Determination of activity coefficients and diffusion coefficients of LiClO4 in ethylene carbonate +water mixtures based on potentiometric measurements at T=(298.2, 308.2, and 318.2) K

ABSTRACT We studied the thermodynamic properties of the lithium perchlorate (LiClO4) + ethylene carbonate (EC) +water ternary system by using cell potential measurements. Thermodynamic properties reported were obtained using the electrochemical cell: Li-ISE|LiClO4(m)|ClO4-ISE in a variety of mixed solvent systems containing 0, 10, 20 and 30% mass fractions of ethylene carbonate in water + EC mixtures (wEC/wmixture% = 0, 10, 20 and 30) on the wide range of ionic strength from 0.0090 to 2.4900 mol.kg−1 at T = (298.2, 308.2 and 318.2) K. The obtained results were analysed using Extended Debye-Huckel equation and Pitzer model. The values of Pitzer ion-interaction parameters β(0), β(1) and Cϕ were used to drive the values of thermodynamic properties such as the excess Gibbs free energy, the solvent activity, mean activity coefficients, the osmotic coefficients and diffusion coefficients for this system.


Introduction
Today, we are facing the widespread use of chemistry in medicine, agriculture, as well as in industry and trade, and human's life is directly related to chemistry. Humanity has always strived to use chemistry to provide an advanced and at the same time a safe and comfortable life. One of these developments is use of this science in the field of industry. Electrolytes and thermodynamic properties of electrolyte solutions are important for many industrial chemical processes, and the chemical industry depends greatly on fluid thermodynamic properties. The ability to consider thermodynamic properties has an important role in designing and functioning of chemical industrial processes. A great deal of studies have been performed for the measurement of electrolyte thermodynamic properties in aqueous-organic solvent mixtures [1,2], which may be related to their use in a variety of fields such as biochemistry [3], geology [4], oceanography [5], meteorology [6,7], engineering process design [8][9][10][11], electrochemical investigation [12] and batteries [13]. Also, in order to show the ideal mixing behaviour, properties such as excess Gibbs free energy (G E ), the solvent activity (a s ), mean activity coefficients (γ � ), and the osmotic coefficients (φ) are required to design and operate industrial processes, including electrolytic solutions [14].
In theoretical and applied chemistry studies, adding some organic solvents to the electrolyte solution or adding some mineral salts to the solvent mixture (water + organic solvent) can alter the main system's physical and chemical properties to some degree. Moreover separation and lithium cell has a voltage greater than 3.6 V and more than the water dissociation voltage. Also because lead-acid batteries are heavy, using LIBs in conventional vehicle significantly makes the weight lighter.
On the other hand there are many aprotic solvents chosen as electrolyte one in LIBs such as EC and PC which they have similar structures and their difference is just having one more methyl group in PC. But using PC and most of other solvents in LIBs cause exfoliation of graphite. But EC has ideal electrochemical behaviour as electrolyte solvent in LIBs [13,43,44].
Also, knowing a series of coefficients such as diffusion coefficients in LIBs, especially fast charging type, helps to improve its performance. Currently, the main anode material of LIBs is graphite and the diffusion coefficient of lithium ion is less than 10 −10 cm 2 s −1 and it is hard to adapt to the super quick charge in pursuit. In this way by developing of new electrode materials with greater lithium-ion diffusion coefficients can solve the problems associated with the fast-recharging of LIBs. However, the chemical diffusion coefficient of lithium ions varies depending on the potential of all the materials investigated [45,46].
In this research, the determination of the γ � for LiClO 4 in different mixed solvent system containing 0, 10, 20, and 30% mass fractions of EC in water + EC mixtures (w EC /w mixture % = 0, 10, 20 and 30) at specified temperatures were reported. To correlate the experimental data, the Pitzer ion-interaction model and Extended Debye-Hückel equation were used. Thermodynamic properties such as the excess Gibbs free energy, the solvent activity, mean activity coefficients and the osmotic coefficients were determined.Also, for the first time, transport properties such as diffusion coefficients were estimated using the thermodynamic properties based on Pitzer model.

Apparatus and reagents
All reagents used as part of the study were acquired from Sigma-Aldrich, Fluka and Merck company and were illustrated in Table 1. All the apparatus were used according to previous works [47,48].

Preparation of electrodes
Li-ISE, ClO 4 -ISE and Ag-AgCl electrodes were prepared in accordance with the procedure described in the literatures [48][49][50]. In order to check electrode response, all were calibrated against a saturated calomel reference electrode in LiClO 4 standard solutions with concentration (10 −3 to 1 mol.dm −3 ). The ion-selective electrode (ISEs) showed a good Nernst slope

Potentiometric measurements
Potentiometric measurements were carried out in a galvanic cell containing the Li-ISE, ClO 4 -ISE self-made ion selective electrodes. The Nernst equation for this cell is: E, E° and s represent the cell potential, apparent standard potential and slope of Nernst equation, respectively. The electrodes should be calibrated before performing each experiments according to literature [51]. Determination of (γ � ) for LiClO 4 in the ternary system (LiClO 4 /EC/H 2 O) was done through the emf measurements and the standard addition procedure was used to measure the cell potentials in contrast to our past works [42,43].

Extended Debye-Hückel equation
Extended Debye-Hückel Equation was used to correlate the γ � experimental data. This equation contains the specific regression parameters which are determined through experimental data [52][53][54]. For 1-1 type electrolytes, such as LiClO 4 , this equation for γ � is given by where I indicates ionic strength on molality scale, a is the ion size parameter, c and d are ioninteraction parameters and M s is the average molecular mass of mixed solvent system. In addition, A and B (Debye-Hückel constants) provided by

Pitzer model
This model was used to correlation of experimental data [55]. In relation to the Pitzer formalism, mean activity coefficient (γ ± ) for LiClO 4 in the system is obtained by: α and b are constant of Pitzer equation with values of 2.0 and 1.2 kg 1/2 mol −1/2 . B γ and C γ represent the second and third virial coefficients, respectively. β (0) and β (1) show solute-specific interaction parameters of the Pitzer equation. Also, C ϕ indicates triple-ion interaction parameter of Pitzer equation. The symbol A ϕ (Debye-Hückel constant for the osmotic coefficient) is defined by where d s , ε r and T stand for the density, relative dielectric constant and absolute temperature, respectively.

The γ ± measurements
The γ ± for LiClO 4 in (EC+water) system was obtained from measurements of emf using galvanic cell using the equation 1 by varying the concentration of electrolytes using the standard addition method. It is noteworthy that the standard state for γ ± was considered as the ideal dilute solution.
As mentioned in the introduction, thermodynamic data for LiClO 4 in in aqueous solution at 298.15 and 308.18 K are available in the literatures [33,56,57]. Figure 1 represents the comparison between the experimental data from our work and the literatures data at 298.2 K. It shows that the experimental data has good agreement with the literatures data; so this proves the proper experimental procedure developed in this study. Table 2 presents the values of E and γ ± of LiClO 4 in various mixtures of EC+water as a result of LiClO 4 molality (m). The variation of γ ± for LiClO 4 with (I) in water in different % mass fractions of EC in EC+water at defined temperatures are seen in Figures 2-4.
It should be observed that increasing in electrolyte molality, the values of γ± increases at the same values of the % mass fraction of the EC and temperature. Also the values of γ ± for LiClO 4 decreases with increasing the % mass fraction of EC at the same value of molality of electrolyte and temperature. Also, Figure 5 represents the temperature comparison of γ ± data for LiClO 4 + water + EC ternary system with 10% EC mass fraction. It is clear that the values of γ ± is increased with increasing temperature. (See Fig S1 and

Determination of Debye-Hückel parameters
This equation was used for correlating the γ± experimental data for the studied system at defined temperatures. The values of Ms, ds, A, B and adjustable parameters (a, c, and d) were estimated by an iteration minimisation procedure employing the Microsoft Excel (solver program) were illustrated in Table 3.
The resulting values were reported for the system under consideration in Table 4. β (0) represents the total binary ionic interactions and β (1) represents interactions between unlike-charged ions. β (0) and β (1) generally decrease and increases as the temperature increases and increasing the mass fraction  (%) of EC in EC+water at the same temperature, respectively. Depending on the ionic association and β (1) in EC+water mixtures can be explained with changing the dielectric constant of EC+water mixture.

Calculation of thermodynamic properties by Pitzer model
The values of (Φ), (G E ) and (a s ) can be estimated using the equations below by the obtained Pitzer parameters for under investigation system [56,57]: LiCIO 4 expðÀ αI 1=2 Þ (10) The thermodynamic quantities calculated were demonstrated for various series of EC mass fraction in mixed solvents in Tables S1 to S3. Figures 6 to 8 show the plot of (G E ) versus the molal concentration (m) in 0, 10, 20 and 30% mass fractions of EC at specified temperatures. It can be found that an increase in the mass fraction of EC causes decreasing of (G E ) in the system. This can be described as a function of the ion interaction models. Indicating that at higher molality concentration, interactions of the ions with their surrounding and subsequently non-ideal behaviours decrease. Also, Figure 9 shows the temperature comparison of (G E ) data for LiClO 4 + water + EC ternary system with 30% EC mass fraction. It is obvious that as the temperature increases, the values of (G E ) become less negative. For other mass fractions of EC in EC + water, the Table 4. Values of Aφ, β (0) , β (1) , C ϕ and σ for (LiClO 4 + EC + water) system at T = (298.2, 308. 2  corresponding differences were found. At higher temperatures, the effect of temperature on (G E ) can be due to less ion solvation, greater ion interaction, and a decrease in the number of free ions in EC + water. Furthermore, Figures S3-S8 plotted (Φ) and (a s ) versus (m) of electrolyte in defined system and temperatures. It can be noticed that the variation of (Φ) and (G E ) with the EC amount in the solvent is nearly close to that of γ ± .

Determination of diffusion coefficient
Diffusion coefficient is an significant indicator of mobility. For this under investigation system, the chemical diffusion coefficient (D)of electrolyte was estimated based on the Nernst-Hartley expression as[58] Which D* and y are the self diffusion coefficient and activity coefficient on molarity scale respectively [59]. The activity coefficient equation based on Pitzer model was used to calculate the partial derivation. The relative diffusion coefficient (D/D*). The relative diffusion coefficient (D/D*) was estimated using the activity coefficient data . The obtained results were illustrated for various series of EC mass fraction in Table 5. Figures 10 to 12 show the plot of (D/D*) versus the (I) in mass fractions of EC at specified temperatures. It can be noticed from data in tables that an increase in the mass fraction of EC causes decreasing of (D/D*) in the system.   Also, Figure 13 shows the temperature comparison of (D/D*) data for LiClO 4 + water + EC ternary system with 10% EC mass fraction. Obviously, as the temperature increases, the values of (D/D*) increases. For other mass fractions of EC in the system, the relevant differences were observed. At higher temperatures, the effect of temperature on (D/D*) may be caused by greater ionic interaction in EC + water.

Conclusions
The thermodynamic properties of (LiClO 4 + water + EC) ternary system were made by potentiometric measurements with self-manufactured electrodes consisting of Li-ISE and ClO 4 -ISE at certain temperatures. These measurements were performed for LiClO 4 in a variety of EC-water mixed solvent system which w EC /w mixture % = 0, 10, 20 and 30. It was seen that γ ± values reduce with increasing the LiClO 4 molality at the same mass fractions of EC and temperature. Furthermore, γ ± values of LiClO4 rise with growing the % mass fractions of EC at the same value of molality of electrolyte and temperature. The modelling of this ternary system was made by using Extended Debye-Hückel equation and Pitzer model. The values of (G E ), (a S ), (γ � ) and (φ) for the series under studied were reported. The result show that the Pitzer model describes the behaviour system as satisfactory. Also, the chemical diffusion coefficients of electrolyte was predicted based on thermodynamic properties.