Solid−Liquid Phase Equilibrium of Nicotinamide in Different PureSolvents: Measurements and Thermodynamic ModelingHaili Wu, Leping Dang, and Hongyuan Wei*

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, People’s Republic of China

*S Supporting Information

ABSTRACT: The solubility of nicotinamide in water, methanol, ethanol, 2-propanol, n-butanol, and ethyl acetate attemperatures ranging from 288.15 K to 318.15 K was measured via a static gravimetric analytic method, and the meltingtemperature and fusion enthalpy of nicotinamide were obtained using differential scanning calorimetry. The experimentalsolubility data were correlated by the modified Apelblat equation, the van’t Hoff equation, the λh (Buchowski) equation, and theWilson model; the van’t Hoff equation shows the best agreement. Furthermore, the dissolution enthalpy and dissolution entropyof nicotinamide in the corresponding solvents were predicted.

1. INTRODUCTION

Nicotinamide (C6H6N2O, CAS Registry No. 98-92-0), which isalso called pyridine-3-carboxamide (IUPAC name), is theamide derivative of niacin (vitamin B3). Nicotinamide, which isa water-soluble vitamin and a member of the vitamin B groups,has been shown to enhance the solubility of many poorly water-soluble drugs through complexation.1 The molecular structureof nicotinamide is shown in Figure 1.

Many studies have focused on the pharmacological effects ofnicotinamide,2,3 but only a few have attempted to establishpurification methods to obtain products with high purity andyields. Crystallization is often utilized as a method ofproduction, purification, or recovery of solid material. Thesolubility characteristics of solid compounds in given solventshave a considerable influence on the design and operation ofthe solution crystallization process.4 In addition, solubilitydetermines methods of supersaturation generation and the yieldin the crystallization process.5,6

In this study, the solubility of nicotinamide in water,methanol, ethanol, 2-propanol, n-butanol, and ethyl acetatefrom 288.15 K to 318.15 K were measured using a staticgravimetric analytical method to determine the properdissolution solvent and obtain systematic thermodynamicinformation on the crystallization of nicotinamide. Themodified Apelblat equation, the van’t Hoff equation, the λh(Buchowski) equation, and the Wilson model were used tocorrelate the experimental data, based on the pure componentthermodynamic properties (including melting temperature,fusion enthalpy, and mole volume). The melting temperatureand fusion enthalpy of nicotinamide were determined bydifferential scanning calorimetry (DSC). To understand the

solubility behavior of nicotinamide in pure solvent, thedissolution enthalpy and dissolution entropy were calculated.

2. THERMODYNAMIC MODELS

The solubility of a solid in a liquid may be expressed in a verygeneral manner:

γ

− =Δ

− −Δ

+ −

+

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟x

HR T T

c

RTT

TT

ln1 1

ln 1

ln

1mfus

m

p,m

m

m

1 (1)

where x1 is the mole fraction solubility of solute in the solvent,γ1 is the activity coefficient, and ΔHm

fus stand for the enthalpy offusion. T and Tm represent equilibrium temperature andmelting temperature of the solute.7 Δcp,m is the differencebetween the molar heat capacity of the crystalline form and themolar heat capacity of the liquid form at the meltingtemperature.8

Generally, an empirical formula can be applied to calculatethe activity coefficient within a small temperature range:9

γ = +abT

ln 1 (2)

where a and b are empirical constants that are dependent oncomposition. Substituting eq 2 into eq 1 gives

=Δ

−Δ

+ −

+Δ

−Δ

− +Δ

⎡⎣⎢

⎤⎦⎥

⎛⎝⎜⎜

⎞⎠⎟⎟

xH

RT

c

RT a

c T

RHR

bT

c

RT

ln (1 ln )

1ln

1mfus

m

p,mm

p,m m mfus

p,m

(3)

Received: October 27, 2013Revised: December 11, 2013Accepted: January 6, 2014Published: January 6, 2014

Figure 1. Molecular structure of nicotinamide.

Research Note

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Modified Apelblat Equation. Equation 3 can be writtenas10

= + +x ABT

C Tln ln1 (4)

where A, B, and C are empirical constants. The values of A andB represent the variation in the solution activity coefficient, andthe value of C reflects the effect of temperature on the fusionenthalpy.11,12

van’t Hoff Equation. The vant’t Hoff equation, whichshows that the logarithm of mole fraction of a solute is a linearfunction of heat and entropy of solution, is as follows:13

= −Δ

+Δ

xH

RTSR

ln sol sol(5)

where x is the mole fraction of solute in the solvent, ΔHsol theheat of solution, ΔSsol the entropy of solution, T thecorresponding absolute temperature, and R the universal gasconstant. Plotting ln x versus reciprocal of absolute temperature(1/T) should result in a straight line with a slope of ΔHsol/R.

14

λh (Buchowski) Equation. The λh equation, whch wasproposed by Buchowski et al., can be also used to correlate thesolubility as expressed below:15

λ λ+−

= −⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟⎤⎦⎥⎥

⎛⎝⎜

⎞⎠⎟

xx

hT T

ln 11 1 11

1 m (6)

λ is the mean association number, i.e., the mean value of thenumber of monomolecules per multimer molecule. h is theenthalpy of fusion at melting temperature divided by the gasconstant. Tm is the melting temperature of nicotinamide.Wilson Model. The difference in heat capacity of the solute

in the liquid state and solid state at temperature T can beconsidered equal to zero. This assumption is commonly usedfor the estimation of solubility,16 and based on empiricalobservations. Therefore, eq 1 can be simplified as follows:17

γ− =Δ

− −⎛⎝⎜

⎞⎠⎟x

HR T T

ln1 1

ln1mfus

m1

(7)

In a binary mixture system, the activity coefficient of Wilsonmodel can be obtained as18

γ = − + Λ +Λ

+ Λ−

Λ+ Λ

⎛⎝⎜

⎞⎠⎟x x x

x x x xln ln( )1 1 12 2 2

12

1 12 2

21

2 21 1

(8)

where

λ λ λ

λ λ λ

Λ = −−

= −Δ

Λ = −−

= −Δ

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

V

V RT

V

V RT

V

V RT

V

V RT

exp exp

exp exp

12m

m

12 11 m

m

12

21m

m

21 22 m

m

21

2

1

2

1

1

2

1

2 (9)

in which Δλ12 and Δλ12 are the cross-interaction energyparameters (J/mol) that can be regressed from theexperimental data. Vm1

and Vm2are the mole volumes of solute

and solvent, respectively.19

3. EXPERIMENTAL SECTION3.1. Materials. Nicotinamide was supplied by Tianjin

Guangfu Fine Chemical Research Institute (Tianjin, PRC) with

the purity of the mass fraction of >99%. All of the solventsincluding water, methanol, ethanol, 2-propanol, n-butanol, andethyl acetate, were analytical grade reagents purchased fromTianjin Kewei Chemical Co. in China without furtherpurification. The main physicochemical properties (includingpurity, molar weight, mole volumes, polarity) of solvents20 arelisted in the Supporting Information.

3.2. Differential Scanning Calorimetry. Thermal analysiswas conducted by differential scanning calorimetry (DSC)(Model DSC 1/500, Mettler−Toledo, Switzerland) under theflow of nitrogen atmosphere. The calibration of the instrumentwas performed using the phase-transition temperature andphase-transition enthalpy of National Institute of Standards andTechnology (NIST) reference materials (indium: Tm = 429.75K, ΔHm

fus = 28.45 J/g; stannum: Tm = 505.10 K, ΔHmfus = 60.21

J/g) before measurement. The samples of 5−10 mg wereprepared in a covered 40-μL aluminum crucible with a hole inthe lid to allow venting.21 An empty crucible was used as areference. The heating rate of 2 K/min from 293.15 K to423.15 K for melting temperature and heat capacity measure-ment was used.

3.3. Solubility Measurements. The solubility of nicoti-namide was measured using a static method, and astraightforward gravimetric analysis was chosen.22 First, differ-ent pure solvents (water, methanol, ethanol, 2-propanol, n-butanol, and ethyl acetate) were prepared,23 an excess mass ofnicotinamide was, respectively, added to these solvents in 50-mL Erlenmeyer flasks. Then, flasks were placed in the constanttemperature water bath oscillator (WE-1, Tianjin HonnourInstrument Co., Ltd., PRC) with agitation over at least 24 h tomake sure the phase compositions reached solid−liquidequilibrium. The temperature was controlled within ±0.02 K.Samples of 1 mL of saturated solution were pipetted out

from the flasks through a 0.45 μm PTFE membrane filter andkept in the previously weighted Petri dish. The samples weredried in the vacuum drying oven (Type DZF-6020, Shanghai YiHeng Scientific Instrument Co., Ltd., PRC) under vacuum at313.5 K, after 6 h, the temperature was raised to 333.15 K untilthe solvent was completely evaporated. The samples wereaccurately weighted before and after solvent evaporation usingan analytical balance (Type FA2004, China) with an accuracyof ±0.0001 g.New samples of saturated solution were again pipetted out

from the flasks after 24 h and worked out as above method, thesame experiment was conducted three times at the sametemperature. The data used to calculate the mole fraction ofnicotinamide in pure solvents were averaged.The mole fraction solubility (x1) of nicotinamide can be

calculated using the solubility data in the following equation:

=+

xm M

m M m M/

( / ) ( / )11 1

1 1 2 2 (10)

where m1 and M1 represent the mass (g) and the molecularweight (g/mol) of nicotinamide; m2 and M2 stand for the mass(g) and the molecular weight (g/mol) of solvent, respectively.

4. RESULTS AND DISCUSSION

4.1. Thermal Properties at Melting Point. The mainvalues of melting temperature (Tm) and fusion enthalpy(ΔHm

fus) of nicotinamide were obtained by DSC analysis, Tm= 401.6 ± 0.3 K, ΔHm

fus = 20.49 ± 0.3 kJ/mol, as presented inFigure 2, which are in good agreement with reported data in the

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literature.24 The fusion enthalpy is also related to entropy offusion:

Δ = ΔH S Tmfus

mfus

m (11)

Thus, ΔSmfus = 50.86 J/(mol K).

4.2. Solubility Data. The measured mole-fraction solubilitydata of nicotinamide in water, methanol, ethanol, 2-propanol, n-butanol, and ethyl acetate are plotted in Figure 3. The solubility

of nicotinamide increases with temperature in each solventmentioned above. At a given temperature, the solubility order iswater > methanol > ethanol > n-butanol > 2-propanol > ethylacetate. Referring to the polarity of the solvents obeys thefollowing order: water (100) > methanol (76.2) > ethanol(65.4) > n-butanol (60.2) > 2-propanol (54.6) > ethyl acetate(23);20 the polarity of solvent was regarded as the key factor todetermine the solubility in all examined solvents.

4.3. Correlation of the Solubility Data. RegressionAnalysis and Prediction. The experimental solubility data ofnicotinamide in water, methanol, ethanol, 2-propanol, n-butanol, and ethyl acetate were correlated by the modifiedApelblat equation, van’t Hoff equation, λh equation, and Wilsonmodel, respectively. The experimental and calculated solubil-ities of nicotinamide in six solvents are given in the SupportingInformation. The relative deviations (RD) between theexperimental and calculated values of solubility were calculatedby eq 12,25 which were also listed in the SupportingInformation:

=−x x

xRD i i

i

1, 1,cal

1, (12)

The mean absolute percentage deviation (MAPD) is ameasure of accuracy of a method for constructing fitted timeseries values in statistics, specifically in trend estimation. Itusually expresses accuracy as a percentage, and is defined by theformula

∑=−

×=

⎛⎝⎜⎜

⎞⎠⎟⎟N

x x

xMAPD

1100

i

Ni i

i1

1, 1,cal

1, (13)

where N is the number of experiment points, and x1,i and x1,ical

represent the experimental solubility and calculated solubility ata temperature corresponding to point i, respectively.The MAPD of each model was calculated for assessing the

accuracy and predictability of correlation models; the overallMAPD values of the four models are 2.15% (Apelblat), 2.33%(van’t Hoff), 3.66% (λh), and 2.31% (Wilson).It is worthwhile to note that the modified Apelblat equation

and the Wilson model use the melting point as the referencestandard state, although this is ∼100 degrees higher than thetemperature at which the solubility data were measured. Onthis basis, and comparing the MAPDs of the four models, thevan’t Hoff equation is better than the other models indescribing the relationship between equilibrium solubility andtemperature of the nicotinamide systems.

4.4. Dissolution Enthalpy and Dissolution Entropy.The van’t Hoff equation relates the logarithm of the molefraction of a solute as a linear function of the reciprocal of theabsolute temperature, as shown in eq 5. Figure 4 shows the plotof ln x1 versus 1/T, which gives the values of dissolutionenthalpy and dissolution entropy from the slope and theintercept, respectively. The estimated values of dissolutionenthalpy and entropy of nicotinamide in different solvents areshown in the Supporting Information.The dissolution enthalpy values of nicotinamide in each

solvent in the experimental temperature range are positive(ΔHsol > 0), indicating that the dissolving process ofnicotinamide in each solvent is endothermic, which explainswhy the solubility of nicotinamide in all examined solventsincreases as the temperature increases.Besides, if the solute and solvent did form an ideal solution,

the mixing enthalpy ΔHmix is zero.9 In a real solution, thedissolution enthalpy is given as ΔHsol = ΔHm

fus + ΔHmix, wherethe mixing enthalpy ΔHmix is a measure of deviation of the realsolubility of a solute−solvent system from its ideal behavior.26

The net variation in ΔHmix values results from the contributionof several types of interaction.27 It is worth noting that theabsolute value of mixing enthalpy in the ethyl acetate andethanol are much higher than that corresponding value in

Figure 2. Differential scanning calorimetry (DSC) curve ofnicotinamide.

Figure 3. Mole fraction solubility of nicotinamide in different puresolvents at temperatures ranging from 288.15 K to 318.15 K: water(black square, ■), methanol (red circle, ●), ethanol (blue uprighttriangle, ▲), 2-propanol (green inverted triangle, ▼), n-butanol (tealdiamond, ◆), and ethyl acetate (purple star, ★). The correspondinglines are calculated values based on the van’t Hoff equation.

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water, methanol, 2-propanol, and n-butanol solvents. It isindicated that solutions of nicotinamide in ethyl acetate andethanol exhibit highly nonideal behavior.

5. CONCLUSIONSExperimental data on the solubility of nicotinamide wereobtained in water, methanol, ethanol, 2-propanol, n-butanol,and ethyl acetate, at temperatures from 288.15 K to 318.15 K.Differential scanning calorimetry (DSC) was employed toobtain the melting temperature and enthalpy of fusion ofnicotinamide. The solubility in six selected solvents increases asthe temperature increases. At the same temperature, thesolubility order in different solvents is water > methanol >ethanol > n-butanol > 2-propanol > ethyl acetate, which is inaccordance with the polarities of solvents. The experimentalsolubility data were correlated by the modified Apelblatequation, the van’t Hoff equation, the λh (Buchowski)equation, and the Wilson model. The van’t Hoff equation isexpected to give the best fit in describing the temperaturedependence of solubility. Finally, the dissolution enthalpy(ΔHsol) and dissolution entropy (ΔSsol) were estimated basedon the van’t Hoff equation. All of the solubility data andcalculation equations in this work could be used as essentialdata for the purification of nicotinamide and furtherthermodynamic research.

■ ASSOCIATED CONTENT*S Supporting InformationPhysicochemical propertied (including purity, molar weight,mole volumes, polarity) of pure components, parameters ofeach model, experimental solubility, calculated values ofsolubility, and estimated values of the dissolution enthalpyand dissolution entropy. This material is available free of chargevia the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*Tel.: +86-22-27405754. Fax: +86-22-27400287. E-mail:crystallization.wei@hotmail.com.

NotesThe authors declare no competing financial interest.

■ NOTATIONS

x1 = experimental solubility of nicotinamide (mol/mol)m1 = mass of nicotinamide (g)M1 = molecular weight of nicotinamide (g/mol)m2 = mass of solvent (g)M2 = molecular weight of solvent (g/mol)Tm = melting temperature (K)ΔHm

fus = enthalpy of fusion at the melting point (J/mol)ΔSmfus = entropy of fusion at the melting point (J/(mol K))Δcp,m = difference in heat capacity of the solute between thesolid and liquidA, B, C = empirical constants for the modified Apelblatequationλ, h = model parameters for the λh equationγ = activity coefficientR = gas constant; R = 8.3145 J/(mol K)Vm = molar volumes (cm3/mol)Δλ12 = cross-interaction energy parameters for the Wilsonequation; Δλ12 = λ12 − λ11) (J/mol)Δλ21 = cross-interaction energy parameters for the Wilsonequation; Δλ21 = λ21 − λ22) (J/mol)x1cal = calculated solubility of nicotinamide (mol/mol)ΔHsol = dissolution enthalpy (kJ/mol)ΔSsol = dissolution entropy (J/(mol K))ΔHmix = mixing enthalpy (kJ/mol)RD = relative deviationMAPD = mean absolute percentage deviation

Subscripts1 = solute (nicotinamide)2 = solvent (water, methanol, ethanol, n-butanol, 2-propanol,and ethyl acetate)

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