Iranian Journal of Chemical Engineering Vol. 10, No. 4 (Autumn), 2013, IAChE. Keywords: Surface Tension, Langmuir, Extended UNIQUAC, Pitzer, Meissner

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1 Iranian Journal of Chemical Engineering Vol. 1, No. 4 (Autumn), 213, IAChE Prediction of Surface Tenion in Single and Mixed Electrolyte Solution M. Dadra, M.R. Dehghani Thermodynamic Reearch Laboratory, School of Chemical Engineering, Iran Univerity of Science & Technology, Narmak, Tehran, Iran Abtract In thi tudy, the Langmuir adorption iotherm ha been coupled with activity coefficient model for prediction of urface tenion of ingle and mixed electrolyte olution. Variou activity model uch a Meiner, Pitzer and extended UNIQUAC have been ued and coupled with Langmuir adorption iotherm. The model parameter were determined through mathematical optimization uing experimental urface tenion data of ingle electrolyte olution. Abolute average deviation wa ued a objective function in optimization procedure. The reult howed that in the cae of ingle electrolyte olution different activity coefficient model have imilar capability while in the cae of mixed electrolyte olution, extended UNIQUAC model give better reult. Keyword: Surface Tenion, Langmuir, Extended UNIQUAC, Pitzer, Meiner 1. roduction Knowledge about the urface tenion of electrolyte olution i eential in chemical engineering procee uch a liquid-liquid extraction, emulification, demulification and variou eparation method. A an example, urface tenion i effective in the fluid flow through porou media [1]. In addition, variation of urface tenion can ignificantly affect the ma tranfer rate in ditillation column [2, 3]. There are imple method for calculation of urface tenion of pure liquid while prediction of urface tenion of mixture i really difficult, epecially for electrolyte olution. Many procee deal with the mixed electrolyte olution uch a mineral indutrie, in thi regard knowledge about urface tenion of mixed electrolyte olution will be ueful. In recent year different method have been preented for calculation of urface tenion of mixture [4-11]. Uing the equality of the chemical potential in the bulk and urface of liquid i one of the mot applicable method. For thi purpoe the activity of the olvent or omotic coefficient hould be known. Yu et al. [4] ued the modified mean pherical approximation model for calculation of Correponding author: m_dehghani@iut.ac.ir 3

2 Prediction of Surface Tenion in Single and Mixed Electrolyte Solution olvent activity and howed that it give a fairly accurate reult for ingle electrolyte olution up to high concentration. Li et al. [5] ued Pitzer equation for calculation of omotic coefficient. Their model could predict the urface tenion of ingle and alo mixed electrolyte olution at different temperature. The interface parameter were evaluated from correlating the urface tenion data of ingle electrolyte aqueou olution at one temperature. Hu et al. [6] utilized Patwardhan and Kumar equation for calculation of water activity in mixed electrolyte olution. They compared their reult with Li et al. work. Hu [7] preented a new imple predictive equation for multicomponent olution, they ued a linear iopietic relation baed on Butler equation. Experimental data on binary ubytem i eential for thi model. In a different approach, the Gibb adorption equation ha been ued [8-1] for prediction of urface tenion of mixture. Our literature review howed that thi approach i more applicable for prediction of urface tenion of mixture a well a mixed electrolyte olution [8-1]. Denoyer et al. [8] utilized thi concept for prediction of interfacial tenion between a mixture of organic olvent and aqueou electrolyte olution baed on Gibb and Langmuir adorption equation. Li and Lu [9, 1] modified Denoyer et al. model through employing the Meiner and Pitzer activity model. Thi method wa uccefully applied for calculation of urface tenion and interfacial tenion of mixed aqueou electrolyte olution. They claimed that in their propoed model, the activity coefficient model ha determinant effect in accurate prediction of urface tenion and interfacial tenion. In a different approach artificial neural network ha been ued for prediction of urface tenion in binary mixture [11]. In mot of the previou work, urface tenion of ingle electrolyte olution ha been correlated uing one or two adjutable parameter. In thi work the capability of different activity model in prediction of urface tenion of mixed electrolyte olution ha been invetigated. 2. Theory 2-1. Surface tenion model for ingle electrolyte olution In the aqueou electrolyte olution, between vapor and liquid at the contant temperature and preure, the Gibb adorption equation tate that [12]: d d d (1) w w ij ij all alt where σ i equilibrium urface tenion, ij, w and ij w, repreent the interfacial exce and chemical potential of water and the electrolyte ij, repectively. For an aqueou olution including a ingle electrolyte, Eq. (1) reduce to: d d d (2) where, w w w and are defined relative to an arbitrarily choen dividing urface. In order to implify the equation (2), it i feaible to locate the arbitrary urface o that w. In thi condition Eq. (2) will hrink to the following form: w d d ln (3) 4 Iranian Journal of Chemical Engineering, Vol. 1, No. 4

3 Dadra, Dehghani In an electrolyte olution, alt chemical potential can be defined a follow: (4) Where, in the molality cale framework we will have: ln RT ln m RT m ln a a RT ln m m RT RT Where, ln (5) (6). After rearrangement, the following relation will be obtained: ln RT ln m RT a Where, a, m and (7) are the molality cale mean ionic activity, the mean ionic molality and mean ionic activity coefficient repectively. If the alt chemical potential i ubtituted in Eq. (3), the following equation will be obtained: w d RT d lna (8) Li and Lu [9, 1] aumed that a a, conequently, alt activity can be calculated uing a a m. By uing Langmuir [13], at equilibrium condition, the rate of adorption and deorption of the electrolyte on urface mut be equal: k 1 a k (9) a d where i the occupied interface fraction by the electrolyte and ka and kd refer to the adorption and the deorption contant rate repectively. Rearranging Eq. (9) lead u to Eq. (1): K a (1) 1 K a a K k k i defined a the adorption d equilibrium contant. On the other hand, by auming mono layer adorption of electrolyte at the interface[13], the occupied interface fraction by electrolyte i defined a: n (11) n Here n, n indicate the number of mole and the maximum number of electrolyte at the interface. By dividing the numerator and the denominator of Eq. (11) by A (the interfacial area) we will have: n / A (12) n / A In Eq. (12), and refer to the interfacial exce of electrolyte and the maximum interfacial exce. The Gibb dividing interface with Г w = yield: (13) w w Iranian Journal of Chemical Engineering, Vol.1, No. 4 5

4 Prediction of Surface Tenion in Single and Mixed Electrolyte Solution In which w and w indicate the interfacial exce and the maximum interface exce repectively when Г w =. Combining Eq. (1) and Eq. (13) lead to the following form: Model 1: w 1 RT ln (18) 1 K a K a 1 K a w w Subtituting Eq. (14) into Eq. (8) yield: (14) Model 2: w Ka RT ln 1 1 Ka (19) w K a d RTd ln a 1 K a egrating Eq. (15) from a = to (15) a lead to the following equation for etimating urface tenion of aqueou ingle electrolyte olution: RT w 1 ln 1 Ka (16) In Eq. (16), σ i the urface tenion of pure water in abence of any electrolyte at the ytem temperature. w and K are the model parameter which are determined by minimizing the following objective function: f 1 calc exp n exp (17) 2-2. Surface tenion model for mixed electrolyte olution Prediction of urface tenion of mixed electrolyte olution can be made by two different model. Li and hi coworker [9, 1] preented two model for non-competing (Model 1) and competing (Model 2) adorption of electrolyte: In the above equation, adjutable parameter w ( K, ) a well a electrolyte mean ionic activity (a ) mut be known for calculation of urface tenion. Uually, adjutable parameter are determined uing experimental data on urface tenion of ingle electrolyte olution. The adjuted parameter can then be ued for mixed electrolyte olution. The accuracy of the model depend on the accuracy of electrolyte activity in the mixed electrolyte olution. In the previou work Meiner a well a Pitzer activity model have been utilized [9, 1]. In order to achieve a general judgment about the capability of variou activity model, in thi work the ability of the extended UNIQUAC model ha been compared with Meiner and Pitzer model. Extended UNIQUAC model wa firt preented by Sander and co-worker [14]. Later it wa modified by Nicolaien et al. [15] a well a Thomen et al. [16]. In thi work the lat verion ha been utilized. The available model parameter in the literature have been ued in thi work [17-2]. Meiner method i an empirical model which include a graphical method for computing water activitie and a technique 6 Iranian Journal of Chemical Engineering, Vol. 1, No. 4

5 Dadra, Dehghani for calculating mean ionic activity coefficient in multi-ion olution. Thee graph are baed on the reduced activity coefficient veru the ionic trength, for different alt [21-23]. The Pitzer model i an extenion of the Debye-Huckel model. In the Pitzer model binary and ternary hort-range interaction have been conidered uing a virial expanion. Thi model i the mot popular model among different theorie for electrolyte olution. Alo, thee equation can be applied in iterative calculation becaue the ion interaction parameter are tated a explicit function of ionic trength and require very few parameter to calculate propertie of both ingle and mixed electrolyte olution [24]. In thi work the activity coefficient of mixed electrolyte olution i calculated utilizing implified Pitzer model [25, 26]. 3. Reult and dicuion In order to check the ability of activity coefficient model in calculation of urface tenion, in the firt tep adjutable parameter uing experimental data on ingle electrolyte olution have been determined. In the cae of the Pitzer model, it i found that the dependency of the parameter to the temperature cannot be ignored, becaue of coniderable error oberved in prediction of urface tenion. However, for mall value of activitie the oberved error wa negligible [9]. In Table 1, the model parameter a well a abolute average deviation (AAD %) of three activity coefficient model have been introduced. In the cae of ingle electrolyte olution it can be een that uing the extended UNIQUAC model yield overall AAD % of.. However, in the cae of Pitzer and Meiner model, the overall AAD % are.26 and. repectively. The reult how that in thi cae all model have imilar performance. In Fig 1, 2 and 3 the experimental value of urface tenion of SrCl 2, HNO 3 and KCl aqueou olution have been depicted in comparion with the modeling reult. In Table 2, the ability of different activity model ha been invetigated in prediction of urface tenion at different temperature. Table 2 indicate that all model can predict urface tenion at different temperature with acceptable accuracy. Conidering the above reult, it can be concluded that in the cae of ingle electrolyte olution, all model have imilar ability with regard to urface tenion. Thee reult can be referred to utilizing two adjutable parameter which have been included in the Gibb adorption model. In order to better judge the ability of the variou activity model, adjuted parameter were ued to predict the urface tenion of mixed electrolyte olution, without uing any additional parameter. In Table 3, the reult of prediction of urface tenion of mixed electrolyte olution uing three activity coefficient model have been reported. Two different adorption model (Eq. 18 and 19) have been utilized for thi purpoe. In the cae of firt adorption model, the reult howed that the extended UNIQUAC model give more accurate reult, the overall AAD % in prediction of mixed electrolyte urface tenion wa 1.49, 6.66 and 4.14 achieved by the extended UNIQUAC, Pitzer and Meiner model, repectively. In the cae of econd adorption model, the overall AAD % Iranian Journal of Chemical Engineering, Vol.1, No. 4 7

6 Prediction of Surface Tenion in Single and Mixed Electrolyte Solution of 1.83, 3.93 and 3.3 have been obtained uing extended UNIQUAC, Pitzer and Meiner model, repectively. Table 1. The model parameter for Surface Tenion of ingle electrolyte olution with three model. Extended UNIQUAC Pitzer Meiner Salt T(K) m Max N w ca K AA D % w ca K AAD % w ca K AAD % NaNO 3 HNO 3 28 KNO 3 NH 4NO e e e e e e e e e e e e KOH e e e NH 4Cl e e e HCl e e e NaCl e e e KCl e e e MgCl 2 31 BaCl e e e e e e CaCl e e e SrCl 2 MnCl 2 32 (NH 4) 2SO 4 33 Na 2CO 3 33 Na 2SO 4 Overall AAD % e e e e e e e e e e e e e e e Molality Figure 1. Comparion between calculated and experimental data ( ) of urface tenion of SrCl 2 veru molality at Langmuir&E.UNIQUAC ( ), Langmuir&Meiner (-----), Langmuir&Pitzer ( ). 8 Iranian Journal of Chemical Engineering, Vol. 1, No. 4

7 Dadra, Dehghani Molality Figure 2. Comparion between calculated and experimental data ( ) of urface tenion of HNO 3 veru molality at Langmuir&E.UNIQUAC ( ), Langmuir&Meiner (-----), Langmuir&Pitzer ( ). Molality Figure 3. Comparion between calculated and experimental data ( ) of urface tenion of KCl veru molality at by Langmuir&E.UNIQUAC ( ), Langmuir&Meiner (-----), Langmuir&Pitzer ( ). Table 2. Predicted Surface Tenion at other temperature with the ame parameter by three model. Salt T(K) m max N Extended UNIQUAC Pitzer Meiner NH 4NO 3 28 KNO , , , , , , , NaCl , 33.15, , KCl , , , (NH 4) 2SO 4 32 Na 2CO 3 33 Na 2SO , 35.65, 33.15, 3.65, , , 29.65, , , , , , , Overall AAD % Iranian Journal of Chemical Engineering, Vol.1, No. 4 9

8 Prediction of Surface Tenion in Single and Mixed Electrolyte Solution Table 3. Prediction of Surface Tenion in mixed electrolyte olution by three model. Extended UNIQUAC Pitzer Meiner Salt T(K) N I max AAD 1% AAD 2% AAD 1% AAD 2% AAD 1% AAD 2% BaCl 2 -HCl SrCl 2 -HCl CaCl 2 -HCl KNO 3 -HNO KNO 3 -NH 4 NO KNO 3-NH 4Cl NH 4Cl-(NH4) 2SO (NH 4 ) 2 SO 4 -NaNO NaCl -Na 2 SO NaCl -MgCl Overall AAD % Reult have been preented in Table 3. It can be concluded that the extended UNIQUAC model ha higher accuracy in prediction of urface tenion of mixture in comparion with the other. Thi concluion i more obviou in the Fig. 4 and 5. The reult indicated that the extended UNIQUAC model can be ued for prediction of urface tenion in mixed electrolyte olution efficiently. Thi i due to the ability of extended UNIQUAC model in prediction of activity coefficient of electrolyte in the mixture. A it i hown in Table 3, the accuracy of Meiner model in prediction of urface tenion of KNO 3 - HNO 3 ytem i relatively lower compared to the other model. The reult preented in Table 3 how that Meiner activity coefficient model give acceptable reult at low ionic trength while at higher concentration the error will reach up to 12 percent. It eem that the accuracy of Meiner model i dependent on acid concentration. For Meiner and Pitzer model, the econd adorption model ha higher accuracy than the firt one, however, it i vice vera for extended UNIQUAC model. On the other hand, the overall AAD % of extended UNIQUAC model for both 1 Iranian Journal of Chemical Engineering, Vol. 1, No. 4

9 Dadra, Dehghani adorption model i lower than Meiner and Pitzer model. So, the effect of adorption model in prediction of urface tenion of mixed electrolyte olution i lower than the accuracy of activity coefficient model. 4. Concluion A modified model ha been propoed baed on the Gibb and Langmuir adorption model for prediction of urface tenion in mixed electrolyte olution. Three activity coefficient model including extended UNIQUAC model, Pitzer equation and Meiner method have been utilized for thi purpoe. The model parameter were etimated uing mathematical optimizing and baed on ingle electrolyte experimental data. The modified model (extended UNIQUAC model+ Langmuir adorption model) can correlate urface tenion of ingle electrolyte with overall abolute average deviation of.%. Alo, overall abolute average deviation of Pitzer equation and Meiner method were.26% for.%, repectively. The mentioned reult howed that in the cae of ingle electrolyte olution, teted activity coefficient model have imilar performance in correlation of ingle electrolyte data while in prediction of mixed electrolyte urface tenion, the reult howed that Extended UNIQUAC model i more capable in comparion with Pitzer and Meiner model. Thee reult can be due to the capability of extended UNIQUAC model in prediction of accurate activity coefficient in mixed electrolyte olution. Finally, it can be concluded that the accuracy of activity model i very important in accurate prediction of urface tenion in mixed electrolyte olution. Figure 4. Comparion between calculated and experimental data ( ) of urface tenion of BaCl 2 -HCl veru total molality at Langmuir&E.UNIQUAC ( ), Langmuir&Meiner (-----), Langmuir&Pitzer ( ). Iranian Journal of Chemical Engineering, Vol.1, No. 4 11

10 Prediction of Surface Tenion in Single and Mixed Electrolyte Solution Figure 5. Comparion between calculated and experimental data ( ) of urface tenion of (NH 4 )2SO 4 -NaNO 3 veru total molality at Langmuir&E.UNIQUAC ( ), Langmuir&Meiner (-----), Langmuir&Pitzer ( ). Nomenclature A interfacial area (m 2 ) a a + a - K ka kd m m m activity of the electrolyte (cationanion) activity of cation activity of anion adorption equilibrium contant adorption rate contant deorption rate contant mean ionic molality (mol/kg) molality of anion (mol/kg) molality of cation (mol/kg) n number of mole of electrolyte at the interface n maximum number of mole of electrolyte at the interface R ga contant (cm 3 kpa mol -1 K -1 ) T temperature (K) Greek Symbol mean ionic activity coefficient activity coefficient of anion activity coefficient of cation interfacial exce electrolyte (cation- anion) w ij w maximum interfacial exce of electrolyte (cation- anion) interfacial exce of water interfacial exce of electrolyte ij interfacial exce of electrolyte by Г w = w maximum interface exce of electrolyte by Г w = fraction of interface occupied by the electrolyte chemical potential of electrolyte chemical potential of anion chemical potential of cation tandard mean ionic chemical potential tandard chemical potential of anion tandard chemical potential of cation toichiometric coefficient of anion toichiometric coefficient of cation 12 Iranian Journal of Chemical Engineering, Vol. 1, No. 4

11 Dadra, Dehghani chemical potential of electrolyte ij ij at interface w chemical potential of water at interface chemical potential of electrolyte (cation- anion) at interface equilibrium interfacial tenion (mn/m) equilibrium interfacial tenion in abent of electrolyte (mn/m) Reference [1] De Never, N., Fluid mechanic for chemical engineer, 2 nd ed., McGraw Hill, New York, (1991). [2] Eckert, C.A. and Praunitz, J.M., "Statitical urface thermodynamic of imple liquid mixture", AIChE J., 1, 677, (1964). [3] Zuiderweg, F.J. and Harmen, A., "The influence of urface phenomena on the performance of ditillation column", Chem. Eng. Sci., 9, 89, (1958). [4] Yu, Y.X., Gao, G.H. and Li, Y.G., "Surface tenion for aqueou electrolyte olution by the modified mean pherical approximation", J. Fluid Phae Equilib., 173, 23, (2). [5] Li, Z.B., Li, Y.G. and Lu, J.F., "Surface tenion model for concentrated electrolyte aqueou olution by the Pitzer equation", Ind. Eng. Chem. Re., 38, 1133, (1999). [6] Hu, Y.F. and Lee, H., "Prediction of the urface tenion of mixed electrolyte olution baed on the equation of Patwardhan and Kumar and the fundamental Butler equation", J. Colloid erf. Sci., 269, 442, (24). [7] Hu, Y.F., "A new predictive equation for the urface tenion of aqueou mixed ionic olution conforming to the linear iopietic relation", J. Solution Chem., 32, 897, (23). [8] Denoyer, C., Mabernat, O. and Gourdon, C., "Predictive model for the calculation of interfacial tenion in nonideal electrolytic ytem", J. Colloid erf. Sci., 191, 22, (1997). [9] Li, Z. and Lu, B.C.Y., "Surface tenion of aqueou electrolyte olution at high concentration- repreentation and prediction", Chem. Eng. Sci., 56, 2879, (21). [1] Li, Z. and Lu, B.C.Y., "Prediction of interfacial tenion between an organic olvent and aqueou olution of mixed-electrolyte", J. Fluid Phae Equilib., 2, 239, (22). [11] Parhizgar, H., Dehghani, M.R., Khazaei, A. and Dalirian, M., "Modelling of vaporization enthalpie of petroleum fraction and pure hydrocarbon uing genetic programming", Ind. Eng. Chem. Re., 51, 75, (212). [12] Adamon, A.W. and Gat, A.P., Phyical chemitry of urface, 6 th ed., Wiley & Son Inc., New York, (1997). [13] Langmuir, I., "The adorption of gae on plane urface of gla, mica and platinum", J. Am. Chem. Soc., 4, 1361, (1918). [14] Sander, B., Fredenlund, A. and Ramuen, P., "Calculation of vapourliquid equilibria in mixed olvent/alt ytem uing an extended UNIQUAC equation", Chem. Eng. Sci., 41, 1171, (1986). [15] Nicolaien, H., Ramuen, P. and Sørenen, J. M., "Correlation and Iranian Journal of Chemical Engineering, Vol.1, No. 4 13

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