Measurment, correlation and DFT study for solubility of glutaric acid in water+ethanol binary solvents at T = (293.15 to 313.15) K

R. R. Pawar, S. B. Nahire^*

Department of Chemistry, M.S.G. College Malegaon (M.S.) India

*Email :- nahiresandip@gmail.com

ABSTRACT:

The solubility of Glutaric acid in water, ethanol and water + ethanol binary solvent was determined over the entire composition range between 0 to 1 weight fraction of ethanol at (293.15, 295.15, 298.15, 300.15, 303.15, 305.15, 308.15, and 313.15) K. The Apelblat and van’t Hoff equation was used to correlate the experimental solubility data and the equations provide better correlation in this study. The activity coefficients were calculated to evaluate molecular solute-solvent interaction. DFT was carried out to correlate solubility in various solvents system. Thermodynamic properties (, %ζH, %ζTS) of solution were calculated using van’t Hoff equation.

KEY WORDS: Solubility, Glutaric acid, Apelblat equation, DFT

INTRODUCTION

Glutaric acid is an important chemical raw material which is widely used in the production of plastics, dyes, surfactants, polyamides, and polyurethanes, particularly for the manufacture of pharmaceuticals, agricultural chemicals, synthetic rubbers, and so forth^1-3. In industrial manufacturing processes, glutaric acid can be obtained via crystallization from mixed dibasic acids. So, it is difficult to obtain high purity glutaric acid. Therefore, it is important to separate and recover glutaric acid from the byproducts (mixed dibasic acid)⁴. Pure glutaric acid can be obtained by the method of repeated recrystallization from some common solvents, such as cyclohexanol, cyclohexanone, water, acetone, and so on. It is well-known that solid−liquid phase equilibrium data play an important role in the development and operation of crystallization processes⁵. Solubility is an important basic property of solid–liquid equilibrium (SLE) in the chemical industry. Such data are required for the proper design and optimization of various chemical processes⁶. However, the solubilities of glutaric acid are rarely available. Therefore solubilities of glutaric acid in water, ethanol and water + ethanol binary mixtures over different composition is determined at various temperatures and correlated by Apelblat equation. The activity coefficients were calculated to evaluate molecular solute-solvent interaction.

EXPERIMENTAL

Materials and Apparatus:

In these investigations, triple distilled water was used. Glutaric Acid was supplied by MERCK with purity 99.5% and Ethanol 99.9 % was supplied by Jiangyin Huaxi International Trade Co. (China).

The apparatus and procedures used for solubility measurement have been described earlier in detail^7-9. Briefly in this work; an excess amount of glutaric acid was added to the binary solvents mixtures prepared by weight (Shimadzu, Auxzzo) with an uncertainty of ± 0.1 mg, in a specially designed 100 mL double jacketed flask. Water was circulated at constant temperature between the outer and inner walls of the flask. The temperature of the circulating water was controlled by thermostat to within (± 0.1) K. The solution was continuously stirred using a magnetic stirrer for long time (about 1 h) so that equilibrium is assured and the solution was allowed to stand for 1 h. Then a fixed quantity of the supernatant liquid was withdrawn from the flask in a weighing bottle with the help of pipette which is hotter than the solution. The weight of this sample was taken and the sample was kept in an oven at 343 K until the whole solvent was evaporated. This was confirmed by weighing two or three times until a constant weight was obtained. The solubility has been calculated using weight of solute and weight of solution. Each experimental value of solubility is an average of at least three different measurements. The saturated mole fraction solubility (X_b), initial the mole fraction of ethanol (), and initial the mole fraction of water () were calculated using usual Eq. 1 and 2:

(1)

and (2)

Where m_B, m_A, and m_C are the mass of solute, water, ethanol respectively, and M_b, M_A, and M_C are the molecular weight of the solute, water, and ethanol, respectively.

DFT Study:-

Density functional theory (DFT) calculations were carried out using Gaussian 03 method^10,11 to correlate difference in solubilities in pure solvents. Geometry optimizations for all structures carried out at the B3LYP/6-311+ G (d, p) levels. After the geometries of all involving molecules were optimized at this level, the interaction energy E_inter was calculated as¹²:

E_inter = E_glu-sol − E_glu − E_sol (3)

Where E_glu, E_sol, and E_glu−solare the total energies of glutaric acid, solvent and glutaric acid with each solvent, respectively.

RESULTS AND DISCUSSION

Verification of the experimental methods

To verify the reliability and accuracy of the experimental apparatus and method, the solubilities of glutaric acid in pure water (Table 1) were measured and compared with the literature data^13-14 respectively. Our results agree well with the published data which indicates the experimental apparatus and method used in this work is reliable.

Table 1: Comparison of Experimental Solubility of glutaric acid with Literature.

Solvent	T/K	X_b
Solvent	T/K	Expt.	Lit.
Water	293.15	0.1305	0.1385^a
	298.15	0.1544	0.1600^a	0.1789^b
	308.15	0.1976	0.2161^a
	313.15	0.2118	0.2493^a	0.2665^b

Where a = [13], b = [14]

Solubility Data

The experimental solubility (X_B) data of glutaric acid in water, ethanol and water + ethanol mixtures at (293.15, 296.15, 298.15, 300.15, 303.15, 305.15, 308.15, 310.15 and 313.15) K is listed in Table 2.

Table 2. Mole fraction solubility X_b of glutaric acid in water + ethanol binary mixtures for various initial mole fractions ( ) of ethanol.

	X_b
	293.15	296.15	298.15	300.15	303.15	305.15	308.15	310.15	313.15
0.0000	0.1305	0.1448	0.1544	0.1547	0.1845	0.1819	0.1976	0.1915	0.2118
0.0416	0.1435	0.1632	0.1711	0.1813	0.1972	0.2133	0.2278	0.2399	0.2461
0.0891	0.1621	0.1930	0.1860	0.1959	0.2185	0.2501	0.2577	0.2560	0.2676
0.1435	0.1763	0.1874	0.1998	0.2057	0.2258	0.2351	0.2520	0.2604	0.2766
0.2068	0.1863	0.2001	0.2079	0.2176	0.2356	0.2435	0.2624	0.2763	0.2854
0.2811	0.1835	0.2043	0.2215	0.2361	0.2547	0.2684	0.2822	0.2861	0.3148
0.3697	0.2098	0.2237	0.2367	0.2416	0.2478	0.2662	0.2866	0.3076	0.3185
0.4771	0.2175	0.2360	0.2422	0.2500	0.2621	0.2800	0.2844	0.3158	0.3271
0.6100	0.2242	0.2344	0.2451	0.2555	0.2670	0.2750	0.2922	0.3129	0.3358
0.7787	0.2180	0.2351	0.2440	0.2512	0.2641	0.2784	0.2884	0.2957	0.3055
1.0000	0.2215	0.2276	0.2400	0.2494	0.2683	0.2769	0.2964	0.3081	0.3280
	0.2081	0.2230	0.2335	0.2444	0.2615	0.2735	0.2923	0.3055	0.3262

The results shows that the solubility of glutaric acid in water, ethanol and water + ethanol mixtures increases with temperature at given initial compositions (Fig.1). But solvent composition has different effect on solubilities of glutaric acid (Fig. 2). The solubilities of the glutaric acid in water + ethanol mixtures increases with increasing mole fraction () of ethanol upto ( = 0.6100). But solubility of glutaric acid at ( = 0.7787) was found to be less than the solubilities in pure ethanol. In this work, the solubility of glutaric acid is higher in pure ethanol than water indicates polarity of solvent has no effect on solubility. This can be explained from interaction energy E_inter between glutaric acid and pure solvents (water and ethanol) calculated by DFT.

The minimum energy geometries of glutaric acid, glutaric acid + water, glutaric acid + ethanol are shown in Fig. 3 and Fig. 4. The order of absolute value of E_inter is ethanol (43.848 KJ/mol) > water 43.3912). This result justifies the experimental solubility trend. Means that higher the absolute value of interaction energy, stronger the interaction between solvent and solute molecule, and hence solute dissolve more easily in the corresponding solvents.

Fig.1 Mole fraction solubility (X_b) variation with temperatures

Fig.2 Mole fraction solubility (X_B) variation with initial mole fraction () of ethanol at various temperatures

Fig. 3 Optimized structure of glutaric acid

a) b)

Fig.4) Interaction between glutaric acid and water (a), water + ethanol (b) respectively

Ideal Solubilities and activity coefficients for Glutaric acid

The ideal solubility of glutaric acid (x^idl) was calculated using equation 4. ^15-16

(4)

Here R is universal gas constant (R = 8.314 J mol^-1K^-1) and ΔC_p is difference in molar heat capacity of liquid state from that of crystalline state.

The values of T_fus, ΔH_fus and ΔC_p for glutaric acid have reported in the literature¹⁷. These values were used to calculate using equation 4 and results are listed in table 2.

The activity coefficients (γ) of glutaric acid in each solvent system are calculated using equation 5.

(5)

The γ values for glutaric acid in each solvent system at T = (293.15 to 313.15) K are listed in Table 3.

Table 3: Activity Coefficient (γ) of glutaric acid in water + ethanol binary mixtures at T = (293.15 to 313.15) K

	T / K
	293.15	296.15	298.15	300.15	303.15	305.15	308.15	310.15	313.15
0.0000	1.5940	1.5407	1.5121	1.5791	1.4175	1.5035	1.4792	1.5955	1.5400
0.0416	1.4502	1.3663	1.3643	1.3480	1.3261	1.2819	1.2834	1.2733	1.3253
0.0891	1.2837	1.1554	1.2553	1.2476	1.1966	1.0934	1.1341	1.1932	1.2190
0.1435	1.1801	1.1898	1.1689	1.1879	1.1580	1.1632	1.1602	1.1730	1.1791
0.2068	1.1169	1.1144	1.1232	1.1230	1.1097	1.1230	1.1140	1.1055	1.1429
0.2811	1.1340	1.0916	1.0543	1.0349	1.0265	1.0188	1.0357	1.0679	1.0362
0.3697	0.9918	0.9971	0.9865	1.0114	1.0553	1.0274	1.0199	0.9931	1.0239
0.4771	0.9569	0.9451	0.9640	0.9775	0.9976	0.9768	1.0277	0.9672	0.9971
0.6100	0.9283	0.9514	0.9526	0.9565	0.9795	0.9943	1.0005	0.9762	0.9713
0.7787	0.9544	0.9487	0.9569	0.9730	0.9900	0.9822	1.0135	1.0332	1.0678
1.0000	0.9397	0.9799	0.9730	0.9799	0.9744	0.9877	0.9862	0.9914	0.9944

It was observed a very little effect in the values of γ with temperature at initial composition of ethanol. The values of γ do not depend only on temperature but also on ideal solubility and fusion temperature. But the values of γ for glutaric acid were found to be decreases with the increase in concentration of ethanol in the solvent mixture at each experimental temperature. This trend of γ for glutaric acid were in good agreement with solubility results that the solubility of glutaric acid increases with mole fraction () of ethanol. Based on these results, for glutaric acid, higher solute-solvent molecular interactions were observed in water+ ethanol mixtures as compared to pure water as a solvent.

Correlation of Experimental Data

The experimental mole fraction solubilities of glutaric acid were correlated with two different equations including “Apelblat and van't Hoff equations”

The Modified Apelblat equation is a semi-empirical equation, which is widely used to correlate the solid-liquid equilibrium. In this work, the solubility of glutaric acid at different temperatures was described by the modified Apelblat equation¹⁸.

(6)

Where X_b and T are mole fraction of solute and absolute temperature, respectively and A, B, and C are empirical constants. The A and B reflecting the non-idealities of the real solution in term of variation of activity coefficient in the solution, and C representing the effect of temperature on the fusion enthalpy^19,20. The experimental mole fraction solubility in Table 1 was correlated with eq. 6 and the parameter values of A, B, and C is given in Table 4.

The van't Hoff equation is widely used to describe the relationship between solute and the temperature T/K considering the influence of the solvent as an ideal solution model, which can be described as

(7)

In this equation, the logarithm of solubility X_b is linear with the reciprocal of thermodynamic temperature. Where T represents the system temperature, and A and B are equation parameters. The values of correlation coefficient (R²) for Apelblat equation and van’t Hoff equation (Table 5) indicated that these equations fit quite well in pure and binary solvents.

Table 4. Parameters of equation 6 for glutaric acid in water, ethanol and binary mixtures

	A	B	C	R²
0.0000	663.063	-31835.41	-97.964	0.9630
0.0416	581.736	-28476.98	-85.647	0.9954
0.0891	685.094	-32984.25	-101.113	0.9448
0.1435	107.849	-6734.86	-15.248	0.9973
0.2068	73.411	-5106.83	-10.153	0.9966
0.2811	691.381	-33273.42	-102.025	0.9935
0.3697	-327.108	13051.70	49.472	0.9847
0.4771	-224.693	8518.77	34.172	0.9816
0.6100	-423.607	17512.60	63.791	0.9951
0.7787	318.056	-15728.26	-46.812	0.9969
1.0000	-208.528	7753.57	31.785	0.9962

Table 5. Parameters of equation 7 for glutaric acid in water, ethanol and binary mixtures

	A	B	R²
0.0000	5.3467	-2155.51	0.9472
0.0416	6.7144	-2528.74	0.9863
0.0891	6.2346	-2350.27	0.9308
0.1435	5.4781	-2115.28	0.9969
0.2068	5.2468	-2030.88	0.9964
0.2811	6.4035	-2363.38	0.9787
0.3697	5.0363	-1936.54	0.9795
0.4771	4.7316	-1834.19	0.9788
0.6100	4.6762	-1813.98	0.9852
0.7787	3.7675	-1545.77	0.9895
1.0000	4.8704	-1876.17	0.9939

Dissolution Thermodynamics

Thermodynamics functions can be used to understand thermodynamics involved in the dissolution process of solute in various solvents. In this work the thermodynamic functions in the process of solution of glutaric acid are calculated on the basis of the solubility of glutaric acid. According to the van't Hoff equation^{21, 22}, the standard molar enthalpy change of solution is generally obtained from the slope of the ln X_bvs. 1/T plot. In the present work, T_mean = 303.03 K and a limited temperature range is 293.15 to 313.15 K in both pure solvents and binary solvent mixtures. The values of are derived using usual Eq 8:

= (8)

The slope and the intercept of the plot ln X_b vs. (1/T - 1/ T_mean) for each solvent and binary mixture are listed in Table 6.

Table 6. Thermodynamic Functions Relative to dissolution Process of glutaric acid at T_mean = 303.15 K

	slope	intercept	R²	kJK^-1mol^-1	kJK^-1mol^-1	kJK^-1mol^-1	kJK^-1mol^-1	ζH%	ζTS%
0.0000	-2155.5	-1.7662	0.9472	17.9208	4.4499	0.0445	13.4709	57.0877	42.9123
0.0416	-2536.0	-1.6299	0.9872	21.0843	4.1065	0.0560	16.9778	55.3944	44.6056
0.0891	-2404.0	-1.5177	0.9356	19.9869	3.8238	0.0533	16.1631	55.2888	44.7112
0.1435	-2115.3	-1.5021	0.9969	17.5866	3.7845	0.0455	13.8021	56.0284	43.9716
0.2068	-2030.9	-1.4550	0.9964	16.8849	3.6658	0.0436	13.2191	56.0886	43.9114
0.2811	-2363.4	-1.3954	0.9788	19.6493	3.5157	0.0532	16.1336	54.9125	45.0875
0.3697	-1936.5	-1.3541	0.9796	16.1001	3.4116	0.0419	12.6885	55.9253	44.0747
0.4771	-1834.2	-1.3211	0.9789	15.2495	3.3285	0.0393	11.9211	56.1251	43.8749
0.6100	-1814.0	-1.3098	0.9853	15.0816	3.3000	0.0389	11.7816	56.1422	43.8578
0.7787	-1545.8	-1.3334	0.9896	12.8518	3.3595	0.0313	9.4923	57.5175	42.4825
1.0000	-1876.2	-1.3208	0.9940	15.5987	3.3277	0.0405	12.2710	55.9701	44.0299

The standard molar Gibbs energy change for the solution process , can be calculated by Eq. 9:

(9)

The standard molar entropy change is obtained from Eq.10:

(10)

Both D and pertain to the mean temperature T_mean = 303.03 K. The results are shown in Table 6, together with %ζH and %ζTS. The %ζH and %ζTS represent the comparison of the relative contributions by enthalpy and entropy respectively, which are calculated by Eq. 11

% and (11)

The standard Gibbs free energy D represents the minimum energy that requires for the dissolving glutaric acid under experimental condition. Table 3 shows that the values of Dare positive and decreases with increase in mole fraction of ethanol in binary solvent system. So, the solubility of glutaric acid increases with increasing fraction of ethanol. The positive values of indicates dissolution of glutaric acid in water, ethanol and binary mixture is endothermic process. In this work, the entropy of solution is positive for all mole fraction of ethanol indicating the entropy as driving the solution process. It is observed that the main contributor to the positive standard molar Gibbs energy Dof solution of glutaric acid is the enthalpy during dissolution because the values of %ζ_Hare greater than 50%.

CONCLUSIONS

Solubility of the glutaric acid in water, ethanol and water + ethanol mixture increases with increase in temperature at given initial composition. The solubilities of the glutaric acid in water + ethanol mixtures increases with increasing mole fraction () of ethanol upto ( =0.6100). The solubility of glutaric acid is higher in pure ethanol than water indicates polarity of solvent has no effect on solubility. The calculated values of activity coefficient show higher solute-solvent molecular interactions in water + ethanol than pure water as a solvent. The experimental data are very well correlated by the Apelblat equation. The positive enthalpy and Gibb's free energy of dissolution suggest endothermic and spontaneous dissolution of glutaric acid in all the studied solvents respectively. For all mole fractions () of ethanol, the main contributor to the positive standard molar Gibbs energy of solution of Glutaric acid is the enthalpy. Computational studies based on density functional theory (DFT) were used to explain the solubility between water and ethanol.

ACKNOWLEDGEMENTS

The authors are thankful to Principal of MSG Arts, Science and Commerce College Malegaon for providing laboratory facilities. We also thanks to Prof. Arun B. Sawant for his computational guidance. The authors also express their sincere thanks to Dr Apoorva Hiray (Co-ordinator M.G. Vidyamandir Malegaon).

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Received on 07.02.2020 Modified on 02.03.2020

Asian J. Research Chem. 2020; 13(3):169-174.

DOI: 10.5958/0974-4150.2020.00033.4