Comparison Among Pitzer Model and Solvation Models. Calculation of

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Comparison Among Pitzer Model and Solvation Models. Calculation of Osmotic and Activity Coefficients and Dilution Enthalpy for Single-Electrolyte Aqueous Solutions Javier Temoltzi-Ávila, Gustavo Arturo Iglesias-Silva, and Mariana Ramos-Estrada Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00699 • Publication Date (Web): 05 Jul 2018 Downloaded from http://pubs.acs.org on July 12, 2018

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Industrial & Engineering Chemistry Research

Comparison Among Pitzer Model and Solvation Models. Calculation of Osmotic and Activity Coefficients and Dilution Enthalpy for Single-Electrolyte Aqueous Solutions

Javier Temoltzi-Avila, Gustavo A. Iglesias-Silva* Departamento de Ingeniería Química Instituto Tecnológico de Celaya Celaya, Guanajuato, CP 38010 (México) and Mariana Ramos-Estrada Facultad de Ingeniería Química Universidad Michoacana de San Nicolás de Hidalgo Morelia, Mich. CP 58030 México Abstract

We have compared the performance of the Pitzer model and solvation models in the correlation of the mean activity and osmotic coefficients of 338 electrolyte solutions at 298.15 K and the temperature dependence of 47 electrolyte solutions. We have collected and compared their performance using experimental data for 1:1, 1:2, 1:3, 1:4, 2:1, 2:2, 3:2, and 4:1 electrolyte solutions. We show that the performance of the Pitzer model is about 54 % better than the other two models of all cases. The average standard deviations are 0.63, 1.41, and 1.47, for the Pitzer, and the solvation models, respectively, at 298.15 K. In the case of the temperature dependence, Pitzer model is 91 % better for the correlation of the activity and osmotic coefficients. However, it is better only the 9 % in the calculation of the dilution enthalpies where the solvation models perform better.

Keywords: Pitzer, Solvation, Electrolyte Solutions, Aqueous Solutions. * Corresponding author. Tel: 011 52 461 611 7575; fax: 011 52 461 611 7744. Email address: [email protected]

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1. Introduction Electrolyte solutions are used in many different industrial and natural processes1 such as separation, extraction, absorption, desalinization, oil recuperation, residual water treatment, etc. Then there is a need for the development of models to describe the thermodynamic behavior of these systems. Debye and Hückel2,3 develop a model for the representation of the activity coefficient of the electrolyte dilute aqueous solutions. Their model has been used as to represent the long range interactions. The Debye-Hückel equation is modified by Pitzer4 in 1973 and it has been used successfully by its group5-11 and others12-19 to create a virial type equation for the presentation of the osmotic and activity coefficient. For electrolytes 1:1, the model contains a nonlinear term with two fixed parameters and three adjustable parameters obtained from experimental data. For higher valence systems, this equation has four adjustable parameters and three fixed parameters in nonlinear term. The correlative capability of the model is adequate for electrolyte solutions where the concentration of the solute is less than 6 mol kg-1.4,20-23 In 1993, Lin et al.24,25 use the Poisson-Boltzmann equation to describe the long range forces and combine it with a term based upon Coulomb’s law for the electrical potential between ionmolecule. This last term represents the solvation of the molecules and the short range interactions. This model contains three adjustable parameters. Later they proposed several modifications to their model26-28 being the most important the use of Pitzer model4 for the long range interactions. Pazuki et al.29 use the Debye-Hückel equation together with the Coulombic term to represent the activity coefficient of electrolyte aqueous solutions. Ge et al.30,31 use Lin et al. original model but they consider as adjustable parameters: , , and , with the dielectric constant employed as a solute-specific constant and independent of temperature. Later, Ge et al.32,33 modify Lin et al. model by considering an explicit temperature term for the Debye-Hückel equation. In this work, we have compared the performance of Lin et al.,30,31 Pazuki et al.29 and Pitzer4,34 models for the representation of the activity and osmotic coefficients. We have calculated the parameters of 1:1, 1:2, 1:3, 1:4, 2:1, 2:2, 3:1, 3:2 and 4:1 aqueous electrolyte solutions at 298.15 K. In the literature already appears comparisons of the Pitzer model with another models based upon different and similar backgrounds.35,36-41 Among these models are the local composition21,36,37 and the statistical models.38-41 Comparison of the activity and osmotic coefficients from the local composition and the Pitzer models already exists in the literature29,42,43. These comparisons show that the Pitzer model correlates in general better for electrolytes 1:1, 2:1, 2:2, 3:1 and 3:2. The statistical models are equations of state (EOS) for electrolyte solutions. These equations have the capability of predicting more thermodynamic properties than the Pitzer and solvation models. The prediction and/or correlation of activity and osmotic coefficients from the statistical models have been shown at lower concentrations (approximately up to 6 m). It will be unfair a comparison of these models with the Pitzer and solvation models which are developed specifically for activity and osmotic coefficients. Generally, the Pitzer model has the same or better correlative capability the osmotic and activity coefficients than other correlation models. Therefore, this model has become a standard correlation of electrolyte and osmotic coefficients of electrolyte solutions.


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2. Theory In a solution, an electrolyte is solvated when it is dissolved and their ions are surrounded by solvent molecules. If the solvent is water the process is called hydration. The solvation theory is first proposed by Stokes and Robinson44 using the Brunauer-Emmett-Teller (BET) adsorption isotherm45 to represent the interactions between molecules of solute and solvent. Lin et al.24,25 develop a predictive model to calculate the activity and osmotic coefficient of strong electrolyte binary solutions. Their equation for the logarithm of the activity coefficient consists of a long range contribution (ion-ion interaction) and a short range contribution (ionmolecule interactions):

ln γ = ln γ LR + ln γ SR i i i

(1)

The long range contribution is given by a modification of the Debye-Hückel equation due to Pitzer4  I1 2  2 + ln 1 + bi I 1 2  lnγ LR = − zi2 Aφ  1 2 i bi 1 + bi I 

(

)

(2)

where is the maximum approximation parameter; is the ionic strength; zi is the absolute charge number of ion i; and Aφ is the slope of the Debye-Hückel law given by

Aφ

(2πN A ρ )1 / 2  = 3

  4πε ε kT  0 r   e2

3/ 2

(3)

and is the Avogadro number; and are the dielectric constant of the solvent and at vacuum; is the density of the solvent; is the Boltzmann constant; and is the absolute of the electron charge. The values of ε r = 78.38 and ρ = 997 .05 kg ⋅ m -3 are taken from the literature.46 Lin et al.24,25 express the short range interactions with a solvation term based upon the electrical potential between a ion and a solvent molecule

ln γiSR = Si I 2 n

(4)



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where v+ or v- is the stoichiometric coefficient of cation or anion, respectively; is a characteristic parameter obtained from the data; and is the solvation parameter of specie given by

z i2 his e 2 µ Si = 2 B 2 kT

(5)

In the above equation, is the absolute charge number of the ion ; is the water dipole moment; ℎ and are constants; is the absolute temperature; and is an adjustable parameter. The subscript stands for ion-solvent. Then  I1 2  2 ln γ i = − z i2 Aφ  + ln 1 + bi I 1 2  + S i I 2 n 12 bi 1 + bi I 

(

ionic

activity

)

coefficient

(6)

The

mean

ln γ MX

  I12 2 S ln 1 + bMX I 1 2  + I 2n = − z M z X Aφ  + 12 bMX 1 + bMX I  (ν + + ν − )

ln γ MX = (ν + ln γ + +ν − ln γ − ) (ν + +ν − ) ,

(

can

be

calculated

)

using

the

definition

(7)

with

S=

e2 µ hcs z+2ν + + has z−2ν − 2B 2 kT

(

)

(8)

where S is the mean solvation parameter In Eq 7 the adjusting parameters are = (an equivalent dielectric constant) and (average maximum approximation parameter). Lin et al.24,25 fix the value of n equal to 0.645. In Eq 8, the subscripts cs and as stand for cation-solvent and anion-solvent, respectively; and v+ or v- is the stoichiometric coefficient of cation or anion, respectively. The osmotic coefficient is obtained from the mean activity coefficient using the relation proposed by Bjerrum47   I12 S  2n  2 n φ − 1 = − z M z X Aφ  +  I 12  1 + bMX I  (ν + + ν − )  1 + 2n 


(9)

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Recently, Ge et al.30,31 use Lin et al. original model but they considered as adjustable parameters: , , and . The dielectric constant is considered a solute-specific constant and is independent of temperature. Then, the activity and osmotic coefficients are  I12 2 S 12  ln γ MX = − z M z X Aφ  ln 1 b I I 2n + + MX + 12 bMX 1 + bMX I  (ν + + ν − )T

(

)

(10)

and 

 I12 S + 12  1 + bMX I  (ν + + ν − )T

φ − 1 = − z M z X Aφ 

 2n  2 n  I ,  1 + 2n 

(11)

respectively. Another equation that uses the solvation term is the equation proposed by Pazuki et al.29 They modified Lin et al. expression27 by using the Debye-Hückel2,3 equation to obtain

  zM z X I12 + SI n ln γ MX = − 3 z M z X Aφ  12  T + b I 1 MX  

(12)

The corresponding osmotic coefficient equation is

φ −1 = −

(

)

3 z M z X Aφ  bMX I 1 2 + 2 2 ln 1 + bMX I 1 2  z M z X  n  n −   SI  + 2 2 T 1 + n bMX I 1 2  bMX + bMX I1 2 bMX I12   

(13)

where the adjustable parameters in Eqs 12 and 13 are the same as in the Ge et al. model: , , and . In Eqs 12 and 13, S = e 2 µ / 2B 2 kT [(hcsν − + hasν + ) / (ν + + ν − )] . An equation that has been used successfully to represent the mean activity coefficient and the osmotic coefficient is the one development by Pitzer.4,34 They use

[( ) (

)]



ln γ MX

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 I1 2  2 = − z M z X Aφ  + ln 1 + bI 1 2  12 b 1 + bI  ( ) 1 α12 I    2ν ν   (0 ) 2 β MX  −α 1 I 1 2  12   α +  M X m 2 β MX + 1 − e 1 + I −  1  α12  2    ν    (2 )  α 22 I    2(ν Mν X )3 2 2 β MX 12 −α 2 I 1 2  12 (0 ) 1 + α 2 I −    + + 1− e z M z X m 2 3C MX 2  α2  2 ν    

(

)

{

(14)

}

and

{

}

I 1 2   2ν M ν X  (0 ) (1) −α I 1 2 ( 2 ) −α I 1 2 +  m β MX + β MX e 1 + β MX e 2 + 12   1 + bI   ν 

φ − 1 = − z M z X Aφ  2(ν M ν X )

32

ν

zM z X

12

{

(0 ) m 2 2C MX

(15)

}

(0 ) (1) (2 ) (0 ) (2 ) where β MX , β MX , β MX , and C MX are characteristic parameters. β MX = 0 for electrolytes with univalent ions in Eqs 14 and 15.

2.1 Temperature dependence In this work we have calculated the dilution enthalpy of a solution containing 1 mol of solute from concentration m1 to concentration m 2 . This thermodynamic quantity is related to the apparent molal enthalpy through ∆H dil (m1 → m 2 ) = Lφ , 2 → Lφ , 1

(16)

with the relative apparent molal enthalpy given for the Pitzer model as

Pitzer

Lφ

 ∂G E  T2  T = =−  n  ∂T    P, I A L L ν z M z X L ln 1 + bI 1 / 2 − 2ν Mν X RT 2 mBMX + m 2ν M z M C MX 2b

(

)

(

(17)

)

L L where BMX , C MX , AL represent the partial derivatives of BMX , C MX and Aφ, with respect to the at constant P and I . AL is given by


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 ∂Aφ AL = 4T  RT  ∂T

  T  ∂ ln V    ∂ ln ε   = −6 Aφ 1 + T   +     ∂T  P , I 3  ∂T  P , I   P, I 

(18)

with ε and V being the dielectric constant and the volume of the solvent, respectively. In this work, we used the temperature dependence given by Silvester and Pitzer48 for the Pitzer model,

1 1  T (0 ) (0 ) (T ) = β MX BMX + q1, 2  −  + q1,3 ln  T Tr   Tr

  + q1, 4 (T − Tr ) + q1,5 T 2 − Tr2 

(

(

(1) (1) (T ) = βMX BMX + q2, 2 (T − Tr ) + q2,3 T 2 − Tr2

1 1 φ (0 ) (T ) = C MX C MX + q 4, 2  −  T Tr

)

(19)

)

 T  + q 4,3 ln   Tr

(20)

  + q 4, 4 (T − Tr ) 

(21)

where , , , , , are characteristic parameters obtained from the experimental data and =298.15 K. The equation for the calculation of the dilution enthalpies according to Ge et al. and Pazuki et al. models are

LGe φ =

ν zM z X 2bT

  I 1 / 2  ALbT − Aφ bL + A b ln 1 + bT I 1 / 2  φ L  1/ 2  1 + b I b T T   

(

) − R TS2n −+ 1S L T



T



 2n  I 

(22)

and

(A b − 2 A b ) b − L T 1/ 2 φ L T  2b  2 I Ab b A b − 3 Aφ bL  + 1/ 2 φ L T 1/ 2 + L T ln 1 + bT I 1 / 2  −ν zM z X I 1 + bT I I 

LφPazuki =

ν zM z X  (ALbT − Aφ bL ) bT2 4 T

(

)

(

)

 TS L − ST R T  n +1

 n  I 

(23)

respectively. In the above equations, bT and S T are functions of temperature and the parameter n has a value of 0.645 and 1.29 for the Ge et al. and Pazuki et al. models, respectively. We used the temperature dependence given by Ge and Wang49 for the solvation models, and bL y STL are

bL  ∂b  = 4T  T  RT  ∂T  P, I

(24)



 ∂S  STL =  T   ∂T  P , I

Page 8 of 38

(25)

and

bT = b + b1, 2 (T − Tr ) + b1,3 (T − Tr ) + b1, 4 (T − Tr ) + b1,5 (T − Tr ) 2

3

4

(26)

ST = S + S2, 2 (T − Tr ) + S2,3 (T − Tr ) + S2, 4 (T − Tr ) + S2,5 (T − Tr ) 2

3

4

(27)

where , ′ and , ′ are characteristic parameters obtained experimental data. In this work we used the temperature-dependence expressions from Fernandez et al.50 for the dielectric constant and its derivatives, and the equations given by International Association for the Properties of Water and Steam IAPWS-IF9751 for the volume and the saturation pressure and its respective derivatives. 3. Methodology First, we have made an analysis of which parameters should be considered as adjustable parameters in the solvation model. The parameters consider in Lin et al.24,25 or as in Ge et al..30,31 models. In this work we have used the following objective function when the dilution enthalpy is available, N

(

J = ∑ ln γ iexp − ln γ icalc i =1

) + ∑ (φ N

2

i =1

exp i

− φicalc

) + ∑ (∆H 2

N

exp dil

calc − ∆H dil

)

2

(28)

i =1

To avoid convergence problems in the object function due to difference of magnitude of the coefficient and the dilution enthalpy, we used the logarithm transformation for the dilution enthalpy data with a value of yc = 1 as suggested by Holste et al.52 Ge et al.30,31 have already correlated the logarithm of the activity coefficient and/or the osmotic coefficient of a great number of electrolyte solutions, they use a standard deviation objective function,

1 J = N

∑ (ln γ N

i =1

exp i

− ln γ

)

calc 2 i

  

12

1 or J =  N

∑ (φ N

exp i

−φ

)

calc 2 i

i =1


  

12

(29)

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Obviously, the minimum is the same using either Eq 28 or 29 if the logarithm of the activity coefficient and the osmotic activity coefficient are correlated simultaneously. However the minimum obtain by Ge et al.30,31 should be smaller if they adjusted only the logarithm of the activity coefficient or the osmotic coefficient. In their work, they do not give information about which coefficient they use in their objective function. Then, we optimize the solvation model suggested by Lin et al.24,25 model, the solvation model with the adjustable parameters suggested by Ge et al.30,31 and we have simply used the parameters obtained by Ge et al.30,31. We have correlated 26 aqueous electrolyte solutions at 298.15 K. The average absolute percentage error is 2.26, 3.15, and 1.09 % for the solvation model using the Lin et al.24,25 adjustable parameters, using the parameters of Ge et al.30,31, and adjusting the parameters suggested by Ge et al.30,31, respectively. This average absolute percentage error corresponds to a value of the average sum of squared using Eq 28 of 7.51904×10-2, 6.31983×10-2 and 1.23279×10-2, respectively. Table 1 shows the sum of squares for the three cases. From these results we conclude that it is better to adjust in the solvation model, the parameters bMX , S and n, as suggested by Ge et al.30,31. Also, in Table 1 we show that some of the parameters reported by Ge et al. correspond to a local minimum. The same conclusion we observe with the parameters of the Pitzer model reported by them. Therefore, in this work, we compare the performance of Pitzer model,4,34 Pazuki et al.29 solvation model and the Ge et al.30,31 solvation model for the correlation of the activity coefficient and the osmotic coefficient. We have used 9183 activity coefficient data points for electrolytes with univalent ions and 211 activity coefficient data points of electrolyte without univalent ions. The same number of data points are used for the osmotic coefficient. For the temperature dependence, we have used 4752 experimental data points for the activity coefficient, 5457 points for the osmotic activity coefficient, and 754 points for the dilution enthalpy. The model parameters are obtained using a least squares optimization program from Wolfram Mathematica with the method developed by Levenberg-Marquardt.53-55 The objective function is Eq 28 and the parameters have 95% confidence level. A summary of the parameters at 298.15 K for each model is given in Table 2. The parameters at 298.15 K are recalculated for the Pazuki et al. and Ge et al. models because the latter suggested to fix =1.29 and =0.645, respectively when the temperature dependence data are used. Also, the parameters are recalculated at 298.15 K for the Pitzer model when it is need it. 4. Results We have calculated the average absolute percentage deviation for each point using  y iexp − y icalc ∆y i =  y iexp 

  ⋅ 100 

(30)



Page 10 of 38

where ! is either the activity coefficient, " or the osmotic coefficient # and exp and calc stand for experimental and calculated. Then, the average absolute percentage deviation is AAPD =

1 N

N

∑ ∆y

(31)

i

i =1

where N is the number of points. Also, we have included the standard deviation together with the bias

(

 N y exp − y calc i SD = ∑ i  i =1 N − N p

bias =

1 N

)

2

  

12

(32)

N

∑ ∆y

(33)

i

i =1

where $ is the number of adjustable parameters of the equation 4.1 Constant temperature (298.15 K) Table S1 shows the AAPD, SD and bias for each system while Table 3 shows a summary of the AAPD, SD, and bias for electrolyte type systems. Parameters for each aqueous system together with their asymptotic standard error are shown in Tables S2-S3 for the Pitzer and the solvation models, respectively. The average absolute percentage deviation, bias and standard deviation is 1.370, 0.630 and 0.075 for Pitzer model, 2.372, 1.415 and 0.194 for Ge et al. model, and 2.231, 1.476 and 0.204 for Pazuki et al. model. The comparison is done over 338 systems. Figures 1 and 2 show a comparison of the activity and osmotic coefficient of the models for (C2H5)4NCl, NiCl2, Yb(NO3)3, and Th(NO3)2 aqueous electrolytic solutions at 298.15 K. We have considered for few cases parameters statistically not valid because the value of the objective function increases significantly when these parameters are not considered in the fit. In the case of the solvation model has two parameters highly correlated S and n. If we delete the parameter the equation reduces to the Debye- Hückel2,3 equation. This can be in some instances avoided by fixing the value of n to the value proposed by the authors. The Pitzer model correlates the activity and osmotic coefficient of all systems better by about 54 % comparing to 18 % and 28 % of Ge et al. and Pazuki et al. models. It is important to mention that in some cases, the capability correlation is similar for all the models and rarely the Pitzer model shows a higher deviation. One exception is for the aqueous system of Th(NO3)4 as shown in Figures 1 and 2. We have also compared the performance of the models in the correlation of the activity coefficient and the osmotic coefficient at concentrations higher than 6 kg mol-1. The average absolute percentage error, bias and standard deviation for each model are 2.331, 0.958 and 0.067


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for Pitzer, 3.745, 2.607 and 0.282 for Ge et al, and 3.423, 2.595 and 0.281 for Pazuki et al., models, respectively. At these concentrations, the Pitzer model correlates better than the other two models as shown in Figures 3 and 4. The overall performance of the three models without temperature dependence data is shown in Figures 5 and 6. The percentage deviations from the Pitzer model for the osmotic and activity coefficients are between ±20 % and ±30 %, respectively, while it is between ±30 % and ±40 % for the solvation models for univalent ion systems. For electrolyte solutions with higher valence, the performance of the Pitzer model is better than the solvation models. 4.2 Temperature dependence We have correlated the osmotic and activity coefficients together with the dilution enthalpy of 47 systems, Table 4 shows the sources of experimental data with the temperature dependence. Table 5, shows the parameters used in the calculation of parameters with temperature dependence for the Pitzer model and solvation models at 298.15 K. Tables 6 and 7 show the AAPD, SD and bias obtained for each system with dependence of temperature. The parameters for the temperature dependence of the different models are depicted in Tables S4-S6. For the osmotic and activity coefficients data, the average absolute percentage deviation, standard deviation and bias are 2.627, 1.002 and 0.064 for the Pitzer model 8.736, 2.561 and 0.201 for the Ge et al. model, and 6.676, 2.502 and 0.207 for the Pazuki et al. model. For the dilution enthalpy, the average absolute percentage deviation, standard deviation and bias are 27.680, 13.499 and -5.322 for Pitzer model, 9.191, 2.576 and -0.161 for Ge et al. model, and 9.242, 2.654 and -0.194 for Pazuki et al. model, for dilution enthalpy data. Figures 7 and 8 show a comparison of the different models when correlating the osmotic and activity coefficient of Na2HPO4 at temperatures from 298.15 K a 523.15 K. The Pitzer model correlates better the activity coefficient and osmotic activity coefficients. In Figures 9-11 shows the correlation of the osmotic and activity coefficient and the dilution enthalpy for the aqueous solution of KOH. For this system and in general the solvation models correlate better the dilution enthalpy than the osmotic and activity coefficients. However, the coefficients correlation is not better than the one from the Pitzer model, as shown in Tables 6 and 7. Figure 12 shows the correlation of the dilution enthalpies of the aqueous solution of CsCl at different temperatures. We have correlated the models using only enthalpy data since there is only activity and osmotic coefficients for this systems at 298.15 K. The correlation is similar for the three models, but it is slightly better for the solvation models, as shown in Table 7. The overall performance of the three models with respect to temperature dependence data is shown in Figures 13 and 14. As mention before, the Pitzer model correlates better the activity and osmotic coefficients than the solvation model at expense of the correlation of the enthalpy. In our results, we do not use any statistical weight to skew the correlation to any data. The percentage deviations from the Pitzer model for the osmotic and activity coefficients are between ±25 % while for the solvation models is between ±50 %. For the enthalpies, these intervals are between (75 and -100) % and (50 and -100) % for the Pitzer and solvation models, respectively. 5. Conclusions



We have compared the Pitzer and solvation models for the correlation of the activity and osmotic coefficient of electrolyte aqueous solutions at 298.15 K. The Pitzer model correlates better by than the solvation models. For electrolyte aqueous solutions 1:3, 1:4, 2:2 and 4:1, the solvation model correlates the activity and osmotic coefficients somewhat better than the virial expansion. Even though, Pazuki et al. model correlates the activity and osmotic coefficient better than the other models for electrolyte solutions 4:1, this result is not conclusive since there are only three systems. In general, the three models can be used for the correlation of the activity and osmotic coefficients with almost the same degree of reliability. The main advantage of the solvation models is that uses only three adjustable parameters while the Pitzer model uses three and four adjustable parameters for electrolytes with and without univalent ions, respectively. In the case of correlating temperature dependence data, the correlation of the osmotic and activity coefficient is better using the Pitzer than the solvation models, if the data are not statistical weighted. However this is at expense of correlating worse the dilution enthalpy. The temperature dependence correlation are used as suggested in the literature. The solvation models contain one less adjusting temperature dependence parameter than the Pitzer model. Associated Content Supporting information Tables containing a comparison among models and parameters for the different models. Acknowledgments CONACyT and Instituto Tecnológico de Celaya have provided financial support for this work.


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Page 18 of 38

Table 1. Comparison among solvation models for 26 aqueous electrolytes systems according to the value of the objective function. Electrolyte K4P2O7

Na4ATP

Tb(NO3)3

Nd(NO3)3

La(NO3)3

CuCl2

Mg(NO3)2

C2H6S2O6

K2CrO4

Na2CO3

GuCl

KOH

CsNO3

%&' ()*+ 0.24043a 2.14518b 1.31564c 0.24778 a 30.38294 b 1.99632 c 3.11800 a 2.07902 b 0.13125 c 7.48227 a 3.35133 b 0.27855 c 3.22326 a 2.09180 b 0.12803 c 13.51178 a 18.77978 b 5.75653 c 2.93530 a 2.74908 b 0.15949 c 43.91933 a 16.16907 b 0.97550 c 0.27255 a 17.69825 b 0.03196 c 0.60308 a 14.28539 b 0.18517 c 0.14642 a 3.12271 b 0.08735 c 98.61355 a 22.93009 b 11.36152 c 0.01321 a 0.13867 b 0.02909 c

%&' (, 0.10302 a 5.18151 b 1.23372 c 0.34939 a 31.76415 b 3.62586 c 4.17833 a 0.97684 b 0.15250 c 9.67029 a 1.56052 b 0.26897 c 4.35123 a 0.82734 b 0.12601 c 8.72239 a 7.53220 b 3.15278 c 2.09279 a 0.97214 b 0.09535 c 31.76529 a 8.25617 b 0.84726 c 0.19466 a 12.29925 b 0.01091 c 0.40475 a 9.68538 b 0.11767 c 0.14695 a 2.45454 b 0.08310 c 72.92722 a 17.07560 b 10.42198 c 0.00790 a 0.07508 b 0.02385 c

%&' (-.-/0 0.34345 a 7.32669 b 2.54936 c 0.59717 a 62.14708 b 5.62218 c 7.29633 a 3.05586 b 0.28375 c 17.15256 a 4.91185 b 0.54751 c 7.57449 a 2.91914 b 0.25404 c 22.23417 a 26.31198 b 8.90931 c 5.02809 a 3.72122 b 0.25484 c 75.68461 a 24.42524 b 1.82276 c 0.46722 a 29.99750 b 0.04287 c 1.00784 a 23.97077 b 0.30284 c 0.29338 a 5.57726 b 0.17046 c 171.54078 a 40.00569 b 21.78350 c 0.02111 a 0.21375 b 0.05293 c

Electrolyte RbF

LiI

HBr

(CH3)4NBr

(CH3)4NCl

HoCl3

Mn(ClO4)2

LiOH

CaI2

SrBr2

MgI2

MgBr2

MgCl2

%&' ()*+ 0.24547 a 1.16889 b 0.12973 c 0.10209 a 0.47378 b 0.11137 c 14.91435 a 5.48445 b 3.00764 c 0.23995 a 3.26251 b 0.20636 c 10.13449 a 10.89663 b 4.67100 c 6.44566 a 3.32879 b 2.14317 c 0.78477 a 3.44222 b 0.36224 c 0.25418 a 6.92964 b 0.29055 c 0.42636 a 5.87790 b 0.12816 c 0.06448 a 6.56335 b 0.11266 c 3.86646 a 7.16943 b 0.47032 c 6.09493 a 8.56859 b 0.43872 c 0.75563 a 1.28546 b 0.16649 c

%&' (, 0.15525 a 0.63200 b 0.09229 c 0.07005 a 0.26796 b 0.09305 c 12.19155 a 4.57229 b 2.76311 c 0.13529 a 3.27073 b 0.12111 c 9.11400 a 4.64457 b 2.89995 c 7.14430 a 2.72553 b 2.16422 c 0.47148 a 0.71839 b 0.12955 c 0.16509 a 2.79421 b 0.19162 c 0.22803 a 1.83129 b 0.07598 c 0.02696 a 2.45090 b 0.05594 c 2.55567 a 2.09337 b 0.21657 c 4.28904 a 2.96629 b 0.29007 c 0.87326 a 0.62815 b 0.17710 c

%&' (-.-/0 0.40072 a 1.80089 b 0.22202 c 0.17214 a 0.74173 b 0.20442 c 27.10590 a 10.05674 b 5.77075 c 0.37524 a 6.53324 b 0.32747 c 19.24849 a 15.54120 b 7.57095 c 13.58996 a 6.05432 b 4.30740 c 1.25625 a 4.16061 b 0.49180 c 0.41927 a 9.72384 b 0.48216 c 0.65439 a 7.70919 b 0.20414 c 0.09144 a 9.01425 b 0.16860 c 6.42213 a 9.26280 b 0.68689 c 10.38397 a 11.53488 b 0.72879 c 1.62889 a 1.91361 b 0.34359 c

a .Using Eqs 7 and 9. b. Using parameters reported by Ge et al. 30,31, with Eqs 10 and 11. c. With parameters readjusted in this work, using Eqs 10 and 11.

Table 2. Parameters used in the models at 298.15 K. Parameter

Pitzer et al. 4,34

Lin et al. 24,25

Ge et al. 30,31

2 2 3 4 34 34 3 4 5

Regarded as a constant 1.2 2.0/1.4b 12a Fit to experimental data Fit to experimental data Fit to experimental dataa Fit to experimental data No required No required

Fit to experimental data Fit to experimental data No required No required No required No required No required No required Fit to experimental data 1.29

Regarded as a constant Fit to experimental data No required No required No required No required No required No required Fit to experimental data Fit to experimental data

a. b.

Not required for electrolytes with univalent ions. For electrolytes without univalent ions.


Ge et al. readjusted This work Regarded as a constant Fit to experimental data No required No required No required No required No required No required Fit to experimental data Fit to experimental data

Pazuki et al. 29 Regarded as a constant Fit to experimental data No required No required No required No required No required No required Fit to experimental data Fit to experimental data

Page 19 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Summary of performance of models for aqueous electrolytes systems at 298.15 K Type 1:1 1:2 1:3 1:4 2:1 2:2 3:1 3:2 4:1 UI WUI Total UI. WUI.

Quantity

Pitzer 4,34 SD

AAPD 122 1.15947 0.23722 46 0.97410 0.00878 6 1.35653 0.01533 7 2.92367 0.02237 77 1.46890 1.06570 10 1.11892 0.00888 63 1.66572 1.60245 4 2.15605 0.00883 3 3.42800 0.03385 324 1.36789 0.65651 14 1.41524 0.00886 338 1.36986 0.62968 With univalent ions. Without univalent ions.

bias 0.01561 -0.00012 0.00306 -0.00133 0.08167 -0.00087 0.27617 0.00037 0.00225 0.07902 -0.00052 0.07572

Ge et al. 30,31 AAPD SD bias

Pazuki et al. 29 AAPD SD bias

2.49795 1.21674 1.35309 2.35274 3.59822 1.15371 1.54413 6.01115 2.20377 2.36500 2.54155 2.37232

2.29100 1.38005 2.60251 4.43429 2.28609 4.98260 1.76812 5.51151 1.75857 2.10597 5.13372 2.23138

0.70434 0.01017 0.01172 0.01862 2.22314 0.00871 3.49310 0.02933 0.02085 1.47502 0.01461 1.41453

0.07494 0.00064 0.00154 -0.00567 0.23391 -0.00152 0.61239 -0.01238 0.00133 0.20289 -0.00462 0.19430


0.69646 0.01108 0.02222 0.03058 2.23102 0.03365 3.82233 0.02511 0.01759 1.53850 0.03121 1.47606

0.07363 0.00022 0.00591 -0.00507 0.23753 -0.00529 0.66228 -0.00193 -0.00006 0.21298 -0.00433 0.20398


Page 20 of 38

Table 4. Systems with temperature dependence and experimental sources. System

variable(s)

Citric-acid CsBr CsCl CsI CsOH HBr HCl KBr KCl KF KH2PO4 KI KOH LiBr LiCl LiOH NaBF4 NaBr NaCF3SO3 NaCl NaH2PO4 NaI NaOH RbCl (NH4)2SO4 Cs2SO4 K2HPO4 Na2HPO4 Na2SO4 Rb2SO4 BaBr2 BaCl2 Ca(NO3)2 CaBr2 CaCl2 CaI2 CdBr2 CdCl2 CdI2 MgCl2 NiCl2 SrBr2 SrCl2 SrI2 ZnCl2 ZnI2 MgSO4

", # ", # ΔABC # ", # " ", ΔABC ", # ", #, ΔABC # ", # # ", #, ΔABC ", # ", #, ΔABC ", # ", # ", # ", # ", # ", # # ", #, ΔABC # ", # ", # ", # ", # # ", # # ΔABC ", #, ΔABC # ", #, ΔABC # " " " ", #, ΔABC ΔABC # # # " " #

Data set Size 220 289 122 71 138 176 330 293 242 126 268 92 395 323 500 670 162 328 100 487 294 146 591 94 410 100 284 254 97 86 124 126 342 164 1202 101 110 62 116 149 152 120 124 116 94 98 69

67,8 5 8 1 1 7 9 7 7 9 1 7 1 19 6 5 14 3 7 2 9 7 1 13 1 5 2 7 7 1 2 1 1 6 1 12 1 5 3 6 2 1 1 1 1 5 5 1

78 (K) range 298.15-318.15 298.15-523.15 298.15 298.15 273.15-523.15 273.15-343.15 273.15-323.15 273.15-523.15 273.15-313.15 298.15 298.15-523.15 298.15 273.15-523.15 298.15-498.15 273.15-373.15 298.15-363.15 288.15-308.15 273.15-523.15 298.15-323.15 273.15-473.15 298.15-523.15 298.15 273.15-523.15 298.15 273.15-373.15 273.15-323.15 298.15-523.15 298.15-523.15 298.15 298.15-323.15 298.15 298.15 273.15-373.15 298.15 273.15-373.15 298.15 278.15-313.15 273.15-313.15 278.15-313.15 298.15-313.15 298.15 298.15 298.15 298.15 283.15-313.15 278.15-313.15 298.15

67,9 5 6 1 6 3 1 1 6 2 4 7 6 4 7 5 17 3 8 2 9 7 8 4 6 5 2 7 7 2 2 6 1 6 6 12 6 1 1 1 2 1 6 6 6 1 1 3

79 (K) range 298.15-318.15 298.15-498.15 298.15 298.15-343.15 383.25-443.09 298.15 298.15 298.15-498.15 273.15-298.15 283.15-348.15 298.15-523.15 298.15-343.15 298.15-443.09 273.15-523.15 273.15-373.15 298.15-443.09 288.15-308.15 283.15-498.15 298.15-323.15 273.15-473.15 298.15-523.15 283.15-348.15 298.15-443.15 298.15-343.15 273.15-373.15 273.15-323.15 298.15-523.15 298.15-523.15 273.15-298.15 298.15-323.15 298.15-343.15 298.15 273.15-373.15 298.15-343.15 273.15-373.15 298.15-343.15 298.15 298.15 298.15 298.15-313.15 298.15 298.15-343.15 298.15-343.15 298.15-343.15 298.15 298.15 273.15-383.15.15


67,∆; 3 6 3 4 3 4 3 3 3 3 3 -

7?; (K) range 573.15-623.15 523.15-643.15 573.15-623.15 573.15-643.15 573.15-623.15 573.15-643.15 573.15-623.15 347.35-372.15 573.15-623.15 573.15-623.15 298.15-318.15 -

Experimental source [56] [57] [58, 59] [58] [60] [61] [62-64] [57] [47, 59, 65, 66] [67] [68] [58] [60, 63, 69] [57] [59, 70] [60, 71] [72] [57, 67] [73] [74] [68] [67] [60, 63, 69, 75] [58] [76] [77] [68] [68] [65] [77] [58] [58, 64] [78] [58] [64, 67, 79, 80] [58] [47] [47] [47] [64, 81, 82] [83] [58] [58] [58] [47] [47] [65, 84]

Page 21 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 5. Parameters used in the calculation of parameters with temperature dependence for the Pitzer model and solvation models at 298.15 K.

Electrolyte Citric-acid CsBr CsCl CsI CsOH HBr HCl KBr KCl KF KH2PO4 KI KOH LiBr LiCl LiOH NaBF4 NaBr NaCF3SO3 NaCl NaH2PO4 NaI NaOH RbCl (NH4)2SO4 Cs2SO4 K2HPO4 Na2HPO4 Na2SO4 Rb2SO4 BaBr2 BaCl2 Ca(NO3)2 CaBr2 CaCl2 CaI2 CdBr2 CdCl2 CdI2 MgCl2 NiCl2 SrBr2 SrCl2 SrI2 ZnCl2 ZnI2 MgSO4

JKL

Pitzer 3%4 JKL

MKL

0.08498 0.02129 0.03593 0.02251 0.13603 0.23438 0.20283 0.05522 0.04639 0.09886 -0.11249 0.07301 0.17279 0.23866 0.20411 -0.04912 -0.02243 0.10921 0.13100 0.07631 -0.05158 0.13382 0.15900 0.04625 0.04014 0.09489 0.06041 -0.02314 0.02137 0.06861 0.31606 0.29270 0.13990 0.42517 0.40810 0.42893 0.01609 -0.01064 0.25940 0.35605 0.39249 0.31932 0.27937 0.38573 0.08253 0.31184 0.26645

1.52491 0.07579 0.03385 0.05868 0.36282 0.17422 0.15804 0.23435 0.22102 0.09312 0.05704 0.26670 0.04006 -0.17670 1.18253 0.17480 0.22750 0.41339 0.27246 0.05831 0.25995 -0.30744 0.14310 0.62489 0.58925 1.07477 1.25596 1.02371 0.67751 1.51802 1.21123 2.03281 1.01415 0.54928 1.89163 -4.76838 -3.41068 -9.68269 1.59552 1.31623 1.86061 1.53952 2.05558 2.52141 3.52142 6.67830

0.00088 0.00066 -0.00044 -0.00175 0.00232 -0.00181 -0.00074 -0.00020 -0.00074 0.01001 -0.00197 -0.00128 -0.00127 -0.00200 0.00757 0.00067 -0.00063 -0.00553 0.00062 0.00370 -0.00053 -0.00153 -0.00079 -0.00034 -0.00026 -0.00232 0.00274 .00183 -0.00102 -0.00574 -0.01109 -0.00112 -0.00074 -0.00496 0.00073 0.00066 -0.02517 0.00183 -0.00583 0.00182 0.00277 0.00049 -0.00855 -0.00440

3&4

3&4

Ge et al. (D = &. FGH) NKL O 2.50951 1.47109 1.62544 1.51120 3.65159 2.03125 13.18069 2.38198 2.19023 3.43623 0.83656 2.77520 9.31389 13.54726 17.26120 8.21092 1.34782 3.25679 5.75677 2.64300 0.83802 4.48294 15.25597 2.02277 1.54969 1.66031 2.02329 1.86907 1.63254 1.68488 3.19066 2.73806 4.47135 4.89403 9.79021 3.85343 0.21404 0.44350 3.33498 17.82261 19.76935 3.38886 2.99492 3.89607 2.96457 14.57842 2.44917

5.74931 14.23718 12.54581 3.21545 90.78510 136.57469 72.38382 20.90807 19.54788 33.27366 -45.54899 25.44154 57.67616 89.48994 62.64362 -12.50151 -9.31430 49.41528 5.37766 42.14834 0.76397 59.11053 35.09336 14.90613 5.63328 23.74432 -11.50603 -22.34035 8.45132 9.35725 76.81561 61.14621 11.47807 105.15707 55.13051 145.01420 81.50700 29.71503 155.72864 62.07830 44.14285 102.59208 79.35782 131.87553 14.58075 24.78466 15.80988


Pazuki et al. (D = %. 'I) NKL O 3.51059 0.86218 0.90306 0.90560 1.92170 3.04411 4.88189 1.31125 1.22265 1.65546 0.53456 1.51541 3.63696 4.79463 5.71028 3.77921 0.77282 1.66784 2.78481 1.42233 0.51117 2.13802 4.84920 1.11325 0.82777 0.91766 1.19430 1.04834 0.88723 0.95096 1.65452 1.86001 1.48448 2.11712 3.52613 1.98044 0.14183 0.27670 0.00002 1.67936 2.13025 1.75527 1.51142 1.99697 1.45100 5.27444 1.19608

22.87466 3.83819 4.44865 -3.15071 42.32971 59.72516 35.82867 7.44581 6.59682 15.71751 -27.66595 9.23455 28.45409 44.50629 31.15865 -8.58680 -6.78477 22.81836 15.35494 18.46062 -2.01897 28.31646 17.46028 5.16950 -0.15249 2.07692 -7.59333 -6.38204 -0.03260 -0.99167 10.58313 1.70147 7.15879 17.07804 9.00848 21.60556 12.58403 3.79996 25.92002 17.48056 11.68856 14.71637 11.87348 19.45027 1.49642 3.82835 0.24764


Page 22 of 38

Table 6. Activity and osmotic coefficients comparison between Pitzer model and solvation models for aqueous electrolyte solutions with temperature dependence. Electrolyte Citric-acid CsBr CsCl CsI CsOH HBr HCl KBr KCl KF KH2PO4 KI KOH LiBr LiCl LiOH NaBF4 NaBr NaCF3SO3 NaCl NaH2PO4 NaI NaOH RbCl (NH4)2SO4 Cs2SO4 K2HPO4 Na2HPO4 Na2SO4 Rb2SO4 BaBr2 BaCl2 Ca(NO3)2 CaBr2 CaCl2 CaI2 CdBr2 CdCl2 CdI2 MgCl2 NiCl2 SrBr2 SrCl2 SrI2 ZnCl2 ZnI2 MgSO4 Total

AAPD 2.5244 0.3669 0.2969 0.4156 0.3974 3.3006 2.3195 0.4171 0.3827 1.2491 1.9847 1.1984 6.1754 2.3203 3.7825 2.9313 0.0446 0.4070 0.0563 0.1648 1.7332 0.7482 6.3896 0.5248 0.5911 0.2307 3.1468 3.9901 0.4291 0.3407 0.7076 0.1242 5.5017 4.9383 4.9272 0.8116 13.0084 4.5146 23.9529 2.8326 1.1974 1.2684 1.6722 0.5669 1.7147 5.2205 1.6397 2.6268

Pitzer SD 0.0404 0.0038 0.0031 0.0084 0.0059 0.4265 0.8227 0.0050 0.0045 0.0317 0.0126 0.0213 0.5083 9.1232 0.7522 0.0362 0.0003 0.0056 0.0009 0.0017 0.0110 0.0219 0.5535 0.0107 0.0050 0.0021 0.0218 0.0160 0.0033 0.0026 0.0166 0.0012 0.0792 33.5361 0.4506 0.0240 0.0763 0.0364 0.1093 0.0801 0.0343 0.0464 0.0370 0.0160 0.0130 0.0757 0.0125 1.0023

Bias 0.0055 0.0003 0.0001 -0.0004 0.0004 0.0096 0.0341 0.0001 -0.0001 -0.0010 0.0011 0.0007 -0.0585 0.3211 0.0056 0.0021 0.0001 -0.0006 0.0000 -0.0001 0.0010 -0.0004 -0.0706 0.0000 -0.0003 -0.0001 -0.0028 -0.0025 0.0006 -0.0001 -0.0004 0.0003 0.0158 2.6644 -0.0053 0.0001 0.0274 -0.0107 0.0437 0.0180 0.0002 -0.0017 0.0009 -0.0006 0.0001 -0.0016 -0.0001 0.0637

AAPD 1.4522 0.4261 0.8436 0.0973 0.5970 4.3359 13.1234 0.5701 1.0400 3.2409 3.6342 1.9534 13.0245 4.1256 12.7308 3.8275 2.5052 0.8658 1.6215 0.3503 3.6554 2.4492 22.5028 0.6432 1.9974 1.0929 4.2895 15.0785 3.3345 1.3461 1.0000 1.2920 13.2516 6.0343 21.3459 0.8411 26.1547 16.0940 82.7658 30.8523 22.5810 1.7743 1.6915 0.6818 4.0419 30.8471 22.5810 8.7359

Ge et al. SD 0.0304 0.0045 0.0094 0.0017 0.0081 0.9635 4.3614 0.0073 0.0102 0.0997 0.0214 0.0326 1.8778 30.6075 3.3836 0.0415 0.0195 0.0132 0.0190 0.0041 0.0219 0.0709 3.1249 0.0123 0.0133 0.0082 0.0285 0.0559 0.0255 0.0098 0.0212 0.0114 0.1958 67.9064 3.8432 0.0218 0.1242 0.0863 0.2073 0.9815 0.4758 0.0506 0.0371 0.0265 0.0359 0.9815 0.4758 2.5611

Bias -0.0028 0.0002 0.0004 0.0001 -0.0005 0.0314 0.6097 -0.0008 0.0009 -0.0095 0.0042 0.0036 0.0002 1.8419 0.0917 0.0042 -0.0010 -0.0019 -0.0007 -0.0003 0.0038 -0.0049 -0.4506 0.0001 0.0019 0.0010 0.0090 0.0117 -0.0014 0.0010 0.0007 0.0023 0.0092 7.3989 0.1738 0.0007 0.0412 -0.0074 0.0844 -0.0962 -0.0996 0.0039 -0.0005 0.0003 0.0029 -0.0962 -0.0996 0.2013


AAPD 1.4522 0.4261 0.4737 0.0973 0.5970 4.3359 12.5376 0.5701 0.9642 3.2409 3.6342 1.9534 11.1626 4.1256 11.9788 3.8275 2.5052 0.8658 1.6215 0.3503 3.6554 2.4492 20.7883 0.6432 1.9974 1.0929 4.2895 15.0785 3.3345 1.3461 1.0000 0.4236 10.0547 6.0343 19.0837 0.8411 26.1547 16.0940 82.7658 2.9323 5.0309 1.7743 1.6915 0.6818 4.0419 5.0006 8.7482 6.6755

Pazuki et al. SD 0.0304 0.0045 0.0058 0.0017 0.0081 0.9635 4.3424 0.0073 0.0093 0.0997 0.0214 0.0326 1.8213 30.6075 3.3604 0.0415 0.0195 0.0132 0.0190 0.0041 0.0219 0.0709 3.1156 0.0123 0.0133 0.0082 0.0285 0.0559 0.0255 0.0098 0.0212 0.0038 0.1834 67.9064 3.6802 0.0218 0.1242 0.0863 0.2073 0.0401 0.2423 0.0506 0.0371 0.0265 0.0359 0.0835 0.0599 2.5018

Bias -0.0028 0.0002 0.0002 0.0001 -0.0005 0.0314 0.6288 -0.0008 -0.0002 -0.0095 0.0042 0.0036 -0.0688 1.8419 0.0814 0.0042 -0.0010 -0.0019 -0.0007 -0.0003 0.0038 -0.0049 -0.4696 0.0001 0.0019 0.0010 0.0090 0.0117 -0.0014 0.0010 0.0007 0.0007 0.0165 7.3989 0.1066 0.0007 0.0412 -0.0074 0.0844 0.0158 0.0144 0.0039 -0.0005 0.0003 0.0029 -0.0117 0.0060 0.2071

Page 23 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 7. Dilution enthalpy comparison between Pitzer model and solvation models for aqueous electrolyte solutions with temperature dependence Electrolyte CsCl HCl KCl KOH LiCl NaOH BaCl2 Ca(NO3)2 CaCl2 MgCl2 NiCl2 Total

AAPD 4.5863 41.7116 15.9270 34.9092 21.5079 38.6055 3.7816 19.6174 86.9058 35.1413 1.7798 27.6794

Pitzer SD 1.0692 8.4381 4.7973 15.0521 8.6272 15.8501 3.4466 0.6429 60.9928 29.2809 0.2906 13.4989

Bias -0.0861 -2.4662 -1.5723 -6.6842 -3.7364 -6.6641 -0.5946 -0.0933 -26.1089 -10.5312 -0.0022 -5.3218

AAPD 2.0343 23.4523 1.8267 17.5111 5.8019 12.2413 3.6089 10.8009 17.1047 4.2483 2.4691 9.1909

Ge et al. SD 0.4750 3.9869 0.6422 5.8725 0.9281 4.4848 2.2149 0.2637 6.4630 2.6056 0.4024 2.5763

Bias 0.0033 0.2463 0.0873 -1.0026 0.2158 0.6989 -0.3855 -0.0431 -1.1260 -0.5158 0.0553 -0.1606


AAPD 2.5992 20.4827 1.8264 17.4865 5.4081 12.8730 4.1270 10.9690 17.7163 5.2369 2.9417 9.2424

Pazuki et al. SD 0.6556 4.3955 0.5863 5.8002 0.7702 3.5435 2.8084 0.3298 6.9619 2.9004 0.4411 2.6539

Bias -0.0128 0.9226 0.0852 -0.8728 0.1696 -0.4412 -0.5937 -0.0150 -1.0345 -0.5051 0.1627 -0.1941

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Figure 1. Correlative capability of several models for the mean activity coefficient of (C2H5)4NCl, NiCl2, Yb(NO3)3, and Th(NO3)2 aqueous solutions at 298.15 K.


Page 24 of 38

Page 25 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Figure 2. Correlative capability of several models for the osmotic coefficients of (C2H5)4NCl, NiCl2, Yb(NO3)3, and Th(NO3)2 aqueous solutions at 298.15 K.



Figure 3. Correlative capability of several models for the mean activity coefficients of HNO3, Ca(NO3)2, and NaCNS aqueous solutions at high concentrations.


Page 26 of 38

Page 27 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Figure 4. Correlative capability of several models for the osmotic coefficients of HNO3, Ca(NO3)2, and NaCNS aqueous solutions at high concentrations.



Figure 5. Percentage osmotic and mean activity coefficients deviations of electrolyte solutions with univalent ions from different correlations at 298.15 K.


Page 28 of 38

Page 29 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Figure 6. Percentage osmotic and mean activity coefficients deviations of electrolyte solutions without univalent ions from different correlations at 298.15 K.



Figure 7. Correlative capability of several models for the mean activity coefficient of Na2HPO4 aqueous solutions with temperature dependence.


Page 30 of 38

Page 31 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Figure 8. Correlative capability of several models for the osmotic coefficients of Na2HPO4 aqueous solutions with temperature dependence.



Figure 9. Correlative capability of several models for the mean activity coefficients of KOH aqueous solutions with temperature dependence.


Page 32 of 38

Page 33 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47




Figure 10. Correlative capability of several models for the osmotic coefficients of KOH aqueous solutions with temperature dependence.


Page 34 of 38

Page 35 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Figure 11. Correlative capability of several models for the dilution enthalpy of KOH aqueous solutions with temperature dependence.

Figure 12. Correlative capability of several models for the dilution enthalpy of CsCl aqueous solutions with temperature dependence.



Figure 13. Percentage osmotic and mean activity coefficients deviations of electrolyte solutions from different correlations with temperature dependence.


Page 36 of 38

Page 37 of 38 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Figure 14. Percentage dilution enthalpy deviations of electrolyte solutions with temperature dependence.



TOC

Table of Contents Graphic “for Table of Contents use only”


Page 38 of 38

Comparison Among Pitzer Model and Solvation Models. Calculation of

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