Document Type: Original Research Article
Authors
 Essamhassan G Arafa Gomaa ^{} ^{1}
 Moged A. Berghout ^{1}
 Mohamed R. Moustafa ^{2}
 Fathy M. El Taweel ^{2}
 Hader M . Farid ^{1}^{, 2}
^{1} Chemistry Department, Faculty of Science, Mansoura University, 35516Mansoura, Egypt
^{2} Chemistry Department, Faculty of Science, Damietta University, Damietta, Egypt
Abstract
The molar solubility for 2amino4,5dimethylthiophene3carboxamide (ADTC) in pure ethanol and mixed ethanol (EtOH) water solvents were measured at five different temperatures, 293.15, 298.15, 303.15, 308.15, and 313.15 K in the used mixed solvents, the solubility were increase by increase in the mole fraction of ethanol in the mixtures and increase of temperature due to more salvation parameters. All the solvation and thermodynamic parameters for ADTC in mixed EtOH+ H_{2}O solvents were evaluated like solubility products, Gibbs free energies, enthalpies and entropies of solvation and discussed. Theoretical calculations for (ADTC) were done quantum mechanically by using Gaussian on set of calculations in ethanol for evaluating the different thermodynamic parameters.
Graphical Abstract
Highlights
 Experimetal evaluation of the thermodynamic parameters from solubility measurements.
 Theoretical calculation of the thermodynamic parameters of the used material.
 Trying to explain the experimental values theoretically.
Keywords
1. Introduction
Cosolvents (any solvent other than the first solvent) are known to affect the solubility of solutes in solutions. Theory of effects of cosolvents is desirable in order to understand the molecular interactions for changes in solubility and improve the properties of solutions [1]. The Kirhwood – Buff theory (KBT) of solutions [2] has been used to explain the effects of cosolvents on the solubility of solutes in terms of intermolecular distributions [2, 3]. KBT is an exact theory of solution mixtures and provide information for solute understanding effects [4]. The general idea for solubility of molecules to explain the local microscopic experimental results. Also studying the intermediates for salvation processes are also needed. Also explaining the chemical potentials of the solute can also be expressed by statistical thermodynamic calculations [3, 4]. Studies for a quantitative description of metal ion–solvent binding are of immense importance in various fields of chemistry, physics and biology, as well as in the technological development of various practical separation processes. The subject has drawn across the board consideration [514].
Experimental
2.1. Materials
The chemicals used 2butanone, ethyl cyanoacetamide; sulfur and morpholine are provided from Sigma Aldrich chemical company. All chemicals are used without purification to reserve them in their states. Absolute ethanol provided from ElNasr Chemical and Pharmaceutical Company was used. High conductivity water was used.
2.2. Synthesis
The starting 2amino4,5dimethylthiophene3carboxamide(ADTC) 4 was obtained via Gewald reaction by condensation of 2butanone 1 with ethyl cyanoacetamide 2 in the presence of elemental sulphur and morpholine 3 (base) as in Scheme 1. The structures were confirmed by various spectroscopic techniques, including IR, 1H NMR and mass spectroscopy. The IR spectra of compound showed characteristic absorption bands in the region within υ = 34113163 cm–1 due to the stretching vibrations of 2 NH_{2} groups. The bands in the region within υ = 1670 cm–1 are due to the stretching vibrations of carbonyl group. The absorption bands in the region within υ = 12651280 cm–1 are assigned to the stretching vibrations of 2 CH_{3} groups.
Scheme 1. 2amino4,5dimethylthiophene3carboxamide (4) was obtained via Gewald reaction by condensation of 2butanone (1) with ethyl cyanoacetamide (2) in the presence of elemental sulfur and morpholine (3).
Beside the expected signals in the 1H NMR spectrum of compound, it displayed a characteristic broad signal at d 12.97 and 13.15 ppm assigned to 2NH_{2} groups and a broad signal d 2.30 due to the methyl group protons. The mass spectrum of the compound showed the molecular ion peaks at m/z 172 (M++2), 171 (M++1), 170 (M+) which is in agreement with molecular formula of the compound C_{7}H_{10}N_{2}OS.
2.3. Preparation of saturated solutions.
The saturated solutions of 2amino4,5dimethylthiophene3carboxamide (ADTC) in mixed EtOHH_{2}O solvents were prepared by dissolving solid material (ADTC) in closed test tubes containing different mole fractions of ethanolwater solvents. The tubes were put in water thermostat of type assistant for a period of one day at temperatures 293.15, 298.15, 303.15, 308.15, and 313.15 K till equilibrium reached. The solubility of (ADTC) was measured by taking 1ml of each saturated solution putting in a small weighed beaker (10ml) and evaporate under I.R. Lamp till dryness and then weights [1517].
3. Results and discussion
3.1.Calculation of thermodynamic parameters of solvation
3.1.1.Molal solubility
The molal solubility of compound ADTC in mixed ethanol – water solvent was evaporated till dryness in small beaker.
Molal solubility (S) = (W×1000)/(M.wt)(d) (1)
W is the weight of the residue in the beaker. M.wt is the molecular weight of the compound. d is the density of solvent.
3.1.2. Solubility product
The solubility product of compound (ADTC) was calculated by using (eq. 2)
Where Pk_{sp} is the solubility product and S is the molal solubility and all the data at different temperatures were calculated in tables 15.
Table 1: Molal solubility (S), Log S, log activity coefficient (log γ), solubility product (pK_{sp}), Gibbs free energy (ΔG) , transfer Gibbs free energy (ΔG_{t}) for ADTC at different mole fraction (X_{s}) and different concentrations of EtOH in EtOH – H_{2}O mixtures at 293.15 K.
EtOH vol. % 
X_{s} 
S 
Log S 
log 
pK_{sp} 
ΔG_{s} in (kJ mol^{1}) 
ΔG_{t} in (kJ mol^{1}) 
0 
0 
0.0163 
1.788 
0.0507 
3.6782 
20.646 
0.000 
20 
0.0717 
0.0263 
1.579 
0.06299 
3.2846 
18.436 
2.209 
40 
0.1708 
0.0371 
1.43 
0.07493 
3.0103 
16.897 
3.749 
60 
0.3166 
0.0707 
1.151 
0.10013 
2.502 
14.043 
6.602 
80 
0.5527 
0.6334 
0.198 
0.21273 
0.8221 
4.6144 
16.031 
100 
1 
1.9717 
0.2948 
0.63966 
0.6897 
3.871 
16.775 
Table 2: Solubility S, Log Solubility, log activity coefficient (log γ), solubility product (pK_{sp}), Gibbs free energy (ΔG) , transfer Gibbs free energy (ΔG_{t}) for ADTC at different mole fraction (X_{s}) and different concentrations of EtOH in EtOH – H_{2}O mixtures at 298.15 K.
EtOH vol. % 
X_{s} 
S 
Log S 
log 
pK_{sp} 
ΔG_{s} in (kJ mol^{1}) 
ΔG_{t} in (kJ mol^{1}) 
0 
0 
0.0189 
1.724 
0.05397 
3.5566 
20.304 
0.000 
20 
0.0717 
0.032 
1.495 
0.06815 
3.1265 
17.848 
2.456 
40 
0.1708 
0.0425 
1.372 
0.07903 
2.9014 
16.563 
3.740 
60 
0.3166 
0.11 
0.959 
0.11511 
2.1475 
12.259 
8.044 
80 
0.5527 
0.6974 
0.157 
0.21781 
0.7487 
4.2739 
16.030 
100 
1 
2.0133 
0.3039 
0.65124 
0.6947 
3.9657 
16.338 
Table (3): Solubility S, Log Solubility, log activity coefficient (log γ), solubility product (pK_{sp}), Gibbs free energy (ΔG) , transfer Gibbs free energy (ΔG_{t}) for ADTC at different mole fraction (X_{s}) and different concentrations of EtOH in EtOH – H_{2}O mixtures at 303.15 K.
EtOH vol. % 
X_{s} 
S 
Log S 
log 
pK_{sp} 
ΔG_{s} in (kJ mol^{1}) 
ΔG_{t} in (kJ mol^{1}) 
0 
0 
0.0195 
1.709 
0.05534 
3.5291 
20.484 
0.000 
20 
0.0717 
0.0386 
1.413 
0.07351 
2.9728 
17.256 
3.229 
40 
0.1708 
0.045 
1.347 
0.08084 
2.856 
16.577 
3.907 
60 
0.3166 
0.1141 
0.943 
0.1176 
2.121 
12.311 
8.173 
80 
0.5527 
0.7717 
0.113 
0.22356 
0.6723 
3.9022 
16.582 
100 
1 
2.2286 
0.348 
0.66681 
0.6376 
3.7007 
16.784 
Table 4: Solubility S, Log Solubility, log activity coefficient (log γ), solubility product (pK_{sp}), Gibbs free energy (ΔG) , transfer Gibbs free energy (ΔG_{t}) for ADTC at different mole fraction (X_{s}) and different concentrations of EtOH in EtOH – H_{2}O mixtures at 308.15 K
EtOH vol. % 
X_{s} 
S 
Log S 
log 
pK_{sp} 
ΔG_{s} in (kJ mol^{1}) 
ΔG_{t} in (kJ mol^{1}) 
0 
0 
0.0215 
1.669 
0.0581177 
3.4533 
20.375 
0.000 
20 
0.0717 
0.0389 
1.41 
0.07705477 
2.9747 
17.551 
2.824 
40 
0.1708 
0.0467 
1.331 
0.08757112 
2.8373 
16.74 
3.635 
60 
0.3166 
0.119 
0.925 
0.13776618 
2.1246 
12.536 
7.839 
80 
0.5527 
0.906 
0.043 
0.28244954 
0.6506 
3.8388 
16.536 
100 
1 
2.4116 
0.3823 
0.6889448 
0.6133 
3.6186 
16.756 
Table 5: Solubility S, Log Solubility, log activity coefficient (log γ), solubility product (pK_{sp}), Gibbs free energy (ΔG) , transfer Gibbs free energy (ΔG_{t}) for ADTC at different mole fraction (X_{s}) and different concentrations of EtOH in EtOH – H_{2}O mixtures at 313.15 K
EtOH vol. % 
X_{s} 
S 
Log S 
log 
pK_{sp} 
ΔG_{s} in (kJ mol^{1}) 
ΔG_{t} in (kJ mol^{1}) 
0 
0 
0.0234 
1.631 
0.0607354 
3.3829 
20.284 
0.000 
20 
0.0717 
0.043 
1.367 
0.0818743 
2.8971 
17.371 
2.913 
40 
0.1708 
0.0499 
1.302 
0.093041 
2.7904 
16.731 
3.552 
60 
0.3166 
0.1236 
0.908 
0.1519647 
2.1198 
12.71 
7.574 
80 
0.5527 
0.933 
0.03 
0.2996969 
0.6597 
3.9553 
16.328 
100 
1 
2.6349 
0.4208 
0.727544 
0.6136 
3.6788 
16.605 
Table 6: Enthalpy change (ΔH ) and entropy change (ΔS ) of solvation for ADTC in (EtOH–H_{2}O) mixed solvents at different temperatures in (kJ mol^{1}).
EtOH vol. % 
X_{s} 
Δ H (kJ mol^{1}) 
Δ S 293.15K 
Δ S 298.15K 
Δ S 303.15K 
Δ S 308.15K 
Δ S 313.15K 
0 
0 
24.423 
0.0129 
0.0138 
0.0130 
0.0131 
0.0132 
20 
0.0717 
32.757 
0.0489 
0.0500 
0.0511 
0.0493 
0.0491 
40 
0.1708 
17.797 
0.0031 
0.0041 
0.0040 
0.0034 
0.0034 
60 
0.3166 
28.094 
0.0479 
0.0531 
0.0521 
0.0505 
0.0491 
80 
0.5527 
14.991 
0.0354 
0.0359 
0.0366 
0.0362 
0.0352 
100 
1 
8.222 
0.0148 
0.0143 
0.0149 
0.0149 
0.0145 
3.1.3. Activity coefficient
The activity coefficients were calculated using Debye – Hückel equation (3) [18] and their values and the solubilities are given in tables 1 &2.
log =  0.5062 x (S)^{0.5} (3)
3.1.4. Free energy of solvation
From the solubility products the Gibbs free energies of solvation and the transfer Gibbs free energies from water to mixed solvents were calculated by using equations 4 & 5.
Δ G_{s} = RT ln pK_{sp} (4)
Δ G_{t} = Δ G_{S} – Δ G_{w} (5)
All the data are tabulated in tables 15 at different temperatures and shown in figures 3 &4 .
3.1.5. Enthalpies and entropies of solvation
Enthalpies can be calculated by drawing a relation between log Ksp for ADTC against 1/T, the slope=∆H/2.303R. So, the entropy (ΔS) of solvation for ADTC concentration solutions can be calculated using GibbsHelmholtz equation [1925].
Δ G = Δ H  T Δ S_{ } (6)
All the data are tabulated in table 6. The solvation experimental thermodynamic parameters ΔG and ΔS for ADTC in mixed EtOHH_{2}O solvents are increased with increase in the percentage (mole fraction) of ethanol in the mixed solvents favoring more solutesolvent interactions.
The enthalpy changes are decrease with increase of the ethanol percentage favoring more endothermic solvation process. Little effect of temperature is noticed experimentally for solvation of ADCT in mixed EtOHH_{2}O solvents due to small entropies of solvation and the endothermic reaction happened.
3.2. Theoretical Thermochemistry of the new Schiff base, ADTC
The equation used entropy, energy and heat capacity resulting from the calculation frequencies using Gaussian 09 package are given below [2630]:
Where N = n N_{A} , K_{B} = R , N_{A} is Avogadro's number , R is gas constant and Q is the partition function changing into logarithm we obtain:
Where Q is the partition function (total), the Q_{t}, Q_{e}, Q_{r}, Q_{v}, denote, the translational, electronic, rotational and vibrational partition function. The thermal energy can be obtained from the partition function:
The heat capacity can be obtained by using equation 10 :
Where CV is the heat capacity at constant volume, is the difference in internal energy , is the difference in temperatures used, N is the number of particles, . υ is the vibrational quantum number The above equations will be used for estimation the available thermodynamic for the organic compounds used from the evaluated partition functions. The calculations were done from the contributions for the translation, rotational motion and electronic contributions from vibrational mode of contribution.The data were obtained from frequency analysis by the need or partition function. For vibrational motion, choosing the first vibrational energy K, level to be zero level, the corresponding partition function is expressed as [31, 32].
Where KB is Baltzmann constant (K_{B} =1.38066 X 10^{23} J/K), h is planck's constant (h=6.626 x 10^{23} J.S) and hυk / K_{B}T = v, k is defined as vibrational frequency of mode k. The zero of energy is defined as the fully dissociated limit (free electrons and bore nuclei), at absolute zero temperature, which is the small motion of molecules and is called “the zeropoint vibrational energy” (ZPVE or ZPE). The ZPVE must be added to obtain energy at absolute zero temperature (T=0 K). For all the 3N6 (3N5 for linear molecules) vibrational modes, the total ZPVE [2830]is:
The ZPVE is calculated for compounds using the data are given in table (7, 8 and 9) for the different solutions [33, 34].
3.2.1. Different contributions of Motions
The different types of motions were theoretically studied for the schiff bases and summarized in the next text.
3.2.1.1. Contributions from translation
The translational partition function is used to calculate the translational entropy (which donate the factor e which comes from Stirling's approximation [3036]:
The contribution to internal energy is:
Finally, the heat capacity at constant volume is given by
3.2.1.2. Contributions from electronic motion
The contributions can be calculated from electronic partition function
Where w is the degeneracy of energy level, En is the energy in nth level.
The entropy due to electronic motion is:
Since there are no temperature dependent terms in partition functions, the electronic capacity and internal energy due to electronic motion are both zero.
3.2.1.3. Contribution from rotational motion:
For linear molecules, the rotational partition function is:
Where _{r} = h^{2} / 8 ^{2} I k_{B }, I is the moment of inertia. _{r} is the rotational diameter. The rotational contribution to the entropy is:
The contribution to rotation for for internal energy is:
And the contribution to the heat capacity is:
For our general case which is nonlinear, the rotational energy and heat capacity are:
3.2.1.4. Contributions from vibrational motion
The contributions follow equation (19):
The total entropy, energy and C_{υ} from the vibrational partition function are:
3.2.1. Thermochemistry studies of 2amino4,5dimethylthiophene3carboxamide (ADTC)
Different partition functions (Q) values for compound ADTC in ethanol were studied by three different methods i.e. Hartreefock 6311g(d,p), PM3 and AM1 and tabulated in table 7. As concluded, the vibration partition function (Q) values for all ADTC are greater than transitional and rotational values. In table 8, Different quantum chemical results for compound ADTC in ethanol were calculated by three different methods (HartreeFock 6311g(d,p), PM3 and AM1). The dipole moment, HOMO and LUMO energy levels are also calculated for ADTC in the table. As shown in the table 9, the Sum of electronic and zero point energies, Sum of electronic and thermal energies, Sum of electronic and thermal enthalpies and Sum of electronic and thermal free energies for ADTC in ethanol by three different methods were tabulated. The basis set used for calculations is 6311g for HartreeFock method. Electronic, translational and rotational partition functions are calculated for ADTC in pure ethanol solvent. Most of the data obtained theoretically are approximately similar other than parameters like the total energy of ADTC, HOMO, LUMO energies.
Table. 7.Different partition functions (Q) values for compound ADTC in ethanol by using three different methods (Hartreefock 6311g(d,p), PM3 and AM1).

Hartreefock 6311g 
PM3 
AM1 


Q 
Ln (Q) 
Q 
Ln (Q) 
Q 
Ln (Q) 
TotalBot 
0.307740D64 
148.543946 
0.213198D57 
132.792885 
0.358527D60 
139.180856 
Total V=0 
0.121789D+18 
39.341070 
0.238734D+19 
42.316710 
0.185038D+18 
39.759339 
Vib (Bot) 
0.331913D78 
180.704520 
0.225949D71 
164.970988 
0.390508D74 
171.331603 
Electronic 
0.100000D+01 
0.000000 
0.100000D+01 
0.000000 
0.100000D+01 
0.000000 
Translational 
0.871617D+08 
18.283275 
0.871617D+08 
18.283275 
0.871617D+08 
18.283275 
Rotational 
0.106374D+07 
13.877299 
0.108255D+07 
13.894828 
0.105334D+07 
13.867472 
Table. 8. Different quantum chemical results for compound ADTC in ethanol by three different methods (Hartreefock 6311g(d,p), PM3 and AM1).

Hartreefock 6311g 
PM3 
AM1 
Eps 
24.852000 
20.493000 
24.852000 
SCF Done (A.U.) 
E(RHF)= 852.330476048 
E(RPM3) = 0.479586987603E01 
E(RAM1) = 0.604958234463E01 
Dipole moment (Debye) 
4.6889 
2.9204 
3.4629 
HOMO 
0.29205 
0.32233 
0.31447 
LUMO 
0.12374 
0.01781 
 0.00573 
KE 
8.492668572995D+02 
3.860527198823D+01 
3.795418230410D+01 
Rotational temperatures 
0.06745 K 
0.06596 K 
0.06767 K 
Rotational constants (GHZ) 
1.40541 
1.37434 
1.40991 
Exact polarizability 
159.455 
144.205 
163.291 
Zeropoint vibrational energy 
111.31918 
103.74992 
106.01950 
Stoichiometry C7H10N2OS, Deg. of freedom 57, Full point group C1
Table. 9. Theoretical thermodynamic parameters for compound ADTC in ethanol by three different methods (Hartreefock 6311g(d,p), PM3 and AM1)

Hartreefock 6311g 
PM3 
AM1 
Sum of electronic and zeropoint Energies 
852.153078 
0.117377 
0.108457 
Sum of electronic and thermal Energies 
852.141726 
0.130063 
0.120356 
Sum of electronic and thermal Enthalpies 
852.140782 
0.131007 
0.121300 
Sum of electronic and thermal Free Energies 
852.190223 
0.077422 
0.070917 
Table 10. Different thermodynamic parameters such as thermal, heat capacity at constant volume CV, entropies for the electronic, translational, rotational and vibrational movement for ADTC in ethanol by applying three different methods

Hartreefock 6311g 
PM3 
AM1 


E (Thermal) KCal/mol 
CV Cal/molKelvin 
S Cal/molKelvin 
E (Thermal) KCal/mol 
CV Cal/molKelvin 
S Cal/molKelvin 
E (Thermal) KCal/mol 
CV Cal/molKelvin 
S Cal/molKelvin 
Total 
118.442 
42.304 
104.058 
111.710 
44.762 
112.778 
113.486 
43.623 
106.041 
Electronic 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
Translational 
0.889 
2.981 
41.301 
0.889 
2.981 
41.301 
0.889 
2.981 
41.301 
Rotational 
0.889 
2.981 
30.558 
0.889 
2.981 
30.593 
0.889 
2.981 
30.538 
Vibrational 
116.665 
36.343 
32.199 
109.933 
38.801 
40.885 
111.709 
37.661 
34.202 
Kinetic energy, rotational constant, polarizability, zero point vibrational energy are calculated by applying the three methods and found that they are greater on using Hartreefock method than others. Sum of electronic+ zero point energies, sum of electronic + thermal energies and sum of electronic+ thermal enthalpies was calculated by using the above mentioned methods and found to be greater using Hartreefock method than others. The different thermodynamic parameters such as thermal, heat capacity at constant volume CV, entropies for the electronic, translational, rotational and vibrational movement for ADTC in ethanol were also calculated by applying the three different methods theoretical and found to give the greatest values on using PM3 method supporting the activity of ADTC in ethanol medium (table 10). The electronic gap energy E(LUMO)–E(HOMO) gave bigger result 0.4157 eV (electron Volt) in case of Hartreefock method than other methods indicating the applicability of this compound ADTC as semiconductor. As shown in Fig. 5, the shape of HOMO and HOMO1 indicate that HOMO orbitals are full occupied than that of HOMO1. Also LUMO orbitals are clear to have more orbital free to be occupied than that of LUMO+1orbitals.
Fig. 6. The HOMO1, HOMO, LUMO, LUMO+1 for ADTC in ethanol.
Conclusions
The solvation experimental thermodynamic parameters ΔG and ΔS for ADTC in mixed EtOHH_{2}O solvents are increased with increase in the percentage (mole fraction) of ethanol in the mixed solvents favoring more solutesolvent interactions. The enthalpy changes are decreased with increase of the ethanol percentage favoring more endothermic solvation process. Different methods of calculation were proceeded like, HartreeFock 6311g (d,p), PM_{3} and AM1 fore estimating the different thermodynamic parameters in ethanol. The different thermodynamic parameters like thermal, heat capacity at constant volume CV, entropies for the electronic, translational, rotational and vibrational movement and other theoretical parameters for ADTC in ethanol were also calculated by applying the three different methods theoretical and found to give the grate values supporting the activity of ADTC in ethanol medium. This indicates that the solubility of ADCT is increased by increase in ethanol mole fraction in the mixed solvents.
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