Mingxia Guo ,Qiuxiang Yin ,2,Chang Wang ,Yaohui Huang ,Yang Li,Zaixiang Zhang ,Xia Zhang ,Zhao Wang ,2,Meijing Zhang ,2,Ling Zhou ,*

1 School of Chemical Engineering and Technology,State Key Laboratory of Chemical Engineering,Tianjin University,Tianjin 300072,China

2 The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin,Tianjin University,Tianjin 300072,China

1.Introduction

Metamizol monohydrate(C13H18N3NaO5S,CAS Registration No.5907-38-0,Fig.1)is a well-known and widely used analgetic and antipyretic drug employed for multicomponent preparations.It is also one of the five active ingredients of Pentalgin-FS tablets produced by Farmstandart-Leksredstva[1].However,some problems are still urgent in the industrial producing process of metamizol monohydrate,such as the long production period,small particle size,maldistribution and long drying and filtration time.Optimizing the cooling crystallization process and determining the optimum operating curve of the high-quality products are supposed to be the best way to solve these problems[2].

In the pharmaceutical manufacturing industry,the unit operation of crystallization plays a major role which can determine the final product qualities like crystalsize distribution,crystalform,productpurity and so on.Moreover,the design of this significant crystallization process partly relies on the solid-liquid equilibrium solubility of the product,which is deeply influenced by the temperature and the solvent components[3].Therefore,solubility,a basic data of crystallization,is very important when it comes to the control and optimization of the drug producing process.However,poor data about the thermodynamic properties of metamizol monohydrate in the pure and binary mixed solvent systems at different temperatures is available in the existing literature.

In this work,the solubility data of metamizol monohydrate in four pure solvents(methanol,ethanol,n-propanol and isopropanol)and two binary mixed solvent systems(methanol+ethanol)and(methanol+isopropanol)was measured from 283.15 K to 313.15 K at 0.1 MPa by gravimetric method[4-9].The samples were characterized by PXRD which can help to guarantee the same crystalform during the dissolving process.The DSC analysis was also used to determine the melting point and the enthalpy fusion of metamizol monohydrate.Several classical equations were applied to correlate the solubility of metamizol monohydrate in the investigated solvent systems.Among them,the modified Apelblat equation,the CNIBS/R-K equation,the Hybrid equation and the NRTL model were applied to investigate the impact of the temperature and the influence of the solvent components on the solubility,respectively.In addition,the mixing thermodynamic properties of metamizol monohydrate solution were discussed by the NRTL model,like the enthalpy,the Gibbs energy and the entropy during the mixing process in all the discussed solvent systems.

2.Experiment Section

2.1.Materials

Fig.1.Chemical structure of metamizol monohydrate.

Metamizol monohydrate was supplied by the Shandong Xinhua Pharmaceutical Co.,Ltd.,China.Anhydrous methanol,anhydrous ethanol,isopropanol andn-propanol were purchased from Jiangtian Chemical Technique Co.,Ltd.(Tianjin,China).The purity analysis had been done by the suppliers and all chemicals were used without further purification.More detailed information about the materials used in this work has been listed in Table 1.

2.2.Characterization of metamizol monohydrate

To ensure that the crystal form of metamizol monohydrate remains same during the experiments,Powder X-ray Diffraction(PXRD)patterns of excess solid and dried samples of metamizol monohydrate were all measured in the tested solvents at different temperature(T=283.15 K-313.15 K)after stirring 24 h.The PXRD patterns were obtained using Cu Kαradiation(0.154 nm)on Rigaku D/max-2500(Rigaku,Japan).The samples were conducted over a 2-theta range from 2°to 50°at a scanning rate of 1 step per second.

To determine the melting temperature and enthalpy fusion of metamizol monohydrate,a thermogravimetric/differential scanning calorimetry(Mettler-Toledo,Switzerland)was used for thermal analysis experiment under a nitrogen atmosphere.

2.3.Determination of solubility

The solubility of metamizol monohydrate was measured by the gravimetric method which was widely described in literature[10-12].A 50 ml cylindrical double-jacketed crystallizer was used to contain solvents,into which the excess amount of metamizol monohydrate was added.The jacketed temperature was controlled within±0.1 K by a thermostat(XOYS-2006,Nanjing Xianou Instrument Manufacturing Co.,Ltd.,China).The solid-liquid mixtures should be under stirring for 10 h,which was experimentally proved to be long enough to reach equilibrium.Then the agitation was stopped and the solution was kept still for about 4 h to make sure that the undissolved particles settled down.The upper clear saturated solution was filtered with a filter membrane(0.22 μm)and moved into a glass dish.Subsequently,the filtrate was weighed as quickly as possible and dried at 50°C until no mass change was observed.An analytical balance(type AL 204,Mettler Toledo,Switzerland)with uncertainty of±0.0001 g was used to measure all the masses including the solutions and the glass dishes in this work.Each experiment was repeated three times and the average value was used to calculate the mole fraction solubility.

The mole fraction solubility(x1)of metamizol monohydrate in pure solvents was calculated by the following Eq.(1):

wherem1is the mass of the solute,m2is the mass of the solvent;M1andM2are the molecular masses of solute and solvent,respectively.

The molar fraction solubility(x1)of metamizol monohydrate in binary mixed solvent systems and the initial mole fraction(x20)of methanol in the solvent mixtures can be obtained by the following Eqs.((2)-(3)):

wherem1,m2are the mass of metamizol monohydrate and methanol,respectively.m3represents the mass of ethanol or isopropanol which based on the choice of the solvents in the experiments.M1,M2andM3are the corresponding molecular mass of them.

3.Results and Discussion

3.1.Material characterization

Fig.2.Power X-ray diffraction pattern of metamizol monohydrate(T=303.15 K,methanol+ethanol,(=0.5)):a,raw material;b,solid filtered after stirring;c,dried product;d,anhydrous analgin.

Table 1Properties of materials used in this work

In this work,the PXRD pattern of purchased material as well as the sediments and dried sediments were all tested and the results turned out to be as same as the counterpart of metamizol monohydrate.As shown in Fig.2,we take the PXRD patterns of the metamizol monohydrate,solid filtered in solution after stirring 24 h,dried product in the binary solvents(methanol+ethanol,=0.5))at temperatureT=303.15 K as an example.All the PXRD patterns of the tested materials have the same characteristic peaks of metamizol monohydrate.The PXRD pattern of anhydrous analgin which is the dehydrated product of metamizol monohydrate,obtained from the single crystal structure of anhydrous analgin with Mercury 3.3[13],is also showed in Fig.2.It confirms that the solute used in this study is metamizol monohydrate and there is no polymorphism,amorphous or dehydration during the process.

As can be seen from the TGA analysis(Fig.3),there are two stages in the thermal decomposition process.The first one corresponds to crystal water loss which is about4.8%and the second step from 510.15 K with a weight loss because of the decomposition.The DSC analysis indicates that the exothermic and endothermic peaks both appear from 505 K to 525 K which suggests that metamizol monohydrate melt with decomposition.Therefore,the thermal analysis experiment cannot provide the melting temperature,neither nor the enthalpy of fusion of metamizol monohydrate.

Fig.3.Thermal analysis(TGA/DSC)of metamizol monohydrate.The solid and dashed lines are the DSC and TGA curves,respectively.

In this study,the melting temperature and the enthalpy of fusion of metamizol monohydrate have been estimated by a method called group-contribution which has been proved to be accurate enough to determine these properties[14].In the determination of melting properties for more than 2000 materials reported in papers using this method,the absolute errors of melting temperature and fusion enthalpy are less than 33.87 K and 4.160 kJ·mol-1,respectively[14].The melting properties of metamizol monohydrate can be estimated by Eqs.(4)and(5).

whereTm0andHfus0are the parameters,the values of which are 147.45 K and-2.806 kJ·mol-1,respectively.The contribution of the first-order group,second-order group and third-order group for the melting temperature is expressed byTm1i,Tm2jandTm3k,respectively.With respect to the enthalpy of fusion,the contribution of these groups is represented byHfus1i,Hfus2jandHfus3k,respectively.In these equations,the values ofTm1i,Tm2j,Tm3k,Hfus1i,Hfus2jandHfus3kof all the investigated groups can be got through literature[14].With this group-contribution method,the estimated melting point of metamizol monohydrate is 507.30 K and the predicted fusion enthalpy is 17.56 kJ·mol-1.

3.2.Solubility of metamizol monohydrate in four pure solvents

The experimental solubility of metamizol monohydrate in the pure solvents from 283.15 K to 313.15 K is shown in Table 2 and plotted against temperature in Fig.4.It can be seen clearly from the results that the solubility of metamizol monohydrate in methanol,ethanol,n-propanol and isopropanol all increase slowly with the rise of the temperature.The interesting thing is that the dissolving capacity order of the solvents for metamizol monohydrate is as same as the polarity order of these solvents,which can be arranged as methanol＞ ethanol＞n-propanol＞isopropanol in literature[15,16].This coincidence means that the polarity of solvents must play a major role in affecting the solubility of metamizol monohydrate.

In order to research the influence factors of solubility deeply,different models has been introduced to correlate the solubility data.The average relative deviation percentage(ARD)is a useful index which can not only calculate the differences between the experimental and calculated data but can also help us to choose the best model.TheARDis defined as:

Table 2Experimental solubility of metamizol monohydrate in four pure solvents at different temperatures(0.1 MPa)

Fig.4.Experimental solubility data of metamizol monohydrate in four pure solvents:■,methanol;▲,ethanol;? n-propanol;●,isopropanol.The solid lines represent the correlated solubility by a)the modified Apelblat model and b)the NRTL model.

whereNis the number of the experimental points.x1,iandare the experimental and the calculated solubility value,respectively.

MATLAB software,including many correlated equations,was used to correlate the solubility of metamizol monohydrate.Among them,the modified Apelblat equation,a semi-empirical model,has three parameters which is widely used in correlating solubility data[17-20]:

wherex1represents the mole fraction solubility of solute.Tis the absolute experimental temperature.AandBreflect the non-ideality of the real solution because of the variation of activity coefficient in the solution,whileCmeans the effect of temperature on the fusion enthalpy.A,B,andCare all empirical constants.

The correlated solubility data of analgin by modified Apelblat equation is represented in Fig.4a).The values of correlated model parameters and average relative deviation(ARD)are given in Table 3.These results show that the correlation equation in this work can give good correlation results,which means that the solubility has temperature dependence in these dissolving processes.

Table 3Parameters and ARD s of the modified Apelblat equation about the solubility of metamizol monohydrate in four pure solvents(P=0.1 MPa)

The activity coefficient(γ)was introduced to estimate the thermodynamic properties in real solutions,which can be calculated through the local composition model-NRTL model.The correlated solubility data,the enthalpy,the Gibbs energy and the entropy of the mixing process can be also obtained from this model[21].At phase equilibrium including solid and liquid,the fugacity of the solute in the solid phase and that in the liquid phase must be the same one,which can be interpreted as the following Eq.(8):

Adopting some assumptions,the equation can be expressed as follows:

where ΔfusH(enthalpy of fusion)andTm(melting point)were obtained using the group-contribution method mentioned in Section 3.1.

The values of activity coefficient γican be calculated from the following equation in NRTL model:

whereGij,Gji,τijand τjiare the parameters of this model.Their values can be calculated as:

whereais an adjustable empirical constant.τ is a constant used to express the nonrandomness of the mixture.gmeans the Gibbs energy of intermolecular interaction.The calculated solubility values of metamizol monohydrate by NRTL model are plotted in Fig.4b),and the model parameters are listed in Table 4.These results indicate that the good correlation results can be obtained from NRTL model,which means that it can be used in the analysis of the thermodynamic properties during the mixing process in the next section.

Table 4Parameters for the NRTL model in four pure solvents(P=0.1 MPa)

3.3.The thermodynamic properties of mixing in pure solvents

The dissolving process can be divided into three hypothetic steps[22]:

The fusion of the solute,the cooling of the liquid solute and the mixing of the liquid solute constitute this dissolving process.As for the crystal structure of metamizol monohydrate are supposed to determine the fusion properties,the major determined factor to explore this whole dissolving process must be the mixing properties of the solution.

The following equations explain how to calculate the thermodynamic properties of mixing process in four pure solvents.The mixing Gibbs free energy(ΔGm),the mixing enthalpy(ΔHm)and the mixing entropy(ΔSm)can be obtained by:

whereMcan be substituted byG,H,andS.ΔMidis the mixing property of the ideal solution,whileMEis the excess property.

The ΔGm,ΔHmand ΔSmof the ideal solution are calculated by[23]:

wherexiis the mole fraction of every componentin the solution.n is the total components of the solution.n=2 or 3 means the dissolving process happened in pure solvents or in the binary mixed solvent systems respectively.

The excess mixing Gibbs energy(ΔGE),mixing entropy(ΔSE)and mixing enthalpy(ΔHE)are calculated as[24]:

where γiis the activity coefficient of every component in the solution.n=2 or 3 means the dissolving process happened in pure solvents or in the binary mixed solvent systems respectively.

The calculated thermodynamic properties of mixing of metamizol monohydrate are shown in Table 5.The negative values of every ΔGmmean that the mixing process is all spontaneous in the pure solvents used in this work.However,the values of ΔSmare all positive,which illustrates that this process is entropically favorable.Furthermore,the mixing process in n-propanol and isopropanol is endothermic according to the positive values of ΔHmwhile the counterpart in methanol and ethanol is exothermic based on the negative values of ΔHm.

3.4.Solubility of metamizol monohydrate in binary mixed solvent systems

The solubility of metamizol monohydrate in two binary mixed solvent systems containing good solvent and poor solvent was measured to meet the demand of controlling and optimizing the drug producingprocess.As a result,the experimental solubility data of metamizol monohydrate in the binary mixed solvent systems including(methanol+ethanol)and(methanol+isopropanol)from 283.15 K to 313.15 K under atmospheric pressure(0.1 MPa)are shown in Tables 6 and 7 and plotted in Figs.5-8 respectively.From the solubility data,we can easily find that the solubility trends conform to the famous rule “dissolve like dissolve”[25].What's more,the solubility of metamizol monohydrate increases with the rise of the methanol composition in binary mixed solvent systems at a constant temperature.Additionally,although the solvent composition kept unchanged,the solubility of metamizol monohydrate increases with the rise of the temperature.

Table 5The thermodynamic properties of mixing for solution with four pure solvents from 283.15 K to 313.15 K(P=0.1 MPa)

The modified Apelblat equation,the CNIBS/R-K model,the Hybrid model and the NRTL model were all applied to correlate the solubility of metamizol monohydrate in the binary mixed solvent systems including(methanol+ethanol)and(methanol+isopropanol).And the calculated solubilities are all plotted in Figs.5-8,respectively.The modified Apelblat equation was applied to explain the relationship between temperature and solubility;the CNIBS/R-K model was used to explain the relationship between the solvent component and the isothermal solubility;the Hybrid model was supposed to illustrate the relationship among solubility,temperature and solvent component;the NRTL model was applied to correlate the solubility and the thermodynamic properties.

The values of correlated model parameters and average relative deviation(ARD)of modified Apelblat equation mentioned about the solubility of metamizol monohydrate in the component solvent are given in Table 8.The data shows that this modified equation in binarymixed solventsystems gives good correlation results justlike that in the pure solvents,indicating that the solubility has temperature dependence,either.

Table 6Mole fraction solubility(x1)of metamizol monohydrate in the binary(methanol(2)+ethanol(3))solvent mixtures at different temperatures from 283.15 K to 313.15 K(P=0.1 MPa).

The CNIBS/R-K model was introduced to correlate the solubility of metamizol monohydrate in the two binary mixed solvent systems[26,27],which can give us a clearly explain about the effect of solvent component on the solubility ability.The equation can be expressed as:

whereandexpress the initial mole fraction of methanol and the initial mole fraction of ethanol(isopropanol)in the binary mixed solvent system methanol+ethanol(methanol+isopropanol)without solute metamizol monohydrate.Andx1denotes the mole fraction solubility of the metamizol monohydrate,while(x1)iis the mole fraction solubility of the metamizol monohydrate inpure solvent I;sirepresents the model parameter;nrepresents the number of “curve- fit”parameters.In the two binary mixed solvent systems,nshould be assigned a value as two,then the equation can be simplified to the following equation whenreplaced with(1-)in Eq.(20):

Table 7Mole fraction solubility(x1)of metamizol monohydrate in the binary(methanol(2)+isopropanol(3))solvent mixtures at different temperatures from 283.15 K to 313.15 K(P=0.1 MPa).

The model parameters of the(NIBS)/Redlich-Kister model and the calculatedARDs in this correlation are listed in Table 9.The result illustrates that this model is very suitable to correlate the experimental solubility,showing that the solubility data has a great dependence on the solvent component.

Fig.5.Mole fraction solubility(x1)of metamizol monohydrate versus mole fraction of methanolin methanol(2)+ethanol(3)binary mixed solvent systems from 283.15 K to 313.15 K(P=0.1 MPa):■,T=283.15 K; ,T=288.15 K; ,T=293.15 K; ,T=298.15 K;,T=303.15 K;,T=308.15 K;,T=313.15 K.The solid lines represent the correlated solubility by the CNIBS/R-K model.

Fig.6.Mole fraction solubility(x1)of metamizol monohydrate versus mole fraction of methanolin methanol(2)+isopropanol(3)binary mixed solvent systems from 283.15 K to 313.15 K(P=0.1 MPa):■,T=283.15 K; ,T=288.15 K; ,T=293.15 K; ,T=298.15 K;,T=303.15 K;,T=308.15 K;,T=313.15 K.The solid lines represent the correlated solubility by the CNIBS/R-K model.

Taking the in fluence of temperature and solvent component on the solubility of metamizol monohydrate into consideration,the Hybrid model,a combination of the modified Apelblat equation and Jouyban-Acree model,was used to correlate the solubility in two binary mixed solvent systems from 283.15 K to 313.15 at 0.1 MPa[28].The hybrid model can be expressed as:

Fig.7.Mole fraction solubility(x1)of metamizol monohydrate versus temperature T in methanol(2)+ethanol(3)binary mixed solvent systems from 283.15 K to 313.15 K(P=0.1 MPa):■,=0;,=0.1; ,=0.2; ,=0.3;,=0.4;,=0.5;,=0.6;,=0.7;,=0.8;,=0.9;=1.The solid lines represent the correlated solubility by a)the modified Apelblat model,b)the Hybrid model and c)the NRTL model.

Fig.8.Mole fraction solubility(x1)of metamizol monohydrate versus temperature T in methanol(2)+isopropanol(3)binary mixed solvent systems from 283.15 K to 313.15 K(P=0.1 MPa):■,=0;,=0.1; ,=0.2; ,=0.3;,=0.4;,=0.5;,=0.6;,=0.7;,=0.8; ,=0.9;,=1.The solid lines represent the correlated solubility by a)the modified Apelblat model,b)the Hybrid model and c)the NRTL model.

wherex1,andexpress the mole fraction of metamizol monohydrate,the initial mole fraction of methanol and the initial mole fraction of ethanol or isopropanol,respectively.Jiis supposed to be a constant.According to the modified Apelblat equation,(x1)2and(x1)3can be replaced by the following Eqs.((22)-(23)):

Table 9Parameters of the CNIBS/R-K equation for metamizol monohydrate in different binary mixed solvent systems at the temperature from 283.15 K to 313.15 K(P=0.1 MPa)

Table 10Parameters of the Hybrid model for metamizol monohydrate in different binary solvent systems at the temperature from 283.15 K to 313.15 K(P=0.1 MPa)

Table 11Parameters of the NRTL model for metamizol monohydrate in different binary solvent systems at the temperature from 283.15 K to 313.15 K(P=0.1 MPa)

Replacingwith(1-),a new equation can be obtained:

whereA1toA9are the model parameters.

The model parameters and the calculatedARDs of this model are listed in Table 10.The results illustrate that this mixed model is good to correlates the solubility of metamizol monohydrate in the measured binary mixed solvent systems at different solvent component and temperatures,the range of which is confined from 283.15 K to 313.15 K.

The activity coefficients of metamizol monohydrate(γi)in the binary mixed solvent systems including(methanol+ethanol)and(methanol+isopropanol)were also obtained by the NRTL modelmentioned in Section 3.2.The γiin the binary mixed solvent systems can be expressed as:

Table 12The mixing thermodynamic properties of metamizol monohydrate in binary solvent mixtures(methanol+ethanol)from 283.15 K to 313.15 K(P=0.1 MPa)

whereGij,Gik,Gji,Gjk,Gki,Gkj,τij,τik,τji,τjk,τkiand τkjare the model parameters.Their definition is as same as the counterparts in Section 3.2.The binary NRTL parameters can be used for the ternary system prediction,especially in the vapor-liquid equilibria systems[29-31].However,a considerable deviation often exists in solid-liquid equilibrium when using this way to predictthe solubility for the ternary system's complexity[32-35].In order to avoid that deviation,people even developed some revised NRTL equation like NRTL-SAC model to predict ternary solubility depending on the binary parameters to eliminate error as far as possible[34,35].Here,we tried to predict the solubility for the ternary systems using the binary NRTL parameters.However,theARDs were both higher than 20%,which revealed that it was not suitable here to predict the ternary solubility by the binary system parameters in these systems.So,we correlated the solubility data using parameters came from ternary systems for their good correlated results.The optimized fitting model parameters were listed in Table 11.

3.5.The thermodynamic properties of mixing in binary mixed solvent systems

The thermodynamic properties of the mixing process in the two binary mixed solvent systems were calculated by Eq.(13)and represented in Tables 12 and 13 respectively.It can be seen that ΔGm＜ 0 and ΔSm＞0 in both solution systems with binary solvents,indicating that the mixing process in the two binary mixed solvent systems(methanol+ethanol)and(methanol+isopropanol)is spontaneous and entropically favorable.What's more,the mixing processes are both exothermic because of the negative values of the ΔHm.

4.Conclusions

In this work,under the atmospheric pressure(0.1 MPa),the solubility of metamizol monohydrate in four pure solvents(methanol,ethanol,n-propanol and isopropanol)and two binary mixed solvent systems(methanol+ethanol)and(methanol+isopropanol)were measured by gravimetric method from 283.15 K to 313.15 K.

In four pure solvents,the solubility increases with the increasing of the temperature.What's more,under a constant temperature,the dissolving capacity of these solvents corresponded with the polarity order which is methanol＞ethanol＞n-propanol＞isopropanol.The modified Apelblat equation and the NRTL model are verified that both have the ability to correlate the experimental solubility of metamizol monohydrate with the lowARDvalues.The second model also can be used to predict the thermodynamic properties in the four pure solvents.

In the binary mixed solvent systems,the solubility of metamizol monohydrate also shows temperature dependence just like that in the pure solvents.In addition,at a given temperature,the solubility of the metamizol monohydrate is mainly influenced by the different solvent components of the binary solvents.What's more,the results show that the experimental data can be well correlated by several classical models,like the modified Apelblatequation,the CNIBS/R-K equation,the Hybrid model and the NRTL model.

Table 13The mixing thermodynamic properties of metamizol monohydrate in binary solvent mixtures(methanol+isopropanol)from 283.15 K to 313.15 K(P=0.1 MPa)

Furthermore,the thermodynamic properties of the mixing process in four pure solvents and two binary mixed solvent systems were all obtained by NRTL model in order to get a deep understanding about the solubility.It turns out that the mixing process of metamizol monohydrate in all tested solvent systems is always spontaneous and entropically favorable,which has instructional function to the further study about the crystallization of metamizol monohydrate.

Nomenclature

A,B,Cempirical parameter for the modified Apelblat equation

Ai(i=1-9)empirical parameters for Jouyban-Acree equation

ARDaverage absolute deviation between experimental and calculated solubility

aijthe adjustable empirical constant for the NRTL model

Bi(i=1-5)empirical parameters for CNIBS/R-K equation

GEexcess Gibbs energy of solution,J·mol-1

ΔGmthe mixing Gibbs energy of solution,J·mol-1

the mixing Gibbs energy of ideal solution,J·mol-1

Δgijparameters for the NRTL model,J·mol-1

HEexcess enthalpy of solution,J·mol-1

ΔHmthe mixing enthalpy of solution,J·mol-1

the mixing enthalpy of ideal solution,J·mol-1

M1the molecular mass of metamizol monohydrate,g·mol-1

M2the respective molecular mass of pure solvents(methanol,ethanol,n-propanol and isopropanol),g·mol-1

M3the respective molecular mass of the second solventin binary mixed solvent systems(ethanol or isopropanol),g·mol-1

m1the mass of metamizol monohydrate,g

m2the mass of pure solvents(methanol,ethanol,n-propanoland isopropanol),g

m3the mass of the second solvent in binary mixed solvent systems(ethanol or isopropanol),g

Nnumber of experimental points in each system

ppressure,MPa

Rgas constant,J·mol-1·K-1

SEexcess entropy of solution,J·mol-1·K-1

ΔSmthe mixing entropy of solution,J·mol-1·K-1

the mixing entropy of ideal solution,J·mol-1·K-1

Tabsolute temperature,K

x1experimental solubility of the solute,mol·mol-1

the initial mole fraction of methanol in the binary mixed solvent systems,mol·mol-1

γithe activity coefficient at equilibrium

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