ANALYTICAL SCIENCES FEBRUARY 2012, VOL. 28 103 2012 © The Japan Society for Analytical

Reevaluation of Donor Number Using Titration

Misaki KATAYAMA,* Mitsushi SHINODA,** Kazuhiko OZUTSUMI,* Shigenobu FUNAHASHI,** and Yasuhiro INADA*†

*Department of Applied Chemistry, College of Life Sciences, Ritsumeikan University, Kusatsu, Shiga 525–8577, Japan **Laboratory of Analytical Chemistry, Department of Chemistry, Faculty of Science, Nagoya University, Chikusa, Nagoya 464–8602, Japan

Many empirical parameters have been suggested to measure effects in chemical reactions. Gutmann’s donor number has been a successful parameter to quantify the electron-donating property of the solvent molecule; it is defined

as the change of the addition reaction of solvent molecule to SbCl5 in 1,2-dichloroethane. Calorimetric measurements can be applied to determine the quantity. Because the existence of water is critical for reactions in organic , we have analyzed the enthalpy change using the titration calorimetry while considering the complexation with water. The determined donor numbers of formamide, N,N- (DMF), (DMSO), and 1,1,3,3-tetramethylurea (TMU) are 22.4, 26.5, 30.0, and 40.4, respectively. The values of DMF and DMSO are in perfect agreement with those of Gutmann. A reliable value for TMU is obtained for the first time on the basis of the enthalpy change for the addition reaction.

(Received August 8, 2011; Accepted November 4, 2011; Published February 10, 2012)

molecules. Introduction The electron-donating property of solvent is important to interpret the stability and reactivity of metal species in solution. Non-aqueous solvents are useful for many chemical reactions Gutmann has defined it as the absolute value of the enthalpy which do not easily proceed in water. The thermodynamic change for the 1:1 complex formation reaction of the donor properties of a chemical reaction in solution largely depend on molecule with SbCl5 in 1,2-dichloroethane. The SbCl5 molecule the physicochemical properties of the solvent. Many empirical was selected as the standard acceptor molecule because of its parameters have been suggested to compare the solvent effect in strong accepting property for the electron pair of the donor 1 2 3 chemical reactions, such as Kosower’s Z, Dimroth’s ET, Y, molecule. The SbCl5 molecule has only one accepting site and 4 and Ω. The Z and ET values are parameterized using the therefore it forms only the 1:1 complex with the donor molecule charge-transfer absorption band of the probe molecule, with (L), as shown in Eq. (1): which the solvent molecule forms an adduct, in the solvent. The Y value is defined using the rate constant of the solvolysis SbCl5 + L  SbCl5L (1) reaction of t-butyl chloride. The Ω value is obtained from the ratio of the endo-product to the exo-product of the Diels–Alder The molecular geometry changes from trigonal bipyramidal to reaction. The solubility parameter δ, which is defined by the distorted octahedral structure in the complexation reaction, and molar energy of evaporation and the molar volume of solvent, the reaction is not accompanied by dissociation of the chloride is also important to understand the solvent effect.4 These . The formal charge is kept neutral for the reactions with the parameters mainly represent the properties of solvents as the neutral L, and the electrostatic contribution from the electron acceptor, and it is known that they correlate with change is thus almost negligible to the enthalpy change. Mayer’s acceptor number (AN).5 The AN value is defined as Gutmann has experimentally determined the enthalpy change by the relative chemical shift of 31P NMR of trimethylphosphine means of calorimetry and has reported the DN values for many oxide in a solvent, and is widely used as a measure of the donor molecules that are usually used as solvents.7 Gutmann’s accepting property of the solvent molecule when combined with DN is now widely accepted as a good measure of the donating the Gutmann’s donor number (DN),6,7 which is a measure of the property of solvents, and the values help researchers to donating property. The β and α values of Kamlet–Taft are also understand the solvation structure and the solvation equilibrium proposed as the parameters to measure the solvent-solute of metal . The application of these parameters is expanding interaction, which is related to the donating property.8–10 from the basic solution chemistry into applied materials However, these parameters mainly represent the chemistry, such as the estimation of surface functionality of hydrogen-bonding interaction between the solvent and solute mesoporous silica.11 As the importance of the DN increases, a systematic † To whom correspondence should be addressed. knowledge of a variety of solvents becomes necessary to E-mail: [email protected] compare quantitatively the solvent nature. Erlich and Popov 104 ANALYTICAL SCIENCES FEBRUARY 2012, VOL. 28 estimated the value of DN using the linear relationship between solution into the cell. The titrant solution passed through the 23 the chemical shift of Na NMR of the NaClO4 solution and the heat exchanger to maintain constant temperature of the solution known value of DN.12 This approach, however, is based on a and was then introduced into the reaction cell. A DC current hypothesis that the solvation structure of the Na+ ion is the same generator (R6142, Advantest) was used to supply a specified in each solvent. There is a similar attempt using the chemical current to the heater in order to calibrate the potential difference 1 13 shift of H NMR of CHCl3 in the solvent. In this case, the to the generated heat. dipolar interaction between the solvent molecules and CHCl3 is Measurements of the reaction heat were performed by titrating emphasized rather than the electron-donating property. the 1,2-dichloroethane solution of each donor solvent into the

Formamide (FA) and 1,1,3,3-tetramethylurea (TMU) are good 1,2-dichloroethane solution of SbCl5. The initial concentration solvents for electrolytes, and their DN values of 24 and 31 were and volume of titrand (SbCl5 solution) were around 1.0 × reported by Popov et al., respectively.12 The chemical behavior 10–3 mol dm–3 and 60.0 cm3, respectively, and the total volumes in FA is often compared with that in the other amides, such as of the added titrant solution were 11.0 cm3 for DMF, 13.0 cm3 N-methylformamide and N,N-dimethylformamide (DMF). for DMSO, 17.0 cm3 for TMU, and 13.0 cm3 for FA with the Although the DN value of FA (24) is slightly smaller than that concentration of around 2.0 × 10–2 mol dm–3. of DMF (26.6), such a comparison must be carefully done because the value of FA is estimated by a different method from Data analysis that used for DMF.6,7,12 Similarly to the case of FA, although the The heat, q(t), generated per unit time in the solution of the chemical characteristics of metal ions in TMU such as the volume, V, is expressed by Eq. (2), solvation structure are compared with those in the other amides on the basis of DN values,14–16 it should be noted that they are dθ()t ()CVp +Ccell = q() t − λθ()t (2) not determined by the same experimental method. It has been dt reported that the solvation number of the metal ion is variable from 4 to 6 according to the ionic size and charge in TMU with where Cp is the volumetric heat capacity of the sample solution, 14–20 the bulky molecular structure. In order to interpret the Ccell the heat capacity of the blank vessel, θ(t) the temperature of bulkiness effect of TMU on the solvation structure of metal the solution at time t, and λ the heat-transfer coefficient between ions, the donating property of solvent molecules must be the vessel and the atmosphere. The potential difference, e(t), of quantitatively compared with those of other solvents. It is thus the thermistor sensor dipped in the titrated solution is related to important and necessary to reevaluate the DN values of FA and θ(t) by Eq. (3) with a proportional factor, A. TMU based on the original definition. In the present study, we have carried out a reevaluation of the e(t) = Aθ(t) (3) DN values for the donor ligand of FA, DMF, and TMU using titration calorimetry to determine precisely the reaction heat of After finishing generation of the reaction heat, θ(t) follows Eq. (1). Because the water molecule existing in 1,2-dichloroethane Newton’s law of cooling. Thus, the e(t) value is expressed by solution easily binds to SbCl5 and greatly affects the observed Eq. (4) in the time region of t ≥ ts, values of enthalpy change, the dissociation of water has been taken into consideration in analyzing the titration data. The  λ  e() t =e() ts exp − (t− ts ) (4) corresponding value of dimethyl sulfoxide (DMSO) has also  CVp +Ccell  been reevaluated in this study to estimate the validity of our procedures of data analysis, because the DN value of DMSO where ts is the time at which the generation of the heat was was also determined by Gutmann using calorimetry. The values entirely completed. In this study, ts was set as the time when the determined in this study will be compared with those reported e(t) value became 60% of its maximum. Then, the generated previously. gross heat, Q, is given by Eq. (5):

λ ts 1 Q =e() t dt + e() ts()CV p +Ccell (5) Experimental A ∫0 A

Sample solutions Determination of the Q value was performed in the following

Reagent grade 1,2-dichloroethane (Nakarai), N,N-dimethyl- manner. First, the values of e(ts) and (CpV + Ccell)/λ were formamide (Wako), dimethyl sulfoxide (Wako), 1,1,3,3-tetra- estimated by a least-squares fitting of Eq. (4) to the e(t) values methylurea (Wako), and formamide (Wako) were dried over 4 Å for each set of titration data. Second, the λ/A value was molecular sieves and distilled before use. The SbCl5 solution independently determined by Eq. (5) for the measured e(t) was prepared by dissolving SbCl5 (99.99%, Aldrich) in purified values after addition of the known amount of Q using the heater. 1,2-dichloroethane under nitrogen atmosphere. 1,2-Dichloroethane Finally, the value of Q was calculated by Eq. (5) with the values solutions of FA, DMF, TMU, and DMSO were also prepared of (CpV + Ccell)/λ and λ/A. The apparent enthalpy change, h, under nitrogen atmosphere and used as the titrant solution. was then calculated by dividing the obtained Q value by the

total concentration of SbCl5 and the total volume. Titration calorimetry measurements Reaction heats were measured with a twin-type calorimeter (MMC5111S, Tokyo Riko) at 298 K. The calorimeter is Results and Discussion composed of two cells, which are respectively equipped with a thermistor sensor and a heater with a standard resistance of The h values observed during the titration are plotted by the 100.0 Ω. The potential difference generated by the temperature filled circles in Fig. 1 as a function of the ratio of the total difference between the two cells was amplified in a full scale of concentration of DMF (CDMF) to SbCl5 (CSb). The positive value ±10 mV. Two automatic piston burettes (APB-410, Kyoto of h increases with the progress of titration; therefore, the Electronic) were set to introduce the titrand and the titrant addition reaction of DMF to SbCl5 is regarded as exothermic. ANALYTICAL SCIENCES FEBRUARY 2012, VOL. 28 105

Table 1 Thermodynamic parameters for the ligand substitution reaction of SbCl5(H2O) in 1,2-dichloroethane at 298 K

–1 3 –1 –1 –3 Ligand log(K′/mol dm ) ΔH°/kJ mol Hdil/kJ mol cm

DMF 3.5 ± 0.6 –35.5 ± 8.5 –1.2 ± 0.5 DMSO 3.7 ± 0.6 –51.4 ± 8.5 –0.7 ± 0.5 TMU 3.4 ± 0.3 –93.9 ± 9.9 –1.5 ± 0.4 FA 2.8 ± 0.2 –18.5 ± 1.4 –1.2

Fig. 1 Observed h values (filled circles) and h – Hdilv values (open circles) for the measurement with DMF as a function of CDMF/CSb.

The decrease in h at CDMF/CSb ≥ 2 indicates that the heat of dilution becomes predominant because the addition reaction has been almost completed. As clearly seen in Fig. 1, the maximum h value is ca. 20 kJ mol–1 and is much smaller than the corresponding value (111 kJ mol–1) estimated from Gutmann’s 7 DN (26.6). Gutmann measured the heat of reaction in a batch Fig. 2 Observed (open marks) and calculated (solid lines) h values process using a glass ampule filled with SbCl5, and thus the with FA, DMF, DMSO, and TMU as a function of CL/CSb. water content in the solvent was negligible. On the other hand, titration calorimetry is difficult to perform under dried atmosphere and thus the sample solution is reasonably considered to contain a certain amount of water. The  ∆H°[(SbCl5 DMF)]  concentration of water in 1,2-dichloroethane was determined to h = − − Hdilv  (9)  CSb  be 5 × 10–2 mol dm–3 using the Karl–Fischer titration method, and was a sufficiently excess concentration to that of SbCl5. The values of K′, ΔH°, and Hdil were determined by the It is thus reasonable to consider that SbCl5 exists as the adduct least-squares fitting of Eqs. (8) and (9) for the measured values with one water molecule as SbCl5(H2O) in the titrant solution of h. The optimized parameters are summarized in Table 1. under the current experimental conditions. The observed heat is The solid line in Fig. 1 denotes the curve calculated using the then assigned to the following ligand substitution reaction of a determined parameters; it reproduces the experimental data bound water molecule by an incoming DMF molecule: well. The open circles in Fig. 1 show the values of (h – Hdilv) –1 –3 calculated with Hdil = –1.2 ± 0.5 kJ mol cm . The theoretical SbCl5(H2O) + DMF  SbCl5(DMF) + H2O (6) values of –ΔH°[SbCl5(DMF)]/CSb are shown by a dashed line, which is asymptotic to 35.5 kJ mol–1, confirming that the The equilibrium constant of the reaction (6) is defined by stoichiometry of Eq. (6) is appropriate for this system. The Eq. (7): determined enthalpy of the ligand substitution reaction is connected to the enthalpy changes of complexation reactions of [(SbCl DMFH)][ O] SbCl5 with water, ΔH°W, and with DMF, ΔH°DMF, as Eq. (10): K = 5 2 (7) [(SbCl5 HO2 )][DMF] ΔH° = ΔH°DMF – ΔH°W (10) In this study, the total concentration of water is sufficiently –1 larger than CSb = [SbCl5(H2O)] + [SbCl5(DMF)] and thus the The enthalpy changes reported by Gutmann are –26.6 kcal mol –1 7 term of [H2O] can be treated as a constant. The conditional for DMF and –18.0 kcal mol for water, thus the ΔH° value is equilibrium constant, K′, is then redefined as Eq. (8): expected to be –36.0 kJ mol–1 using Eq. (10). This value is in agreement with the determined value (–35.5 kJ mol–1) in this

K [(SbCl5 DMF)] study. It is thus concluded that the DN value of DMF is 26.5 by K′ = = (8) []HO2 [(SbCl5HO 2 )][DMF] the current titration calorimetry and by using the DN value of water reported by Gutmann. The enthalpy of reaction, h, is represented by Eq. (9), using Similar analyses were carried out for the reaction heat with the enthalpy change of reaction, ΔH°, and the heat of dilution DMSO, TMU, and FA. The observed h values are plotted in per unit volume, Hdil, which is proportional to the volume, v, of Fig. 2 as a function of CL/CSb, where CL is the total concentration the titrant solution. of the titrant solution, and the obtained thermodynamic parameters are summarized in Table 1. The determined DN values are 30.0, 40.4, and 22.4 for DMSO, TMU, and FA, 106 ANALYTICAL SCIENCES FEBRUARY 2012, VOL. 28

Table 2 Reevaluated donor numbers difference in the solvation structure of Na+ in TMU, and that the precise determination using titration calorimetry newly evaluates This work Gutmann7 Popov12 the DN values of 40.4 and 22.4 for TMU and FA, respectively. DMF 26.5 26.6 — The reevaluation procedure in this study is based on the DMSO 30.0 29.8 — assumption that the bulkiness of the entering ligand does not TMU 40.4 — 31 cause the dissociation of the chloride ion at the ligand FA 22.4 — 24 substitution reaction. Because such dissociation produces the separated charges, the assumption is considered to be reasonable in 1,2-dichloroethane with low dielectric property. In conclusion, titration calorimetry is useful to obtain reliable values of DN for organic solvents. The reevaluated value (40.4) of TMU is larger than that reported previously, and means that the electron-donating property of TMU is very large in comparison with DMF and DMSO. The solvation structures of metal ions have been previously determined in TMU,14–16,19,20 and the solvation number in bulky TMU found to be smaller than those in other smaller solvents because of the steric repulsion between the bound TMU molecules in the first solvation shell. In addition to the bulkiness of the TMU molecule, its strong donating ability contributes to reduction of the solvation number because of the electronic repulsions on the metal ion.

References

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