Thermodynamic study of proton-bond dimers formation in atmospheric pressure: An experimental and theoretical study

J. Chem. Thermodynamics 63 (2013) 17–23

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Thermodynamic study of proton-bond dimers formation in atmospheric pressure: An experimental and theoretical study Zahra Izadi, Mahmoud Tabrizchi ⇑, Hossein Farrokhpour Department of Chemistry, Isfahan University of Technology, Isfahan 84156-83111, Iran

a r t i c l e

i n f o

Article history: Received 15 December 2012 Received in revised form 11 March 2013 Accepted 29 March 2013 Available online 6 April 2013 Keywords: Thermodynamics Proton bound dimer Ion mobility spectrometry

a b s t r a c t Proton bonding is responsible for many important phenomena in physics, chemistry and biology. Simple proton-bound dimers of the type MHM+ are often used as model systems to investigate the nature of intermolecular interactions such as proton bonding. In this work, the thermochemistry of formation of symmetric proton bond dimmers at atmospheric pressure, in an ion mobility spectrometry (IMS) cell, was studied experimentally and theoretically. To establish equilibrium in the ionization region, the sample concentration was increased until the reaction quotient was independent of the sample concentration. The relative abundances of the monomer and dimer were obtained from the intensity of their corresponding peaks to use them in obtaining the equilibrium constant, Keq = [MHM+]/[MH+][M]. Van’t Hoff plot was then used to extract the enthalpy change of reaction. It was found that the experimental enthalpy is much smaller than expected and it was strongly temperature dependent. These were attributed to hydration of protonated ions. Parallel to experimental study, density functional theory (DFT) calculations at the B3LYP/6-311++G(d,p) level of theory were performed to obtain the enthalpy of the reactions MH+(H2O)n + M M MH+M(H2O)m + (n  m)H2O with different n and m values. The theoretical values of equilibrium constant and enthalpy led to the fact that a mixture of protonated monomers, MH+(H2O)n with different hydration numbers, is in equilibrium with their un-hydrated dimer. For such a complex reaction, an effective equilibrium constant and an effective enthalpy were defined as Keff = 1/R(pn/Kn) and DHeff = RYnDH°n, respectively. p is the partial pressure of water, and Kn and DH°n are the equilibrium constant and the enthalpy of the reaction MH+(H2O)n + M M MH+M + nH2O, respectively. Yn = (pn/Kn)/R(pn/Kn), is the contribution of the nth reaction in the whole reaction, being dependent on the water partial pressure and temperature. Using this model, we predicted the experimental behavior of enthalpy of dimer formation reaction in IMS by the calculation. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Proton-bounded dimers have a major role in the chemistry of hydrogen bond. In addition, a significant ion–molecule reaction, which generally happens in atmospheric pressure chemical ionization techniques, is the formation of proton-bound dimers [1]. There are several examples of chemistry involving ionic hydrogen bound formation, acid–base chemistry, electrolytes, ionic cluster formation and solvation. Hydrogen-bonded dimers are good examples for studying short-range intermolecular interactions, including modification of the electronic structure, and correlated proton or hydrogen atom transfer [2]. Thermodynamic properties of dimers have been experimentally studied by various techniques such as ion cyclotron resonance [3], and high pressure mass spectrometry [4,5]. The thermochemistry ⇑ Corresponding author. Tel.: +98 311 3913272; fax: +98 311 3912350. E-mail address: [email protected] (M. Tabrizchi). 0021-9614/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jct.2013.03.024

and proton bond energies of gas phase proton-bounded dimers of aliphatic alcohols have been studied using ion cyclotron resonance spectrometry [6,7]. Like mass spectrometry, ion mobility spectrometry (IMS) can also be used for studying thermodynamics and kinetics of proton-bounded dimer formation and dissociation in atmospheric pressure [8–11], as well as electron attachment reactions [12]. The advantage is that in IMS, the ions are generated and detected both in atmospheric pressure; hence there is no need for vacuum pumps and interface. In IMS, a continuous current of ions is pulsed by a shutter grid and then drifted under a constant electric field at atmospheric pressure. Ions are separated in the drift region, based on their mobility, which depends on their mass, charge and size. IMS is a sensitive, simple, fast, and portable analytical technique for the detection of trace levels of volatile organic compounds. It plays an important role in practical applications such as environmental monitoring and drug or explosive detection. Protonated molecules (MH+) are usually formed in IMS via proton transfer from the reactant ions, mostly hydronium ion clusters,

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Z. Izadi et al. / J. Chem. Thermodynamics 63 (2013) 17–23

H+(H2O)n, to the analyte molecules. At adequately high concentrations of the analyte, the proton-bound dimer ions (MHM+) may be formed through the following reactions [13].

M þ H3 Oþ MHþ þ H2 O;

ðR1Þ

MHþ þ M MHMþ :

ðR2Þ

Ewing et al. [8], studied the appearance of protonated molecules, proton-bounded dimers and trimers of selected materials including alcohols, ketons, ethers, aliphatic and aromatic amines in IMS cell at the ambient pressure and at different temperatures and concentrations. They also studied the kinetics of the decomposition of some proton-bounded dimers (A2H+ ? AH+ + A) including 1-4-dimethylpyridine and dimethyl methyl phosphonate, using the IMS technique to determine the constant rate of the dissociation [8]. In a similar study, a new method was proposed by the present group to study the kinetics of the formation of the proton-bounded dimers [12]. In that study, the rate constant formation of the symmetrical proton-bounded dimers of methyl isobutyl ketone (MIBK), 2,4-dimethyl pyridine (DMP) and dimethyl methyl phosphonate (DMMP) was measured. In the present study, the enthalpy formation of the symmetrical proton-bounded dimer of MIBK was experimentally determined by IMS. In addition, DFT calculations were performed to back the experimental data. In this study, hydration of reactant and product ions was considered to simulate the real conditions existing in atmospheric pressure IMS. The formation reaction was considered as a series of parallel reactions with different water cluster numbers. The effect of temperature on the contribution of each individual reaction channel and the overall enthalpy formation of proton-bounded dimer was also investigated. 2. Experimental 2.1. Experimental set-up The ion mobility spectrometer used in this study was constructed in our laboratory at Isfahan University of Technology [14]. The ionization region of the spectrometer consisted of five 9.5-mm thick aluminum rings, with 20 mm ID and 55 mm OD. The drift tube consisted of 11 aluminum rings with the same OD size and 36 mm ID. Each ring was connected to the adjacent one via a 5-MX resistor to create a potential gradient in the cell. A continuous corona discharge ionization source was used with a point-to-plane geometry as described elsewhere [15]. A Bradbury–Nielsen type shutter grid was mounted between the ionization region and the drift tube, and a Faraday cup type collector plate (10 mm in diameter) with an aperture grid was used to register the ion current. The IMS cell was housed in a thermostatic oven where temperature could be adjusted from room temperature to 473 K within ±2 K. Nitrogen gas, after passing through a 13 molecular sieve, was passed through the cell at 200 and 700 mL  min1 for the carrier and the drift gas, respectively. The spectrometer was operated in the positive mode with drift field of 437 V  cm1. Typically, a 100 ls gate pulse was used for IMS spectra recording. The ion current received on the collector plate was amplified by an electrometer with a gain of 109 V  A1 and relayed to a computer via an A/D converter (Picoscope ADC212, UK). The digitized signal was averaged over a number of scans and the resulting ion mobility spectrum was then displayed on the monitor. The chemicals used in this study were purchased from Fluka and used without further purification. An NE-1000 syringe pump was used for introducing sample into the carrier gas with flow rates between 5–40 lL  min1. All experiments were performed at ambient pressure and at a temperature of 353–423 K.

2.2. Method To obtain the enthalpy of the proton-bounded dimer formation reaction, the equilibrium constant of reaction (2) was measured form the ion mobility spectra at different temperatures. The method of measuring the equilibrium constant in IMS is well described in reference [10]. The reaction quotient for reaction (2) is defined in equation (1)

Q¼

½MHMþ  : ½M½MHþ 

ð1Þ

The relative abundance of dimer to monomer concentration ([MHM+]/[MH+]) was determined through the intensities of their corresponding peaks in the ion mobility spectrum. The absolute concentration of sample, [M], could also be determined through its vapor pressure and the flow rates of the syringe pump and the carrier gas. However, to simplify and avoid possible errors in calculating the concentration, we substituted the concentration [M], i.e.,

Q¼

½MHMþ  ; gF½MHþ 

ð2Þ

where F is the flow rate of the syringe pump, and g is a proportional constant. In practice, a continuous flow of sample vapor was added into the carrier gas by the syringe pump (figure 1). The syringe was filled with the sample vapor in equilibrium with its liquid at ambient temperature. Introducing the sample resulted in two product ion peaks, the protonated monomer, MH+, and the proton bound dimer, MHM+. The reaction quotient was calculated through equation (2). In principle, if a true equilibrium is established, the value of Q is expected to be independent of the flow rate. Hence, in order to ensure the establishment of a true equilibrium in the ionization region, the sample flow rate was increased at constant temperature, until the value of Q approached a constant value, i.e., Keq, the equilibrium constant. The experiments were performed at different temperatures to obtain the equilibrium constants at different temperatures and then DH° was calculated from the van’t Hoff plot. 3. Theoretical method To evaluate the experimental results, it was decided to calculate the theoretical value of enthalpy using DFT method. To calculate the theoretical value for the enthalpy of reaction (2), the structures of the unhydrated monomer (MH+), dimer (MHM+) and M were fully optimized at the density functional theory (B3LYP) using the 6-311++G(d,p) basis set. The keyword opt = tight was used to increase the convergence criteria of the software and obtain the reliable optimized geometries of the considered molecule. The optimized structures were used to calculate the Gibbs free energy of the selected molecules at standard temperature and pressure at the same level of theory. The calculated vibrational frequencies of the molecules were checked for negative frequency. The DFT results were used to calculate the equilibrium constants using K = exp(DG/RT). For all reactions, the Gibbs free energy, DG, was calculated at standard conditions (T = 298 K, p = 1 bar). The values of K at different temperatures were obtained using the Clausius Clapeyron expression [16]. 4. Results Figure 2 shows a typical ion mobility spectrum of MBIK at 373 K. The first peak corresponds to the reactant ions (RI), H3O+(H2O)n. The other peaks originate from the protonated mono-

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Z. Izadi et al. / J. Chem. Thermodynamics 63 (2013) 17–23

Carrier gas

Syringe Pump

Exit

Guard Rings

Drift Gas Collector Amplifier

Corona Discharge

Ionization Region

Drift Tube Ion Gate

Resistor High Voltage

A/D Computer

FIGURE 1. Schematic diagram of the ion mobility spectrometer used in this study.

0.25

2.5

0.22

MH+M(H2O)m

0.20 T=373K

0.18

0.20

Reaction quotient (Q)

Intensity

2.0

1.5

MH+(H2O)n

1.0

RI 0.5

0.0

T=363K

0.16

Keq

T=383K

0.14 T=353K

0.12

0.15

T=393K

0.10 0.08 340

360

380

400

420

440

T/K

T=403K T=413K

0.10

T=423K

0.05

0

5

10

15

20

Drift Time /ms FIGURE 2. Ion mobility spectrum of MIBK at 373 K.

mer (MH+) and the proton bound dimer (MHM+). The relative intensity of monomer to dimer peak depended on the sample flow rate. At high flow rates, the dimer peak grew while the monomer peak was decreased. However, as described earlier, the quotient value defined in equation (2) reaches a plateau when the sample flow rate was increased. Figure 3 shows the plots of Q versus the sample flow rate at different temperatures. As expected, all plots reach an asymptotic value. The equilibrium constant at each temperature was taken thorough averaging the Q values in the flat part of the corresponding plot. Clearly, the value of K depends on the temperature. The trend of Keq is given as

0.00 0

10

20

30

40

50

60

Flow Rate Sample/ μl.min-1 FIGURE 3. The variation of the reaction quotient, Q, defined in equation (2), versus the sample flow rate at different temperatures for MIBK. The plot of Keq against temperature is given in the inset.

a function of temperature as inset in figure 3. This trend shows that in general, the reaction is exothermic, as expected. However, it is endothermic below 380 K. This unexpected behavior is better shown in the van’t Hoff plot (figure 4), where ln Keq is plotted against 1/T. As can be seen, the variation of ln Keq versus 1/T is not linear. The slope is positive for a wide range of temperatures but it becomes negative at low temperatures. This means that based on the van’t Hoff equation,

d ln K eq DH  ¼ ; dð1=TÞ R

ð3Þ

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Z. Izadi et al. / J. Chem. Thermodynamics 63 (2013) 17–23

consider that a collection of dimer formation reactions are in equilibrium in the IMS cell and each one has its own contribution in the total enthalpy of the dimer formation reaction. To obtain the contribution of each reaction (R3) to given m and n numbers, we calculated the concentration distribution of MH+(H2O)n and MHM+(H2O)m at different temperatures and water partial pressures.

-1.4

-1.6

-1.8

0

-2.0 ΔH/Kcal/mol

lnKeq

5

-2.2

4.1.1. The mole fractions of ions with different hydration numbers An expression for the mole fraction of MH+(H2O)n for different values of n at atmospheric pressure in IMS cell can be derived, based on the equilibrium constant of reaction (4)

-5 -10 -15

-2.4 -20 340

360

380

400

420

440

T/K

-2.6 0.0023

0.0024

0.0025

0.0026

0.0027

0.0028

0.0029

T -1/ K FIGURE 4. The van’t Hoff plot for the formation of proton bound dimer of MBIK. The inset is the enthalpy changes of reaction at different temperatures obtained from the slope.

Kn ¼

½MHþ ðH2 OÞnþ1  : ½MHþ ðH2 OÞn  pH2 O

ð4Þ

For simplicity, we define the value of [MH+(H2O)n] as yn. Hence, the equilibrium constants for the consecutive reactions will be;

K0 ¼

y1 y y ; K 1 ¼ 2 ; . . . ; K n ¼ nþ1 : y0 p y1 p yn p

ð5Þ

Substituting y1 = K0y0p in K1 yields y2 = K1K0y0p2 and consecutively, the enthalpy of the dimer formation reaction is negative at high temperatures and is positive at low temperatures. The change in the enthalpy sign at low temperatures, given as inset in figure 4, can be attributed to hydration of ions to be discussed later when the effect of hydration on the reaction is explained. The linear part of the van’t Hoff plot gives an enthalpy of 6.1 kcal/mol for reaction (2). However, the inset in figure 4 shows that the enthalpy starts from about +5 kcal/mol and goes to 15 kcal/mol. The theoretical value of the enthalpy for reaction 2 and MBIK was obtained to be 25.6 kcal/mol from DFT calculations. It is seen that there is a considerable difference between the theoretical and experimental values. The difference is also attributed to the hydration of monomer and dimer ions at ambient pressure in the IMS cell. 4.1. Hydration

y0 ¼

y1 y2 ynþ1 ¼    ¼ nþ1 Q : ¼ n K 0 p K 0 K 1 p2 p n¼0 K n

ð6Þ

Using equation (6), all yn–0 are calculated as a function of y0;

ynþ1 ¼ y0 pnþ1

n Y

Kn:

ð7Þ

n¼0

The mole fraction of un-hydrated monomer ion, MH+, i.e., X0 = y0/ (y0 + Ryn+1), is calculated as:

X0 ¼

1þ

1 Qn : nþ1 p n¼0 n¼0 K n

Pn

ð8Þ

The mole fractions of the monomer hydrated ions MH+(H2O)n, i.e., Xn = yn/(y0 + Ryn+1), will be:

X nþ1 ¼ X 0 pnþ1

n Y

Kn:

ð9Þ

n¼0

As mentioned before, there is a large difference between the experimental enthalpy and that obtained by theoretical calculations. In addition, the van’t Hoff plot deviates significantly from linearity at low temperatures so that the enthalpy becomes positive. The reason for this discrepancy can be attributed to the hydration of monomer and dimer ions as MH+(H2O)n and MHM+(H2O)m in the IMS cell. Hence, the dimer formation reaction (R2) in the hydration form can be written as:

MHþ ðH2 OÞn þ M $ MHMþ ðH2 OÞm þ ðn  mÞH2 O;

ðR3Þ

where n and m = 0, 1, 2, . . . and n P m. In addition, all ions of the type A+(H2O)x with different x’s are in equilibrium with each other, i.e.,

MHþ ðH2 OÞn þ H2 O $ MHþ ðH2 OÞnþ1

n ¼ 0; 1; 2; . . . ;

ðR4Þ

and

MHMþ ðH2 OÞm þ H2O $ MHMþ ðH2 OÞmþ1

m ¼ 0; 1; 2; . . .

ðR5Þ

In fact, reaction (2) is a complex reaction covering a series of multi equilibrium reactions, rather than a simple reaction happening in IMS. It should be mentioned that monomers with different hydration numbers are not separated in IMS since water exists in the drift tube and the equilibrium continues all over the drifting time. This is also the case for the hydrated dimer ions. Hence, the monomer and dimer peaks in the ion mobility spectrum represent all forms of monomer ions and dimer ions with different numbers of water molecules, respectively. Therefore, it is reasonable to

Equation (8) and (9) show that the concentration of the hydrated monomer ions depends on the water partial pressure in the IMS cell as well as temperature, since the equilibrium constants, Kn, are temperature dependent. The values Kn were obtained using the DFT calculation tabulated in table 1 along with the DH and DG at standard conditions for reaction (4) with different n’s. We carried out the calculation to get n = 4 since at given water concentration (50–100 ppm), the mole fraction of bigger clusters is negligible, even at low temperatures. For the same reason, the DH° and DG° of reaction (5) are given in table 2 for m < 2. Figure 5 shows the distribution of mole fractions of MH+(H2O)n at different temperatures at 1 ppm and 100 ppm water concentrations, using equations (8) and (9) and the Keq values given in table 1. As shown, the concentration of un-hydrated monomer ion (MH+) is increased at high temperatures and low water concentrations,

TABLE 1 The calculated values of DH, DG and equilibrium constant at standard temperature and pressure for reaction (4) with different hydration numbers. MH+(H2O)n + H2O M MH+ (H2O)n+1

n

DH°/kcal  mol 0 1 2 3 4

20.57 14.47 12.08 10.60 9.48

1

DG°/kcal  mol1

Keq

18.83 6.40 4.36 2.95 1.22

5.05  108 4.83  104 1.59  103 144 7.8

21

Z. Izadi et al. / J. Chem. Thermodynamics 63 (2013) 17–23 TABLE 2 The calculated values of DH, DG and equilibrium constant at standard temperature and pressure for reaction (5) with different hydration numbers. MHM+(H2O)m + H2O M MHM+(H2O)m+1

m

0 1

K eff ¼

DH°/kcal  mol1

DG°/kcal  mol1

Keq

6.48 8.15

0.956 0.475

0.199 0.44

while the concentration of the hydrated monomer ions is decreased. Using a similar procedure, we found that the mole fraction of hydrated dimer ions MHM+(H2O)m is too small at a given temperature range and water concentrations. Hence, we considered only the unhydrated dimer ion in the dimer formation reaction. 4.2. Effective equilibrium constant and enthalpy It was noticed that the dimer formation reaction is a complex reaction aided by different hydrated monomers. Therefore, there is no single equilibrium constant or single value for its enthalpy. However, this complex reaction happens in IMS, responding to changes in temperature and water partial pressure. The whole reaction can be considered as a regular reaction with an effective equilibrium constant. Since only the unhydrated dimer is considered, i.e., m = 0 in reaction (3), all dimer formation reactions are summarized in (R6).

MHþ ðH2 OÞn þ M $ MHMþ þ nH2 O; n ¼ 0 . . . 4:

ðR6Þ

The general equilibrium constant for such reaction is:

Kn ¼

½MHMþ ðpH2 O Þn ½MHþ ðH2 OÞn gF

; n ¼ 0 . . . 4;

ð10Þ

where F and g are the flow rate of the syringe pump and the proportional constant, respectively. The concentration of a given monomer ion is Xn  [all monomer ions]. Hence, the equilibrium constant is simplified to;

Kn ¼

ðpH2O Þn ½Dim ; gFX n ½Mon

ð11Þ

where [Mon] represents all monomer ions in different hydration forms and [Dim] denotes all dimer ions. Rearrangement of equation (11) gives:

Xn ¼

ðpH2O Þn ½Dim  : Kn g F ½Mon

1.0

We here define effective equilibrium constant, Keff, as the following ratio:

ð12Þ

½Dim

ð13Þ

gF½Mon

which is constant at a given temperature and sample flow rate. The ratio [Dim]/[Mon] is easily obtained through the dimer and monomer peaks from the ion mobility spectrum. Combining equation (12) and (13) and considering the fact that the sum of all mole fractions is unity, we can yield: 4 4 X X pnH2O X n ¼ K eff ¼ 1: Kn n¼0 n¼0

ð14Þ

If equation (14) is rearranged, it gives the effective equilibrium constant.

1 1 pH2O p2H2O p3H2O p4H2O ¼ þ þ þ þ : K eff K 0 K1 K2 K3 K4

ð15Þ

Equation (15) shows that the effective equilibrium constant, defined in equation (13), depends on all equilibrium constants. The contribution of each channel depends on the value of Kn, which is temperature and water partial pressure dependent. The theoretical values of Keff have been calculated using the Kn values, which are given in table 1, at different water concentration levels. The results, along with the experimental values of Keq defined in equation (2), are plotted as a function of temperature in figure 6. The experimental trend of Keq reflects an increase followed by a decrease well predicted by the model. In addition, the experimental values of Keq lie within the theoretical values corresponding to water content around 90–100 ppm, which is reasonable. 4.3. Effective enthalpy Measuring the enthalpy of individual reactions by analyzing ion mobility spectra is not possible, since different hydration clusters are not separated in IMS. However, like the effective equilibrium constant, one may expect an effective enthalpy for the whole reaction. Differentiation of equation (15) yields 4 d ln K eff X d ln K n n ¼ pH2O : K eff Kn n¼0

ð16Þ

Dividing equation (16) by d (1/T) and using van’t Hoff equation (equation (3)) yields:

1.0

(a)

0.8

(b)

0.8

x1 0.6

x

1

Xn

Xn

0.6

0.4

0.4

x0

x0 0.2

0.0 360

0.2

x

x

0.0

2

380

400

420

T/ K

440

460

360

380

400

420

440

2

460

T/ K

FIGURE 5. The distribution of monomer ion with different hydration numbers as a function of temperature at: (a) 1 ppm, (b) 100 ppm water concentrations.

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Z. Izadi et al. / J. Chem. Thermodynamics 63 (2013) 17–23 5

0.26 0.24 0.22

0

Keq*10-8

0.20

Δ Ηeff Κcal/mol

80 ppm

0.18 90 ppm

0.16 0.14

100 ppm

-5

-10

0.12

100 ppm

0.10

90 ppm 80 ppm 70 ppm

-15

0.08 0.06 340

360

380

T/ K

400

420

440

4 X  d ln K eff 1 DHn pnH2O : ¼ K eff dð1=TÞ n¼0 K n

ð17Þ

Similar to van’t Hoff relation, we defined the effective enthalpy changes for the complex dimer formation reaction as DHeff = Rd(ln Keff)/d(1/T), where R is the gas constant. 4 X  Y n DH n :

ð18Þ

n¼0

Yn is the contribution of each DHn to the effective enthalpy of dimer formation reaction and is defined as:

pnH2O =K n : 1=K eff

Yn ¼

ð19Þ

If Keff from equation (15) is substituted in equation (19), one will see that Yn changes between 0 and unity and the sum of all Yn’s is one. However, it differs from the mole fractions, Xn, defined in equation (9). Similar to mole fraction, the Yn can be assumed as reaction fraction, which depends on temperature and water partial pressure. The Y values were obtained at different temperatures and water concentrations through equation (19) and by the use of the calculated Kn’s. As an example, the values of Yn at constant water concentration are plotted versus temperature in figure 7.

1.0

0.8

0.6

1

Y

Y

0.4

Y

0

0.2

Y

2

Y3

0.0 340

360

380

360

380

400

420

440

T/K

FIGURE 6. The variation of Keff with temperature at different water contents. The experimental values of Keq are also shown.

DHeff ¼

-20 340

400

420

T/K FIGURE 7. The variation of Yn’s defined by equation (19) as a function of temperature at 100 ppm water concentration.

FIGURE 8. The values of DHeff versus temperature at different water concentrations along with those of experimental values.

Figure 7 shows that the contribution of n = 0 reaction is increased with temperature while the contribution of the n = 2 reaction is decreased. The higher order reactions are negligible for the given temperature range. The values of DHeff, defined in equation (18), were calculated using table 1 data and the Yn values, defined in equation (19), at different temperatures and water concentrations. The results are presented in figure 8. The experimental results for DH, which were derived from the data given in figure 4, are also plotted. Again, the trend is well predicted by theory and the experimental results are within the theoretical calculations.

5. Conclusions Dimer formation is generally an exothermic reaction. Increasing temperature should in principle result in lowering the dimer peak and increasing the monomer peak, due to the decomposition of the dimer. However, it was experimentally found that when temperature is increased from room temperature, the dimer peak is unexpectedly increased and then at higher temperatures, it is decreased. In fact, the enthalpy value of the dimer formation reaction, which happens in atmospheric pressure, strongly depends on temperature, even changing to positive at low temperatures. This temperature dependency shows that the formation of the proton bound dimer in IMS is not a simple reaction. Considering the hydration of the monomer ion with different numbers of water molecules, we showed that it is a complex reaction covering a series of multi-equilibrium dimer formation reactions. Such a complex reaction, including all parallel reactions, was treated as a sole simple reaction, with an effective equilibrium constant and an effective enthalpy change. The effective equilibrium constant and the effective enthalpy were defined based on the equilibrium constants and enthalpies of the individual dimer formation reactions, respectively. The variation of the calculated effective enthalpy as a function of temperature was predicted by the proposed model and with the aid of the DFT calculated values for the individual enthalpies. It is in good agreement with the experimental results. The present study shows that the IMS is quite appropriate for the thermodynamic study of such a kind of reactions happening in atmospheric pressure. In addition, knowing the thermodynamic constants of the individual dimer formation reactions, which can be obtained from the DFT calculations, can help predict the temperature behavior of the reactions taking place in IMS.

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References [1] A.J. Bell, K. Giles, S. Moody, P. Watts, Int. J. Mass Spec. Ion Proc. 173 (1998) 65– 70. [2] M. Meot-Ner, Chem. Rev 105 (2005) 213–284. [3] J. W.Larson, R.L. clair, T. B. McMahon, Can. J. Chem 60 (1982) 542-544. [4] J.E. Szulejko, T.B. McMahon, Int. J. Mass Spec. Ion Proc 109 (1991) 279–294. [5] P. Kebarel, Int. J. Mass Spectrom 35 (2000) 804–817. [6] D.S. Bomse, Beauchamp, J. phys. Chem 85 (1981) 488–492. [7] J.W. Larson, T.B. McMahon, J. AM. Chem. Soc 104 (1982) 6255–6626. [8] E. Jazan, M. Tabrizchi, Chem. Phys. 355 (2009) 37–42. [9] R.G. Ewing, G.A. Eiceman, J.A. Stone, Int. J. Mass Spectrom. 193 (1999) 57–68. [10] M. Tabrizchi, S. Shooshtary, J. Chem. Thermodyn. 35 (2003) 863–870.

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[11] R.G. Ewing, G.A. Eiceman, C.S. Harden, J.A. Stone, Int. J. Mass Spectrom. 255– 256 (2006) 57–68. [12] M. Tabrizchi, A. Abedi, J. Phys. Chem. A 108 (2004) 6319–6324. [13] A. Hansel, A. Jordan, R. Holzinger, P. Prazeller, W. Vogel, W. Lindinger, Int. J. Mass Spec. Ion Proc. 149 (150) (1995) 609–619. [14] M. Tabrizchi, Research Grade Ion Mobility Spectrometer, Iranian Patent 42767, 2005. [15] M. Tabrizchi, T. Khayamian, N. Taj, Review of Scientific Instruments 71 (2000) 2321–2328 [16] Atkins, Physical Chemistry, Oxford University Press, Oxford, P. W., 2001. [16] P.W. Atkins, Physical Chemistry, Oxford University Press, Oxford, 2001.

JCT 12-711