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Solubility Measurement and Correlation of Probenecid in 12 Pure Organic Solvents and Thermodynamic Properties of Mixing of Solutions Jiakang Shi,†,‡ Ling Liu,†,‡ Lingyu Wang,†,‡ Zhe Ding,†,‡ and Songgu Wu*,†,‡,§

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†

National Engineering Research Center of Industrial Crystallization Technology, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China ‡ Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, China § Key Laboratory of Modern Drug Delivery and High Efficiency in Tianjin University, Tianjin 300072, China S Supporting Information *

ABSTRACT: The solubility data of probenecid in 12 different organic solvents including methanol, methyl acetate, ethanol, ethyl acetate, n-propanol, n-butanol, butyl acetate, n-pentanol, isopropanol, isobutanol, acetone, and methyl tert-butyl ether was measured using the gravimetric method over the temperatures range from 283.15 to 323.15 K at 0.1 MPa. The acetone had much higher solubility to probenecid than to other solvents. Three models, including the modified Apelblat equation, the van’t Hoff model, and the nonrandom two-liquid (NRTL) model, were applied to correlate the measured solubility data. The correlation results were evaluated by the average relative deviation (ARD). All of the ARD values were less than 4.522%, which indicated that the three models have a satisfactory correlation. The thermodynamic properties of mixing of probenecid in 12 pure organic solvents including the enthalpy of mixing, Gibbs energy of mixing, and entropy of mixing were calculated by the NRTL model using the correlation results.

1. INTRODUCTION

physiology in the human body by the inhibition of the ATP transporter, which is named Pannexin 1, in the collecting duct and proximal tubule. Recent studies showed that probenecid can also protect a mouse against transient global cerebral ischemia/reperfusion injury in mouse model experiments.6,7 Probenecid has prime pharmaceutical value and broad application. Solubility is an important property for pharmaceutical compounds in solid−liquid systems. The purity, particle size, and final yield of the product are related to the solubility as most pharmaceutical compounds are produced by crystallization.8−10 Furthermore, the dissolution rate and pharmacological bioavailability of a pharmaceutical in the human body depend on the solubility of the pharmaceutical compound.11,12

Probenecid (4-[(dipropylamino)sulfonyl]-benzoic acid, C13H19NO4S, CAS registry no. 57-66-9, Figure 1) has been applied in the treatment of gout for decades.1−5 Previous studies showed that probenecid can influence the kidney

Received: September 26, 2018 Accepted: January 10, 2019

Figure 1. Chemical structure of probenecid. © XXXX American Chemical Society

A

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the glass dish including the solid separated from the solution after drying was the mass of solvent evaporated. The difference between the mass of the glass dish including the solid separated from the solution after drying and the mass of the empty glass dish was the mass of solution. The mole fraction solubility of probenecid (x1) was calculated using the mass of the solution and solvent. The dissolution equilibrium reached within 24 h was confirmed by the same solubility measurement results of the experiment in which the slurry was extracted 36 h after the materials were added to the vessel, while the other experimental steps were the same. The measurement in the same solvent and at the same temperature was repeated three times. Then the average value of the three measurement mole fractions was calculated as the experimental mole fraction solubility under the condition that the relative deviation of the three measurement results was less than 1%. The relative standard uncertainty of the solubility measurement was estimated to be 0.01. 2.3. Identification of Polymorphs. The powder probenecid of the raw solid material before the solubility measurement and the solid probenecid obtained from methanol, methyl acetate, ethanol, ethyl acetate, n-propanol, n-butanol, butyl acetate, n-pentanol, isopropanol, isobutanol, acetone, and methyl tert-butyl ether solvents were collected for the identification of the polymorphs. The powder X-ray diffraction (PXRD) patterns of all kinds of collected powder were output by a D/Max-2500 X-ray diffractometer (Rigaku, Japan) with Cu Kα radiation (1.5405 Å). The diffraction angle (2θ) range was from 2° to 50°, and the scanning step size was 0.02°.

Therefore, solubility measurements are crucial to the preparation of the pharmaceutical. Previous studies showed that the solubility of probenecid in water has been investigated and that the solubility is poor based on the results.13 From literature retrieval, there is no record of the solubility of probenecid in other solvents such as organic solvents. Searching for an excellent solvent for probenecid by measuring the solubility as much as possible in different solvents is imperative. In this work, the solubility data of probenecid in 12 different organic solvents including methanol, methyl acetate, ethanol, ethyl acetate, n-propanol, n-butanol, butyl acetate, n-pentanol, isopropanol, isobutanol, acetone and methyl tert-butyl ether were measured using the gravimetric method over the temperatures range from 283.15K to 323.15K at 0.1 MPa.14,15 Three models, including the modified Apelblat equation, van’t Hoff equation, and nonrandom two-liquid (NRTL) model, were applied to correlated the measured solubility data. The thermodynamic properties of mixing were calculated by the correlation results of the NRTL model.

2. EXPERIMENTAL SECTION 2.1. Materials. Probenecid, which was purchased from Adamas-beta Reagent Co., Ltd., had a mass fraction purity of more than 98%. The 12 organic solvents, which were purchased from Jiangtian Chemical Technology Co., Ltd., had a mass fraction purity of more than 99.5%. The details of the materials are shown in Table S2. 2.2. Experimental Apparatus and Methods. The main experimental apparatus includes a jacketed glass vessel with a magnetic stir bar in it and a constant-temperature bath (Julabo CF41, Germany). The uncertainty of the constant-temperature bath is ±0.01 K.16 The water was constantly circulated from the thermostated bath to the jacket of the vessel to maintain the temperature in the jacked glass vessel. The magnetic stir bar, which was driven by the magnetic drive device under the jacketed glass vessel, rotated and mixed the solid powder of probenecid and the liquid organic solvent. A mercury thermometer was inserted into the jacked vessel to measure the temperature of the solid−liquid mixtures in the vessel. The uncertainty of the mercury thermometer was ±0.05 K. The jacked vessel was sealed to prevent the solvent from evaporating. The experimental method for the solubility measurement is the gravimetric method, which was validated by comparing the solubility data of sulfachloropyridazine in methanol and ethanol listed in the published paper with the experimental solubility data measured by this method. (See the Supporting Information and Table S1.) A certain amount of the liquid organic solvent and an excess amount of solid probenecid were added to the vessel and mixed with the rotating magnetic stir bar at constant temperature. Then, the probenecid dissolved until dissolution equilibrium was reached. After 24 h, the slurry was extracted with a syringe from the vessel and injected through a microporous filter membrane with 0.22 μm micropore diameter into a prepared glass dish. The total mass of the glass dish including the clear solution in it was measured with an electronic balance (Mettler Toledo ML204, Switzerland). The uncertainty in the electronic balance was ±0.0001 g. The glass dish with solution in it was dried in a vacuum oven at about 333.15 K until the total mass did not change over time. The difference between the mass of the glass dish including the clear solution before drying and the mass of

3. RESULTS AND DISCUSSION 3.1. Results of the Identification of Polymorphs. The PXRD patterns of probenecid obtained from different solvents including methanol, methyl acetate, ethanol, ethyl acetate, npropanol, n-butanol, butyl acetate, n-pentanol, isopropanol, isobutanol, acetone and methyl tert-butyl ether and raw solid material are presented in Figure 2. There is no new peak that appears as compared to the PXRD patterns of probenecid

Figure 2. PXRD patterns of probenecid obtained from different solvents and raw material. B

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Figure 3. Experimental mole fraction solubility of probenecid in different solvents. Black ■, methanol; red ●, ethanol; blue ▲, n-propanol; pink ▼, n-butanol; green ◆, n-pentanol; blue ◀, acetone.

Figure 4. Experimental mole fraction solubility of probenecid in different solvents. Black ■, isopropanol; red ●, isobutanol; blue acetate; pink ▼, ethyl acetate; green ◆, butyl acetate; blue ◀, methyl tert-butyl ether.

▲,

methyl

probenecid in acetone was the highest compared to that of other solvents, and the lowest solubility was in butyl acetate. The sequence of the experimental solubility data can be ranked as acetone > alcohols (i.e., n-pentanol, n-butanol, n-propanol, ethanol, methanol) > methyl tert-butyl ether > esters (i.e., methyl acetate, ethyl acetate, butyl acetate), and the acetone had much higher solubility to probenecid than did other solvents. Some properties of the solvents which usually have a remarkable influence on solubility, including polarities, dipole moments, dielectric constants, and solubility parameters, are collected and listed in Table 1.39 In Table 1, the 12 solvents were classified as polar protic solvents and polar aprotic solvents to discuss the differences in solubility. The polar protic solvent group included methanol, ethanol, n-propanol,

obtained from 12 different solvents to that of the raw material probenecid. That there is no phase transformation for probenecid before and after the solubility measurement experiments in these different solvents was confirmed by the identical PXRD patterns.17 3.2. Results of Solubility Measurement and Solubility Data. The experimental solubility data of probenecid in these 12 different organic solvents over the temperatures range from 283.15 to 323.15 K at 0.1 MPa are presented in Figures 3 and 4 and are listed in Table S3. The logarithm of the experimental mole fraction solubility versus the reciprocal of the absolute temperature is plotted in Figures 5 and 6. From the data presented in Figures 3 and 4, the experimental solubility of probenecid increases with increasing temperature in each organic solvent. The solubility of C

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Figure 5. Plots of the logarithm of experimental mole fraction solubility versus the reciprocal of the absolute temperature in different solvents. Black ■, methanol; red ●, ethanol; blue ▲, n-propanol; pink ▼, n-butanol; green ◆, n-pentanol; blue ◀, acetone.

Figure 6. Plots of the logarithm of experimental mole fraction solubility versus the reciprocal of the absolute temperature in different solvents. Black ■, isopropanol; red ●, isobutanol; blue ▲,methyl acetate; pink ▼, ethyl acetate; green ◆, butyl acetate; blue ◀, methyl tert-butyl ether.

n-butanol, n-pentanol, isopropanol, and isobutanol, and the polar aprotic solvents group included methyl acetate, ethyl acetate, butyl acetate, acetone, and methyl tert-butyl ether. In the polar protic solvents group, the solubility was increased with decreasing polarity for the alcohols with an n-alkyl chain. For example, the solubility can be ranked as methanol (polarity 76.2) < ethanol (polarity 65.4) < n-propanol (polarity 61.7) < n-butanol (polarity 60.2) < n-pentanol (polarity 56.8). For the alcohols with an i-alkyl chain, the solubility was also increased with the decreasing polarity and ranked as isobutanol (polarity 55.2) < isopropanol (polarity 54.6), but the solubility was not increased with decreasing polarity compared to that of the nalkyl chain alcohols and i-alkyl chain alcohols. It suggests that the polarity of solvents might not be the only factor in the solubility.

In the polar aprotic solvents group, there is no obvious relationship between the solubility and the polarity of the solvents. For methyl acetate, ethyl acetate, butyl acetate, and acetone, it can been seen that the solubility was increased with the increasing solubility parameters. The solubility can be ranked as butyl acetate (solubility parameter 8.6) < ethyl acetate (solubility parameter 9.1) < methyl acetate (solubility parameter 9.6) < acetone (solubility parameter 10), but for methyl tert-butyl ether, the solubility was higher than the solubility in methyl acetate (solubility parameter 9.6) whereas it has the lowest solubility parameter of 7.4 in the polar aprotic solvents group. From Table 1, the very small polarity of methyl tert-butyl ether (polarity 14.8) compared to the polarities of other four polar aprotic solvents, as another factor except for D

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Table 1. Properties of 12 Organic Solvents solvents

polarity (water 100)

dipole moment (298.15 K) μ/(D)

dielectric constant (293.15 K) ε/(F·m−1)

solubility parameter δ/(J·m−3)1/2

76.2 65.4 61.7 54.6 60.2 55.2 56.8

1.7 1.7 1.7 1.66 1.66 1.7 1.7

32.6 22.4 20.1 18.3 18.2 17.7 13.9

14.5 13.4 11.9 11.5 11.4 10.7

29 23 24.1 14.8

1.7 1.7 1.8 1.2

35.5

2.9

Polar Protic Solvents methanol ethanol n-propanol isopropanol n-butanol isobutanol n-pentanol Polar Aprotic Solvents methyl acetate ethyl acetate butyl acetate methyl tert-butyl ether acetone

6.7 6.02

9.6 9.1 8.6 7.4

4.5 20.6

10

Table 2. Equation and Model Parameters in 12 Organic Solvents Apelblat

van’t Hoff

NRTL −3

−1

Δg12/(J · mol )

solvents

a

b

c

A/(K)

B

methanol ethanol n-propanol isopropanol n-butanol isobutanol n-pentanol methyl acetate ethyl acetate butyl acetate methyl tert-butyl ether acetone

84.00 −133.6 39.82 −187.8 4.354 −11.71 −35.02 27.77 −59.50 −133.2 −52.29 −63.17

−7744 2444 −5335 5546 −3136 −2963 −1040 −4143 −416.6 2859 −566.8 442.1

−11.03 21.19 −4.645 28.90 0.3211 2.932 6.016 −3.285 9.811 20.79 8.6616 10.14

−4408 −3963 −3929 −3187 −3233 −3849 −2859 −3150 −3260 −3422 −3185 −2623

9.964 8.675 8.641 6.158 6.510 7.971 5.354 5.723 5.995 6.292 5.844 4.904

−1.134 −3.101 −2.637 −5.331 −4.199 −5.097 −4.555 −6.714 −6.667 −6.789 −0.6714 −4.721

F=

∑ (xi − xical)2

the solubility parameter, might enhance the solubility in methyl tert-butyl ether. In general, the solubility behavior is influenced by many factors, and it is difficulty to explain with a single reason. The factors usually include polarities, molecular shape and size, aprotic or protic, functional group, and other properties of solvents. 3.3. Correlation of the Experimental Solubility Data Values. The experimental solubility data values of probenecid were correlated with three models including the modified Apelblat equation, van’t Hoff equation, and NRTL model. 3.3.1. Modified Apelblat Equation. The modified Apelblat equation, which is a commonly applied empirical correlation equation, describes the relationship between the mole fraction solubility data and the absolute temperature.18−21 The equation is expressed as follows ln x1 = a +

b + c ln T (K) T (K)

10

i

10−3 Δg21/(J · mol−1)

α

−1.808 1.360 0.5140 8.965 5.293 6.593 6.821 12.47 12.62 13.68 1.245 6.548

0.4000 0.4000 0.4000 0.4000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.3000 0.4000

(2)

where xi refers to the mole solubility of probenecid obtained from the experimental measurement and xcal refers to the i calculated mole solubility. The correlation results, which include the calculated mole solubility, xcal 1 , and the values of parameters a, b, and c are listed in Table S3 and Table 2. 3.3.2. van’t Hoff Equation. The van’t Hoff equation describes the linear relationship between the logarithm of the mole fraction solubility data value and the reciprocal of the absolute temperature.22 The equation is expressed as follows ln x1 =

A +B T (K)

(3)

where x1 refers to the mole fraction solubility of solute probenecid, T is the absolute temperature (K), and A and B are parameters of the van’t Hoff equation which are determined by fitting the experimental mole solubility fraction values and the absolute temperature.23,24 The mathematical method and the objective function used in the van’t Hoff equation were same as used in the modified Apelblat equation. The correlation results, which include the calculated mole solubility, xcal 1 , and the values of parameters A and B, are listed in Table S3 and Table 2.

(1)

where x1 refers to the mole solubility fraction of solute probenecid, T is the absolute temperature (K), and a, b, and c are empirical regression parameters which are determined using least-squares fitting of the experimental mole fraction solubility values and the absolute temperature. The mathematical method was nonliner regression, and the objective function is expressed as follows E

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3.3.3. NRTL Model. The NRTL model is commonly applied to predict nonideal solution properties.25−28 The model is expressed as follows ÅÄÅ ÑÉÑ 2 2 Å ÑÑ τ21G21 τ12G12 ÑÑ ln γ1 = x 22ÅÅÅÅ + ÅÅÇ (x1 + G21x 2)2 (x 2 + +G12x1)2 ÑÑÑÖ (4) where x 2 = 1 − x1

Table 3. ARD for 3 Models and 12 Solvents

(5)

Δg zy ji G12 = expjjj−α12 12 zzz j RT z{ k

(6)

Δg yz ij G21 = expjjj−α12 21 zzz j RT z{ (7) k where x2 refers to the mole solubility fraction of solvent. α12 stands for the nonrandomness of the system. Δg21 and Δg12 stand for the cross-interaction energy. Δg21, Δg12, and α12 are parameters of the NRTL model which are determined by fitting the experimental mole solubility fraction values and the absolute temperature. The mathematical method was nonliner regression, and the objective function is expressed as follows F=

∑ (ln γi − ln γical)2

ARD% =

100 Np

∑ i=1

x1, i − x1, i

NRTL

1.516 2.152 1.735 2.072 0.530 1.160 0.962 0.634 1.188 2.219 1.594 1.129

1.377 2.503 1.789 2.762 0.561 1.125 3.589 4.522 2.564 3.589 4.279 1.177

Δmix S° = Δmix Sid + S

(11)

E

(12)

Δmix H ° = Δmix Hid + HE

(13)

where ΔmixG°, ΔmixS°, and ΔmixH° refer to the Gibbs energy change, the entropy change, and the enthalpy change of the mixing process, respectively. ΔmixGid, ΔmixSid, and ΔmixHid refer to the ideal Gibbs energy of mixing change, the ideal mixing entropy change, and the ideal enthalpy change, respectively. GE, SE, and HE refer to the excess Gibbs free energy, the excess entropy, and the excess enthalpy, respectively. ΔmixGid, ΔmixSid, and ΔmixHid can be calculated with the following equations

(9)

where x1 refers to the mole fraction of solute probenecid; T is the absolute temperature (K); ΔmH refers to the melting enthalpy of probenecid with a value of 40 900 J·mol−1 and an uncertainty of 200 J·mol−1; Tm refers to the melting temperature of probenecid with a value of 472.05 K and an uncertainty of 0.06K;29 and R is the gas constant with a value of 8.314 J·mol−1·K−1. Equation 9 is the thermodynamic framework that describes the relationship between the activity coefficient and the mole fraction solubility. The correlation results, which include the calculated mole solubility, xcal 1 , calculated with eq 9 using the finale value of ln γcal and the i values of parameters Δg21, Δg12, and α12, are listed in Table S3 and Table 2. 3.3.4. Average Relative Deviation. The average relative deviation (ARD) is commonly applied to evaluate the correlation,15,30 which is expressed as follows Np

van’t Hoff

1.327 3.398 1.732 1.628 0.522 1.078 1.006 0.562 1.313 4.244 1.384 1.238

Δmix G° = Δmix Gid + GE

where ln γi refers to the logarithm of the activity coefficient which was calculated using the experimental mole solubility in eq 9, expressed as follows; ln γcal refers to the calculated i logarithm of the activity coefficient i Δ H yij 1 1 yzz ln γ1 = ln x1 − jjj m zzzjjj − z j T (K) zz{ k R {k Tm

Apelblat

3.4. Thermodynamics Properties of Mixing. The thermodynamic properties of mixing are commonly characterized by the changes in Gibbs energy, enthalpy, and entropy in the mixing process of the solute and solvent. For a real solution obtained from the nonideal mixing process, the thermodynamic properties of mixing consist of the ideal mixing properties and the excess thermodynamic properties.31,32 These are expressed as follows

(8)

i

ARD % methanol ethanol n-propanol isopropanol n-butanol isobutanol n-pentanol methyl acetate ethyl acetate butyl acetate methyl tert-butyl ether acetone

Δmix Gid = RT (x1 ln x1 + x 2 ln x 2)

(14)

Δmix Sid = −R(x1 ln x1 + x 2 ln x 2)

(15)

Δmix Hid = 0

(16)

where x1 refers to the mole fraction of solute and x2 refers to the mole fraction of solvent. On the basis of the solubility correlation results of the NRTL model, GE, SE, and HE were calculated with the following equations GE = RT (x1 ln γ1 + x 2 ln γ2)

∂ ln γ2 yz i ∂ ln γ1 zz HE = −RT 2jjjjx1 + x2 ∂T z{ k ∂T

x1,cali (10)

where Np refers to the number of experimental data points in the selected solvent; x1,i refers to the experimental solubility data; and xcal 1,i refers to the calculated solubility data calculated by the selected model. The calculated ARD values for the selected solvents and the selected models or equations are listed in Table 3. The highest ARD value is 4.522%, which indicates that the three models are applicable to the binary solid−liquid systems composed of probenecid and 1 of the 12 organic solvents.

(17)

(18)

HE − GE (19) T Then ΔmixG°, ΔmixS°, and ΔmixH° were calculated with eqs 11−19. The calculation results are listed in Table S4. All values of ΔmixG° are negative, which indicates that the mixing process in the above 12 organic solvents are spontaneous.33−35 Furthermore, the absolute values of ΔmixG° increase with increasing temperature, which can be explained by the fact that SE =

F

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the solubility increased with increasing temperature and the dissolution capacity is enhanced by the increasing temperature. According to classical thermodynamics theory, the higher absolute value of ΔmixG° in the mixing process is helpful for the dissolution process and contributes to a higher thermodynamic solubility. As all values of ΔmixG° are negative, and the values of ΔmixG° decrease with increasing temperature. All values of ΔmixH° are negative, which indicates that the molecular interaction between probenecid and each of the 12 organic solvents is attractive. All values of ΔmixS° are positive, which suggests that the entropy increases during the mixing process, thus favoring the mixing process.36−38

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00863. Detailed information on the Materials; experimental and correlated mole fraction solubilityl calculated thermodynamic properties of mixing; and comparison of the solubility data of sulfachloropyridazine in methanol and ethanol listed in the published paper with the experimental solubility data measured by the authors (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel: 86-22-27405754. Fax: +86-22-27374971. E-mail: [email protected]. ORCID

Songgu Wu: 0000-0003-4329-4654 Notes

The authors declare no competing financial interest.

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REFERENCES

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4. CONCLUSIONS The solubility of probenecid in 12 pure organic solvents was determined. The sequence of the experimental solubility data can be ranked as acetone > alcohols (i.e., n-pentanol, nbutanol, n-propanol, ethanol, and methanol) > methyl tertbutyl ether > esters (i.e., methyl acetate, ethyl acetate, and butyl acetate). The acetone showed much higher solubility to probenecid than to other solvents, while the butyl acetate showed the lowest solubility. The experimental solubility data was positively correlated by the modified Apelblat equation, van’t Hoff model, and NRTL model. All of the ARD values of these models are lower than 5% (maximum 4.522%). The thermodynamic properties of mixing of probenecid in these solvents, including the Gibbs energy of mixing, enthalpy of mixing, and entropy of mixing, were calculated by using the correlation results of the NRTL model. The spontaneity of the dissolution process was analyzed by the Gibbs energy of mixing. The molecular interaction between solute and solvents was analyzed by the enthalpy of mixing.

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ACKNOWLEDGMENTS

The authors are grateful for the financial support of Major National Science and Technology Projects (2017ZX09101001 and 2017ZX07402003) and the National Natural Science Foundation of China (91634117 and 21676179), G

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DOI: 10.1021/acs.jced.8b00863 J. Chem. Eng. Data XXXX, XXX, XXX−XXX