Solubility and Solution Thermodynamics of Diphenoxylate in Different

May 13, 2015 - models, including the ideal solution model, the modified. Apelblat equation and the Buchowski-Ksiazaczak λh equation, were applied to ...
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Solubility and Solution Thermodynamics of Diphenoxylate in Different Pure Solvents Xue-Yan Qing, Hua-Lin Fu,* Gang Shu, Meng-Jiao Liu, Jian-Yu Zhou, Wen-Bin Wu, Yan-Li Zhang, and Jun-Jie Zhou Department of Pharmacy, College of Veterinary Medicine, Sichuan Agricultural University, Yaan, Sichuan 625014, People’s Republic of China ABSTRACT: The solubility data of diphenoxylate in pure solvents of water, methanol, ethanol, acetone, acetonitrile, 2propanol were measured within the temperature range of 293.15−318.15 K by a static analytical method under atmospheric pressure. Several commonly used thermodynamic models, including the ideal solution model, the modified Apelblat equation and the Buchowski-Ksiazaczak λh equation, were applied to correlate the experimental solubility data. The experimental results show that the solubility increases with the increasing temperature, and the highest solubility is in methanol, the lowest in pure water. Results of these measurements were well-correlated with the three equations above, but the modified Apelblat equation is more suitable in regressing the solubility data of diphenoxylate. Through the Van’t Hoff equation, the enthalpy and the entropy in different solvents can be calculated.

1. INTRODUCTION Diphenoxylate (ethyl 1-(3-cyano-3,3-diphenylpropyl)-4-phenylpiperi-dine-4-carbo-xylate; CAS: 915-30-0; Figure 1), a well-

In the present study, the solubilities of diphenoxylate in the pure solvents water, methanol, ethanol, acetone, acetonitrile, and 2-propanol were measured within the temperature range of 293.15 K to 318.15 K by a static analytical method under atmospheric pressure. The ideal solution model, the modified Apelblat equation, and the Buchowski-Ksiazaczak λh equation were used to correlate the experimental data and calculate the thermodynamic parameters.

2. EXPERIMENTAL SECTION 2.1. Materials. A detail description of the chemicals used in this paper is given in Table 1. 2.2. Apparatus and Procedure. The experimental setup for the solubility measurement is similar to that described previously.6,7 A gravimetric method was used to measure the compositions of the saturated solution. A certain amount of each selected solvent and an excess of diphenoxylate were added into 150 mL volumetric Erlenmeyers flasks. The volumetric Erlenmeyers were stoppered by glass stopper to prevent evaporation of solvents. Then the Erlenmeyers were placed in a thermostatic mechanical shaker (HZS-H water bath oscillator, China) for 24 h to ensure solid−liquid equilibrium before sampling. The temperature of the inner Erlenmeyer flask was confirmed by a mercury thermometer (uncertainty of ± 0.05 K). After equilibrium was reached, the supernatant

Figure 1. Chemical structure formula of diphenoxylate.

known opioid agonist and antidiarrheal agent, can increase circular muscle activity of the intestine resulting in a constipating action and clinically combine with atropine to treat the protracted diarrhea in children.1−4 More specifically, it can impact the intestinal smooth muscle by inhibiting the intestinal mucosa receptor, eliminating the peristaltic reflex of local mucosa to weak intestinal peristalsis and increasing intestinal segmental contraction to the benefit of the absorption of water, therefore showing strong antidiarrheal effect. Until now, the solubility of organic compounds in different solvents has played an important role in their separation and purification, and also the solubility behavior of drugs remains one of the most challenging aspects in formulation development.5 To the best of our knowledge, the solubility of diphenoxylate in pure solvents has not been reported in the literature. © 2015 American Chemical Society

Received: November 1, 2014 Accepted: May 6, 2015 Published: May 13, 2015 1629

DOI: 10.1021/je5010033 J. Chem. Eng. Data 2015, 60, 1629−1633

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3. RESULT AND DISCUSSION 3.1. Experimental Results. The experimental solubility data of diphenoxylate in the pure solvents of water, methanol, ethanol, acetone, acetonitrile, and 2-propanol at different temperatures are shown in Table 2 and graphically displayed in Figure 3. It was found that the solubility is a function of temperature and increases with the increasing temperature, which denotes that the process of diphenoxylate dissolving in the solvents in the experimental temperature range is endothermic. In Figure 3, it can be seen that the solubility decreases as the following order: methanol > acetonitrile > acetone > ethanol > 2-propanol > water, which can give us a reference to choose solvents in separation, purification, or the formulation design of diphenoxylate. The order of polarities of the solvents is water > methanol > ethanol > 2-propanol > acetonitrile > acetone. The solubility does not decrease with the decreasing polarity of the solvents. It suggests that the solubility of diphenoxylate in pure solvents was not only affected by the polarity of the solvents, but also by the ability of the solvent to form hydrogen bonds with diphenoxylate and also intermolecular interaction. First, the solubility of diphenoxylate in water is much lower than in other solvents, showing that diphenoxylate is poorly soluble in water. Second, solvents used in this study can be divided into two categories, protic solvent (methanol, ethanol, and 2-propanol) and aprotic solvent (acetonitrile and acetone). For the protic solvents, methanol, ethanol, and 2-propanol are alcohols, which have a hydrogen bond donor (−OH) and an acceptor group (−OH). The only difference of structure among them is the length of hydrocarbon chain, and the hydrocarbon can hinder the formation of hydrogen bonds between solute and solvents. For the aprotic solvents, acetonitrile and acetone can unite with diphenoxylate by high intensity van der Waals forces, dispersion forces, and some weak hydrogen bonds.8 This may explain why the solubilities of diphenoxylate in acetonitrile and acetone are higher than that for the other solvents except methanol. Then, compared with acetone, acetonitrile may unite with diphenoxylate by a stronger intermolecular interaction. Therefore, the solubility of diphenoxylate in acetonitrile is higher than that in acetone.

Table 1. Characteristics of Chemicals Used in This Study chemical name

source

diphenoxylate

Wuhan Dinghui Chemical Reagent Co., Ltd. Chengdu Kelong Chemical Reagent Co., Ltd. Chengdu Kelong Chemical Reagent Co., Ltd. Chengdu Kelong Chemical Reagent Co., Ltd. Chengdu Kelong Chemical Reagent Co., Ltd. Chengdu Kelong Chemical Reagent Co., Ltd. double-distilled water prepared by the laboratory

methanol ethanol acetone acetonitrile 2-propanol water

a

purification method

mole fraction purity

analysis method

none

99.5 %

HPLCa

99.5 % 99.7 % 99.5 % 99.0 % 99.7 %

High performance liquid chromatography.

solution was taken by a preheated injector and filtered through a microporous membrane (0.22 μm) before analysis. A 1 mL sample was removed by a precise preheated pipet (uncertainty of 0.05 mL) to weigh the mass, using an ESJ200-4B analytical balance with sensitivity of ± 0.0001 g,. The sample was then appropriately diluted with acetonitrile for high performance liquid chromatography (HPLC) analysis. All the experiments were conducted three times, and the mean values were used to calculate the mole fraction solubility. The standard curve of concentration versus HPLC peak area is shown in Figure 2. 2.3. Chromatographic Conditions. The HPLC (LC2010C HT, Shimadzu, Japan) system was used to determine the concentration of diphenoxylate. All chromatographic analyses were performed on a Kromasil ODS C18 column (250 mm × 4.6 nm, 5 μm) with the wavelength of the detector set at 208 nm. The mobile phase, at a flow rate of 1.0 mL· min−1, was composed of acetronitrile and an aqueous solution having a mass fraction of 0.5 % sodium dodecyl sulfate (SDS) using phosphoric acid to adjust the pH to 2.7 in a volume ratio of 73:27. The injection volumes of sample and reference standard solutions were 10 μL. All chromatograph procedures were performed at 30 °C.

Figure 2. Standard curve of concentration versus HPLC peak area. 1630

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Table 2. Experimental Molar Solubility of Diphenoxylate (x) in Pure Solvents at Temperatures Ranging from 293.15 K to a cal cal 318.15 K (p = 0.1 MPa), and the Predicted Solubilities (xcal 1 , x2 , and x3 ) Obtained from Equations 1, 2, and 3 xcal 1 T/K

a

3

10 x

293.15 298.15 303.15 308.15 313.15 318.15

5.9834 7.9090 10.4685 12.2881 14.3506 18.4451

293.15 298.15 303.15 308.15 313.15 318.15

4.2571 4.7895 5.5891 6.0804 6.6359 7.7593

293.15 298.15 303.15 308.15 313.15 318.15

0.2585 0.4419 0.6267 0.8591 1.0787 1.5625

eq 1 methanol 6.3262 7.9284 9.8639 12.1865 14.9564 18.2398 acetone 4.2599 4.8242 5.4411 6.1132 6.8430 7.6332 2-propanol 0.3008 0.4264 0.5976 0.8284 1.1365 1.5438

xcal 2

xcal 3

eq 2

3

T/K

eq 3

10 x

6.4434 7.9509 9.8065 12.089 14.892 18.333

6.3228 7.9267 9.8651 12.1893 14.9585 18.2371

293.15 298.15 303.15 308.15 313.15 318.15

1.6893 1.9849 2.3008 2.6996 3.2494 4.3192

4.3483 4.7887 5.3319 5.9976 6.8108 7.8029

4.2706 4.8250 5.4348 6.1044 6.8386 7.6426

293.15 298.15 303.15 308.15 313.15 318.15

4.2723 4.9962 6.014 7.2717 9.1926 12.363

0.3176 0.4331 0.5931 0.8153 1.1244 1.5555

0.3008 0.4264 0.5976 0.8284 1.1365 1.5437

293.15 298.15 303.15 308.15 313.15 318.15

0.0086 0.0119 0.0145 0.0196 0.027 0.0328

xcal 1

xcal 2

xcal 3

eq 1

eq 2

eq 3

1.5290 1.8846 2.3232 2.8638 3.5296 4.3492

1.4982 1.8775 2.3359 2.8864 3.5434 4.3234

3.9085 4.8717 6.0857 7.6172 9.5505 11.9925

3.7924 4.8415 6.1310 7.7041 9.6096 11.9021

0.0088 0.0116 0.0152 0.0198 0.0258 0.0334

0.0087 0.0115 0.0152 0.0199 0.0258 0.0332

ethanol 1.4963 1.8765 2.3358 2.887 3.5443 4.3234 acetonitrile 3.7920 4.8405 6.1295 7.7027 9.6095 11.9054 water 0.0087 0.0115 0.0152 0.0199 0.0258 0.0333

Standard uncertainties u are u(T) = 0.1 K, u(x) = 0.06x.

equations to correlate the solubility data such as the ideal model, the modified Apelblat equation, and the λh equation. 3.2.1. Correlation with the Ideal Model. Assuming the solution is an ideal solution, the ideal model can be used to correlate the experimental data and can be expressed by eq 1.9

ln x = a +

b T /K

(1)

where x is the mole fraction solubility of diphenoxylate, T is the corresponding temperature, and a and b are the parameters of the equation which are listed in Table 3, together with R2, the relative average deviation (RAD) and the root-mean-square deviations (RMSD). 3.2.2. Correlation with Modified Apelblat Equation. The modified Apelblat equation is simple and commonly used to correlate the relationship between the temperature and solubility. It can be written as follows:10

Figure 3. Mole fraction solubility (x) of diphenoxylate versus temperature (T) in the selected solvents: ⧫, methanol; +, acetonitrile; ▲, acetone; ■, ethanol; ×, 2-propanol; ●, water.

3.2. Correlation of the Solubility Data. Many mathematical models are used for correlating the solubility data, including activity-coefficient-related models based on solid−liquid equilibrium8 and semiempirical equations. In this study, because of the limited knowledge of the activity coefficient, we chose semiempirical temperature-dependent

ln x = A +

B + C ln(T /K) T /K

(2)

where x stands for the mole fraction solubility, T stands for the absolute temperature, and A, B, and C are empirical parameters which are listed in Table 4, also with R2, RAD, and RMSD.

Table 3. Parameters of the Ideal Solution for Diphenoxylate in Selected Solvents from 293.15 K to 318.15 Ka

a

solvent

a

methanol ethanol acetone acetonitrile 2-propanol water

8.4117 ± 0.6453 6.9966 ± 0.3146 1.9700 ± 0.3577 8.9878 ± 0.2645 12.7075 ± 0.3455 5.4653 ± 0.1419

b −3950.2147 −3957.9351 −2177.8259 −4269.1245 −6102.4569 −5019.3689

± ± ± ± ± ±

196.6147 94.8916 114.2819 84.0115 107.3926 44.5087

R2

100·RAD

100·RMSD

0.9904 0.9786 0.9916 0.9813 0.9879 0.9955

3.4242 5.9311 1.8868 3.9718 6.6641 2.8041

4.4087 6.5406 2.4115 4.598 7.9875 3.0961

Standard uncertainties u are u(T) = 0.1 K, u(a, b) = 0.001, u(R2) = 0.001, u(RAD) = 0.001, u(RMSD) = 0.001. 1631

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Table 4. Parameters of the Apelblat Equation for Diphenoxylate in Selected Solvents from 293.15 K to 318.15 Ka −146.1006 −162.3407 −341.1397 −221.4890 −338.0793 −119.3143

methanol ethanol acetone acetonitrile 2-propanol water a

B

C

R2

100·RAD

100·RMSD

3110.0991 ± 172.1194 3783.3399 ± 23.2100 13402.6160 ± 90.8094 6272.6019 ± 75.3614 9979.7849 ± 89.0736 697.1523 ± 37.6183

22.9631 ± 0.1149 25.1645 ± 0.3077 51.047 ± 0.329 52.1031 ± 0.0227 34.2471 ± 0.3290 18.5361 ± 0.0167

0.9937 0.9913 0.9916 0.9991 0.994 0.9956

3.4241 5.9305 1.8867 3.9716 6.6652 2.8477

4.4086 6.5401 2.4115 4.5976 7.9882 3.1349

A

solvent

± ± ± ± ± ±

0.5907 1.7694 0.0985 0.1077 0.0974 0.0983

Standard uncertainties u are u(T) = 0.1 K, u(A, B, C) = 0.001, u(R2) = 0.001, u(RAD) = 0.001, u(RMSD) = 0.001.

Table 5. Parameters of the λh equation for Diphenoxylate in Selected Solvents from 293.15 K to 318.15 Ka λ

solvent methanol ethanol acetone acetonitrile 2-propanol water a

1.5831 0.3475 0.0651 1.4149 1.4093 0.0088

± ± ± ± ± ±

0.4104 0.0423 0.0114 0.1401 0.1738 0.0005

h

R2

100·RAD

100·RMSD

2643.8999 ± 539.8820 11467.786 ± 1214.9667 31313.6967 ± 3049.3046 3045.7151 ± 236.6259 4392.9372 ± 501.6169 567632.556 ± 24873.0581

0.9911 0.9747 0.9900 0.9814 0.9933 0.9948

2.9724 6.6906 1.4626 5.0794 5.7702 2.637

3.7635 7.3538 1.8268 5.9074 7.5661 3.0986

Standard uncertainties u are u(T) = 0.1 K, u(λ, h) = 0.001, u(R2) = 0.001, u(RAD) = 0.001, u(RMSD) = 0.001

3.2.3. Correlation with the λh Equation. The Buchowski− Ksiazczak λh equation is a semiempirical equation and can correlate solubility with activity and temperature.11 The equation can be described as follows:12 ⎛ 1 ⎛ λ(1 − x) ⎞ 1 ⎞ ln⎜1 + ⎟ = λh⎜ − ⎟ ⎝ ⎠ x Tm/K ⎠ ⎝ T /K

3.3. Thermodynamic Properties for the Solutions. In the thermodynamics field, the Van’t Hoff equation is used to relate the mole fraction solubility with temperature, which can be expressed as follows:13 ln x = −

(3)

x exp − x cal x exp

exp

(7)

where x is the mole fraction solubility of solute in solvent, R represents the universal gas constant (8.314 J·mol−1·K−1) and T represents the corresponding absolute temperature. ΔHm and ΔSm are the mean enthalpy and entropy values of the dissolution process from 293.15 K to 318.15 K, which can be calculated from the slope and intercept of the line for ln x plotted with 1/T. The curves are shown in Figure 4.

where x, T, and Tm represent the mole fraction solubility, absolute temperature, and melting point, respectively, and λ and h are the parameters of the equation, which are listed in Table 5 together with the R2, RAD, and RMSD. The relative deviation (RD) between the calculated and the experimental values are calculated according to eq 4. RD =

ΔHm ΔSm + RT R

(4)

cal

where x and x are the experimental and the calculated values, respectively. The relative average deviation (RAD) is defined as follows: RAD =

1 N

∑

|x exp − x cal| x exp

(5)

where N is the number of experimental points. The root−mean−square deviations (RMSD) can be described as eq 6: ⎡ 1 RMSD = ⎢ ⎢⎣ N

⎛ x exp − x cal ⎞2 ⎤ ∑ ⎜ exp ⎟ ⎥⎥ ⎝ x ⎠⎦

1/2

Figure 4. Van’t Hoff plot of logarithm mole fraction solubility of diphenoxylate in different K−1 pure solvents: ⧫, methanol; +, acetonitrile; ▲, acetone; ■, ethanol; ×, 2-propanol; ●, water.

(6)

The RAD and RMSD values were calculated for accessing the accuracy and predictability of correlation model. According to Tables 3 to 5, RAD and RMSD among most of the values do not exceed 6 %, and the R2 values are higher than 0.9, which suggested that the models we chose can fit the experimental solubility data well. In addition, compared to the other two models, the modified Apelblat equation’s R2 are all over 0.99 and the RAD and RMSD of the Apelblat equation are the lowest ones of the three models. So the Apelblat equation is shown to be more accurate for this dissolution system.

According to the study of Zhi et al.,14 the changes of Gibbs free energy ΔGm can be described by eq 8: ΔGm = ΔHm − TmeanΔSm

(8)

where Tmean = 305.65 K represents the mean temperature of the experimental temperatures. To compare the relative contributions of enthalpy and entropy to the standard Gibbs energy in the solution process, the following equations are used:15,16 1632

DOI: 10.1021/je5010033 J. Chem. Eng. Data 2015, 60, 1629−1633

Journal of Chemical & Engineering Data %εH =

|ΔHm| |ΔHm| + |Tmean·ΔSm|

%εs =

|Tmean·ΔSm| |ΔHm| + |Tmean·ΔSm|

■

(10)

The values of %εH and %εs are listed in Table 6 together with ΔHm, ΔSm and ΔGm. Table 6. Thermodynamic Properties Relative to Solution Process of Diphenoxylate in the Selected Solvents at the Mean Temperature 305.65 Ka ΔHm

ΔSm

ΔGm

kJ·mol−1

J·mol−1

kJ·mol−1

%εH

%εS

methanol ethanol acetone acetonitrile 2-propanol water

33.62 29.32 18.00 32.39 53.23 41.72

72.47 46.53 16.06 64.67 113.65 45.39

11.47 15.09 13.10 12.63 18.49 27.85

60.28 67.33 78.58 62.10 60.51 75.04

39.72 32.67 21.42 37.90 39.49 24.96

a

Standard uncertainties u are u(T) = 0.1 K, u(ΔHm) = 0.1, u(ΔGm) = 0.1, u(ΔSm) = 0.1, u(%εH) = 0.1, u(%εS) = 0.1.

Table 6 summarizes all the thermodynamic parameters of the dissolution process within the experimental temperature range. From Table 6, ΔHm, ΔSm, and ΔGm values are positive for all the solvents suggesting that the dissolving process of diphenoxylate is endothermic and not spontaneous in all the solvents studied. Because the values of %εH are all ≥ 59 %, the main contributor is enthalpy. From Table 6, it can be seen that ΔGm increases as the following order: methanol < acetonitrile < acetone < ethanol < 2-propanol < water. The changes of Gibbs free energy ΔGm denote the maximum value of the system to do the nonvolume work. It suggests that the smaller the ΔGm is, the stronger the dissolving power is. So the increasing order of ΔGm should be same as the decreasing order of the solubility theoretically. In this paper, the decreasing order of experimental data is the same as the increasing order of ΔGm, which proved the reliability of the experimental data.

4. CONCLUSION The solubilities of diphenoxylate in pure solvents were measured within the temperature range of 293.15 K to 318.15 K by the saturation method under atmospheric pressure. The results show that the solubility increases with increasing temperature. The experimental solubility data were correlated by the ideal solution model, modified Apelblat equation, and Buchowski-Ksiazaczak λh equation. The modified Apelblat equation is more suitable in describing the solubility data. Finally, with the use of the Van’t Hoff equation, it is seen that the mean dissolution enthalpy, entropy, and Gibbs free energy data in different solvents show that the dissolving process of diphenoxylate is endothermic and not spontaneous.

■

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Corresponding Author

*Tel.: +86 0835 2885614. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 1633

DOI: 10.1021/je5010033 J. Chem. Eng. Data 2015, 60, 1629−1633