N₂ (C₂H₂)_m⁺.nN₂, for different values of m and n. For m = 2, i.e., for the "core ion" (C₂H₂)₂⁺, the values found for DG⁰_{n-1, n} at T = 129 K are 0.87 ± 0.20 kcal/mol for (n-1, n) = (2,3) and 0.88 ± 0.20 kcal/mol for (n-1, n) = (3,4). For m = 3 ("core ion" (C₂H₂)₃⁺), the free energy changes were found to be 0.91 ± 0.30 kcal/mol for (n-1, n) = (2,3), 0.73 ± 0.30 kcal/mol for (n-1, n) = (3,4); 0.65 ± 0.30 kcal/mol for (n-1, n) = (4,5), and 0.58 ± 0.30 for (n-1, n) = (5,6).

Keywords: ion-molecule reactions, mass spectrometry, Titan atmosphere

Introduction

The atmosphere of Titan is mainly composed^1,2 of nitrogen, with a few percent of methane, and acetylene as one of its minor components. In previous studies^3,4 we reported the thermochemical data regarding the clustering of N₂/CH₄ on different core ions of interest in understanding Titan’s chemistry. Pure N₂ and CH₄, as well as N₂-CH₄ mixtures were used to obtain the data. In the present work, we have carried out studies on N₂-C₂H₂ mixtures at high pressures (1-20 Torr). As in previous studies, the main purpose was to obtain thermochemical data on clustering ion-molecule reactions pertinent to the ion chemistry of Titan’s atmosphere. Information of this type is fundamental to an understanding of the complex chemistry associated with planetary atmospheres for the following reasons, among others: (1) ions represent efficient nucleating agents, resulting in the formation of large cluster buildup and eventually droplet formation; (2) clustering modifies the chemistry associated with ion neutralization because the ligands can act both as heat "sinks" for energy released in the neutralization as well as nearest-neighbor partners in chemical reactions; (3) planetary atmospheres contain both polar and non-polar components, which compete both as ligands and as candidates for the core ions within clusters, therefore dictating the terminal ion chemistry. This overall competition is ultimately controlled by the thermochemistry and kinetics associated with each individual clustering and association reaction expected to occur in any given atmosphere because of its composition, particle density, temperature, profile, etc.

The clustering of N₂ on the cluster ions (C₂H₂)_m⁺ was investigated. Reaction-free energy changes, DG⁰_{n-1, n} corresponding to:

were determined at one temperature, with N₂ acting as a third-body.

Very little data regarding clustering with acetylene ions have been reported to date. The formation of acetylene cluster ions, such as (C₂H₂)_m⁺, or mixed clusters, such a ^## [(C₂H₂)_m(N₂)_n]⁺ in N₂-C₂H₂-ionized mixtures, is to be expected.

An efficient charge transfer mechanism from N_i⁺ (i = 1-2) ions assures^5,6 the formation of C₂H₂⁺ ions. This can be understood on the basis of the following considerations:

• In mass spectra obtained in nitrogen and in acetylene, respectively, with high energy alpha-particles, the primary ions N₂⁺ and C₂H₂⁺ are dominant (approximately 80% in each case)⁷. As the fraction of acetylene in the N₂-C₂H₂ mixture is £ 2% in the present experiment, the expected dominant primary ion is N₂⁺, followed by N⁺;

• The first ionization energy (IE) of C₂H₂, to form (C₂H₂)⁺, is only 11.394 eV^8,9, which is low in comparison to those associated with nitrogen (IE[N₂] = 15.5812 eV for N₂⁺, and 24.3 for N⁺). Since the residence time of the reaction chamber is on the order of ms, and IP[C₂H₂] is relatively low, N₂⁺ and N⁺ will lead to the formation of C₂H₂⁺ by fast charge transfer;

• Moreover, the appearance energy (AE) of C₂H₂ to form C₂H⁺ is 17.36 eV. So, even if this minor ion is formed, charge transfer between C₂H⁺ and N₂ will occur, thus also indirectly contributing to the formation of C₂H₂⁺ (C₂H⁺ N₂⁺ C₂H₂⁺).

• Finally, it is easily verified that under the present experimental conditions, the formation of N₃⁺ and N₄⁺ by the ternary reactions:

is expected to be insignificant in comparison to the bimolecular transfer charge from N₂⁺ and N⁺ to C₂H₂. The expected primary ion in the a-particle radiolysis of nitrogen containing trace amounts of acetylene, such as in the present experiment, is thus essentially C₂H₂⁺, which follows the reaction:

This is consistent with the observation of Lind and Bardwell¹⁰, who have shown that irradiation of N₂-C₂H₂ mixtures by a-particles from radon does not lead to the synthesis of nitrogen compounds, the final product being the same as that which is formed in the absence of nitrogen. Nevertheless, they observed that the energy absorbed by the nitrogen contributed to the polymerization of C₂H₂ to form the solid cuprene, [(C₂H₂)_m]. Once formed, C₂H₂⁺ can react with C₂H₂ to give⁵ C₄H₄⁺*, an excited complex, which in turn will be either stabilized by collision with a third body (N₂ ) at higher pressures, or dissociated into the condensation ions C₄H₃⁺ and C₄H₂⁺:

The formation of C₄H₄⁺ (or (C₂H₂)₂⁺) via channel (2) can be represented by the three-body ion-molecule association reaction

where k stands for the effective reaction constant.

These ions can then undergo subsequent clustering reactions with C₂H₂ or N₂. In the present study only reactions corresponding to equilibrium (1) were investigated.

Experimental

The measurements were performed with the High-Pressure Mass Spectrometer at the Université de Paris-Sud/LPGP, where ionization is initiated by alpha-particle bombardment. The experimental system is the same as previously described^4,11. Figure 1 illustrates the overall geometry of the mass spectrometer sampling system. Ions are generated in a field-free stainless steel source, by 5.4 Mev a-particles from three enclosed ²⁴¹Am (» 40 mCi cm^-2) radioactive sources fixed on the source walls. Ions exit the source through a 50 mm diameter hole into a low pressure (P £ 10^-5 Torr) analysis chamber. These ions are accelerated and focused by electrostatic lenses, mass analyzed by a quadrupole mass filter, and detected by a 17-dynode electron multiplier. The highest mass to charge ratio (mass/z) value studied was 246. Since it is known¹² that the transmission in a quadrupole decreases as the value of the ion mass increases, corrections were applied for variations in the mass spectrometer transmission with respect to the selected mass. The neutral gas is pumped by a 600 l/s cryogenic pump which maintains the pressure inside the mass spectrometer at values less than 10^-5 Torr. The reaction chamber is pumped by a 140 l/s turbomolecular pump, yielding a background pressure on the order of 10^-7-10^-8 Torr. A second quadrupole mass spectrometer, Q₂, downstream from the ion-extraction hole was used as a neutral gas analyser, permiting continuous monitoring of the partial pressures of the minority gases. In order to reduce water impurities, the gases flowed through a cold trap at 77 K before being introduced into the reaction chamber.

The gases were supplied by L’Air Liquide and were used as purchased. A N₂-C₂H₂ (98:2) mixture, which according to the supplier contained < 3 ppm O₂, < 2 ppm H₂O, < 2 ppm CO, < 1 ppm CO₂, and 1 ppm PH₃, was used as the initial mixture. Pure N₂ (< 0.1 ppm and < 1 ppm H₂O) was added to the N₂-C₂H₂ mixture to change the concentration of acetylene. Nitrogen (N₂) was used both as the bath and the ligand gas, and acetylene (C₂H₂) was 0.05 to 2% of the total N₂-C₂H₂ gas mixture. Experiments were performed under a total pressure ranging from 5 to 50 Torr, and at temperature values of 129, 132 and 273 ± 2 K. The temperature was measured using a diode, inserted directly in the reaction chamber (see Fig. 1), close to the sample region, and calibrate^### at ambient and liquid nitrogen temperatures. In this range, deviation from linearity can be considered negligible, and so IµV is assumed. A combination of technical difficulties, related to the simultaneous control of temperature and mixture composition, prevented us from obtaining enough data at different temperatures to determine enthalpy changes. Ionization at the source results in rapid primary ion-neutral reactions that generate C₂H₂⁺. Clustering reactions between C₂H₂⁺, C₂H₂, and N₂ then take place, resulting in the equilibrium (1). Under the conditions of the present study, the clustering neutrals (ligands) and the third body necessary for collisional stabilization of the intermediate complex are the same (N₂). Equilibrium constants K_{n-1, n} are calculated as usual

where [I⁺.(n-1)L] and (I⁺.nL) correspond, respectively, to the measured ion intensities of the reactant and product ions of the studied equilibrium (1), and P_L is the pressure of the ligand L in atmospheres. Free energy changes DG⁰_{n-1, n}, were obtained from the thermodynamic relation DG⁰_{n-1, n} = - RT ln K_{n-1, n}, connecting the equilibrium constant K_{n-1, n} and the free energy change DG⁰_{n-1, n}; R is the perfect gas constant. Equilibrium conditions are discussed in Refs. 4 and 11. Furthermore, as will be shown in the next sections, the equilibrium constants were verified to be independent of the ligand (N₂) pressure between 10 and 50 Torr, as well as of the C₂H₂ partial pressure.

The estimated errors associated with the equilibrium constant measurements were 10-20% for m = 2, and 20-30% for m = 3. These errors are mainly related to noise, which often appeared during the peak intensity measurements at low temperatures (in general below 150 K), and for which no explanation could be found in our experiment. As a consequence, a relatively large dispersion of the points was observed in the equilibrium constant plots. Nevertheless, the uncertainties in DG⁰_{n-1, n} are often reported to be in the range of ±0.2-0.5 kcal/mol, and the present results lie within this range.

Results

Figure 2 presents the mass spectra of a N₂-C₂H₂ mixture for P(C₂H₂) = 3 mTorr and two different nitrogen pressures (5 and 30 Torr, respectively) at a temperature of 132 K. At the lower N₂ pressure, the most obvious feature is the grouping of the mass pattern into subpatterns which repeat themselves with a periodicity of 26 mass units. We can reasonably ascribe these peaks to (C₂H₂)_m⁺ ions, with m = 2 to 10 (the peak at m = 1, C₂H₂⁺, i.e., corresponding to mass/z = 26, was observed only at higher temperatures, e.g. at 273 K). At higher N₂ pressures, the shifting of these peaks to higher mass values is obvious. Low intensity peak groups at intermediary mass values also showed an increase in their intensities as the nitrogen pressure was increased. A proposed scheme showing the formation of [(C₂H₂)_m(N₂)_n]⁺ clusters from the primary ion C₂H₂⁺ is given in Fig. 3, where we have also included exchange reactions of N₂ for C₂H₂. Given the greater well depth for C₂H₂ as a ligand (see next paragraph), this exothermic displacement seems to be an essential feature of the schematic of the cluster formation, as observed in other composite cluster systems^13,14.

Although (C₂H₂)_m⁺ ions were clearly predominant at the lower N₂ pressures, as shown in Fig. 2, attempts to investigate the equilibrium

under the experimental conditions used in our experiment were not succesful. The ligand (C₂H₂) pressure investigated ranged from 5 to approximately 260 mtorr. For P(N₂) = 10 Torr, it was observed that at the lowest C₂H₂ pressures (between 5 and 40 mTorr, approximately) the ratio between the product and the reactant ion intensities, [(C₂H₂)_m⁺]/[(C₂H₂)_m-1⁺], tended to increase slightly with pressure, but not directly proportional to pressure as required under equilibrium conditions (I_m+1/I_m = KP_L). Above 40 mTorr, the ratio tended toward a constant value. The reason for this is not clear. The results suggest that at 132 K, lower C₂H₂ pressures might be one of the necessary conditions to achieve equilibrium for the above reactions. We also see that in both spectra of Fig. 2, at 5 and 30 Torr, a series of clusters starting at mass/z = 66 (which possibly corresponds to [X(C₂H₂)_r(N₂)_s]⁺, X being a unknown compound), probably formed in the discharge from impurities or from the gases under study. Nevertheless, this series is out of the scope of the present study.

Figure 4 shows the equilibrium constants K^m_{n-1, n} (m = 2; n = 3-4) for reaction (1) versus the partial pressure of acetylene (5-260 mTorr), for two different values of the nitrogen pressure (10 and 20 Torr). The values of K²_{n-1, n} remain constant as a function of the acetylene pressure over the entire range studied, for both values of the nitrogen pressure. This result is consistent with the attainment of equilibrium in the reaction chamber.

The same checks were made for the K³_{n-1, n} (m = 3; n = 2-6) constants, shown in Fig. 5. Except for K³_1,2 and K³_5,6, they can be considered independent of the C₂H₂ partial pressure within the pressure range 5 to 400 mTorr, for a N₂ pressure of 20 Torr. However, the results for K³_5,6 suggest a tendency towards a constant value for acetylene pressures higher than approximately 200 mTorr. We therefore assume the equilibrium for pressures above 200 mTorr. For practical reasons, the study of the K³_{n-1, n} dependence on the ligand pressure N₂ (Fig. 6) was done at a constant ratio of P(C₂H₂)/P(N₂) = 2 10^-2 (the available initial mixture). In view of their observed independence (again, only K³_1,2, not shown, is not found in equilibrium conditions) as a function of the C₂H₂ concentration, this should not affect our conclusions regarding equilibrium. Both sets of measurements, varying either N₂ or C₂H₂, show the same trend, i.e., the K^m_{n-1, n} (m = 3; n =3-6) are independent of the partial pressures of N₂ and C₂H₂ within the experimental accuracy of ± 30-40% for the equilibrium constants.

The determinations inferred from the experimental results are summarized in Table 1, where the log of the equilibrium constants for reaction (1), as well as the free energy changes for the corresponding forward reactions are shown.

Discussion

McCrumb et al.⁵ have investigated reaction (5). At 2.8 Torr and 300 K, the stabilization of C₄H₄⁺* (channel 2) was dominant, channels (3) and (4) being unimportant in their experiment. The formation of (C₂H₂)₂⁺ was also investigated by Rakshit and Warneck¹⁵, using CO₂ as a third body. They also studied the formation of the clusters (C₂H₂)₃⁺ and C₂H₂⁺.CO₂, as well as the association of C₂H₂ with C₄H₂⁺ and C₄H₃⁺, also with CO₂ as a third body. The measured reaction constants for all these clustering reactions where C₂H₂ was the ligand molecule were very high, whether in N₂ or CO₂, and on the order of 10^-26-10^-27 cm⁶ s^-1. However, for the clustering of CO₂ with C₂H₂⁺,

they found a much lower value for the corresponding reaction constant, k £ 4 10^-30 cm⁶ s^-1. In other words, the clustering of C₂H₂ with C₂H₂⁺ leads to the formation of (C₂H₂)_n⁺ clusters at least 10⁴ times faster than the association of CO₂ with C₂H₂⁺. As a general trend, it is observed that N₂ displays a slower reaction constant than CO₂ as regards its clustering on the same ion. Moreover N₂ is observed to be less efficient than CO₂ as a third body. For example, in the case of the formation of (C₂H₂)₂⁺, the literature gives k = 1.6 10^-26 cm⁶ s^-1 and 0.6 10^-26 cm⁶ s^-1 for CO₂ and N₂, respectively^5,15. This probably reflects the lower number of degrees of freedom in N₂¹⁶. The relative reactivity of the ligands CO₂, N₂, C₂H₂ is thus seen to increase in the order N₂ < CO₂ < C₂H₂. This is quite reasonable in terms of the basicity of these ligands, which is a function of their polarizability, a (a(N₂) = 1.76 ų, a(CO₂) = 2.59 ų and a(C₂H₂) = 3.33 ų). The greater stability of the C₂H₂.C₂H₂⁺ complex, relative to C₂H₂.CO₂ and C₂H₂.N₂ also follows from this order of basicity, and is stressed by our failure to observe equilibria once the (C₂H₂)_m⁺ complexes are formed.

Therefore, it is plausible to expect that in order to have reaction rates on the same order as those leading to the formation of (C₂H₂)_m⁺ clusters, the partial pressure ratio P(N₂)/P(C₂H₂) must be at least 10⁴. This is consistent with the spectra shown in Fig. 2 for P(N₂)/P(C₂H₂) ~10³, where (C₂H₂)_m⁺ clusters are predominant; however, when the pressure ratio is increased to 10⁴, [(C₂H₂)_m(N₂)_n]⁺ clusters are clearly observed.

It should be remembered that the spectra shown in Fig. 2 were obtained at a different temperature than that used by Rakshit (132 K in this work and 300 K for Rakshit with CO₂). The much lower temperature in our work should favor clustering reactions by increasing the corresponding equilibrium constants.

Regarding Table 1, we see that at 129 K all reactions studied are spontaneous. For [(C₂H₂)₃(N₂)_n]⁺ (m = 3), the stability of the clusters increases monotonically with the number of N₂ molecules attached, i.e., in the order A⁺(N₂)₂ < A⁺(N₂)₃ < A⁺(N₂)₄ < A⁺(N₂)₅ < A⁺(N₂)₆, where A = C₂H₂. As for [(C₂H₂)₂(N₂)_n]⁺ (m = 2), the stabilities are found to be roughly the same, whether for n = 3 or n = 4.

Studies involving composite clusters have been reported in the literature (see for ex., Refs. 13 and 14). In these studies, the ligands under investigation were polar (HCN, H₂O, NH₃, H₂S), thus involving ligand-ligand bonds stronger than those in the present case where the ligands are non-polar. Nitrogen and acetylene clusters are much more fragile, raising the questions as to whether changes in the nitrogen pressure also affect the acetylene equilibrium. Even though the estimated values of enthalpy changes are consistent with the expected numbers (see below), we believe that further investigation is needed in order to clarify this point.

The temperature dependence of the equilibrium constants was not investigated in the present study, and so enthalpy changes, DH⁰_{n-1, n}, could not be determined. However, an estimation of DH⁰_{n-1, n} can be made if we attribute the estimated values for the corresponding entropy changes, DS⁰_{n-1, n}. If we estimate DS⁰_{n-1, n} as -20 ± 3 cal/mol K, a range in which most of the values determined for cluster ions of the X⁺(N₂)_n-type fall^14,17,18, then DH⁰_{n-1, n} can be estimated from the thermodynamic relation ln K = DS⁰/R - DH⁰/RT, which connects the equilibrium constant K and the entropy 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 clustering reactions with nitrogen for the same number of clustered molecules. These estimates are merely speculative and are to be used with caution.

To explain the possible formation of organic-nitrogen molecules in the atmosphere of Titan, Capone et al.¹⁹ proposed a mechanism involving exchange reactions between N₂, CH₄ and C₂H₂ in HCNH⁺.(L)_n clusters (L = ligand). Later, HCNH⁺.(N₂)_n, as well as C_pH_q⁺.(N₂)_n and C_pH_q⁺.CH₄ formation in the alpha-particle radiolysis of N₂-CH₄ mixtures was observed at Orsay by these authors^3,4. Hiraoka and Kebarle²¹ studied C_pH_q⁺.(CH₄)_{n = 1-4}. Table 2 shows the estimated DG⁰values corresponding to the formation of these ions at 129 K (the same as in Table 1). This temperature is close to that of the region of maximum cosmic ray-activated chemistry in the atmosphere of Titan, estimated^1,19 as 150-160 K. The comparison of the stabilities found for these clusters and those of the acetylene-nitrogen clusters investigated in the present study show that clusters with the same number of clustered molecules around the core ion present comparable DG⁰. If present in the atmosphere of Titan they could probably all interact by exchange reactions, ultimately leading to the formation of [(C₂H₂)_m(N₂)_n]⁺.

Comments on the errors

In determining the enthalpy and entropy changes in some of our previous work, the temperature ranges for the different reactions studied were relatively small. This is a common feature among previous studies involving ion clustering with N₂ reported by several laboratories. In our earlier studies on the O₂⁺(N₂)_n and NO⁺(N₂)_n¹¹, and HCNH⁺(N₂)_n³ clusters, small ranges of T were also used. Later, good agreement was obtained by Hiraoka and Nakajima¹⁸ between their thermochemical data and our data for O₂+(N₂)₂; good agreement was also found between the theoretical results obtained by Ha and Nguyen²⁰ and our experimental determinations for DH⁰ regarding HCNH⁺(N₂)_n. However, the absolute values of our equilibrium constants were much larger than those measured by Hiraoka and Nakajima, resulting in smaller values for DG⁰. This was particularly true for the larger clusters (n 1), where the DS⁰ values did not lie within the expected range (20 ± 3 cal/mol.K), but rather were lower. Since then, however, in order to avoid collisional induced dissociation when sampling the fragile clusters, more precautions have been taken⁴ regarding the magnitude of the ratio between the product and reactant ions I⁺nL and I⁺ (n-1)L. The results recently obtained⁴ for the clustering of CH₅⁺ and C₂H₅⁺ with CH₄ provide a basis for comparison with the measurements of K made by Hiraoka and Kebarle²¹. The equilibrium constants (and therefore of DG⁰) for these association reactions are in very good agreement. Furthermore, the corresponding DS⁰ values also are within the expected range mentioned above.

Acknowledgments

This work was sponsored in part by the CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnológico do Brasil) and the Université de Paris-Sud. The authors thank Drs. Marcos C. Rezende and José F. Nome (UFSC) for helpful discussions, as well as Dr. Ted R. Taylor (UFSC) for important comments on the text. We are particularly indebted to Mr. Emile Le Duc (UP-Sud) for his invaluable technical assistance.

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16. See for ex. Kebarle, P. In Ion Molecule Reactions, Franklin, J.L., Ed.; Plenum Press; New York, 1972, vol. 1, p. 239.

17. Keesee, R.G.; Castleman, Jr., A.W. J. Phys. Chem. Ref. Data 1986, 15, 1011.

18. Hiraoka, K.; Nakajima, G. J. Chem. Phys. 1988, 88, 7709.

19. Capone, L.A.; Prasad, S.S.; Huntress, W.T.; Whitten, R.; Dubachs, J.; Santhanam, K. Nature 1981, 293, 45.

20. Ha, T.-K., Nguyen, M.T. Z. Naturforsch 1983, 38a, 855.

21. Hiraoka, K.; Kebarle, P. J. Am. Chem. Soc. 1975, 97, 4179-4183; Can. J. Chem. 1975, 53, 970.

^#

Associated to CNRS (URA73).

^##

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

₂H

₂+;

i.e., C

₂H

₂+.(C

₂H

₂)

_m-1 .(N

₂)

_n = [(C

₂H

₂)

_m(N

₂)

_n)]

⁺.

^###

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 compararison with the results reported 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 predominante over those of the temperature.

Publication Dates

• Publication in this collection
  31 Jan 2011
• Date of issue
  June 1997

History

• Received
  07 May 1996
• Accepted
  29 Nov 1996