The activity coefficients of most simple electrolyte solutions have been measured at a temperature of about 25 ° C, while the experimental values ​​of mixed electrolyte solutions are very limited. Therefore, the data of the solution containing the single electrolyte is presumed to be the activity of the multi-component electrolyte solution. The degree coefficient is very valuable, and Pitzer provides such a method.
The Pisch method is the most widely used method now. Its purpose is to derive some compact and convenient equations that can reproduce the measured values ​​within the experimental precision. It requires only a few parameters, and the parameters also have a certain physical meaning. Mathematical calculations are also simple. For solutions containing several electrolytes, the amount of calculation will be larger and a computer can be used.
Like other modifications to the Debye-Hickel's limit equation, the Pete equation is also added to the Debye-Hickel's limit equation to represent the short-range effect. Pize proposed that for a solution containing n w (kg) solvent and n i , n j , ..., mol (i, j, ... as a component), the equation of total excess free energy should be
(1)
In the formula, Gex is the excess free energy of the solution, which is the difference between the actual Gibbs free energy and the ideal Gibbs free energy.
In this formula, f(I) is a function of ionic strength, solvent properties and temperature and represents the effect of long-range electrostatic forces and is therefore related to the Debye-Shockell theory. λ ij (I) represents the action of the short-range force between the components i and j and thus relates to the βI term in the formula (2). The term "three ion" is included in the formula, but it is assumed that μ ijk is independent of ionic strength.
(2)
The equation for the activity coefficient can be written by appropriate derivation of G ex
Where f'=df∕dI; λ' ij =dλ ij /dI and m i =n i ∕n w .
Pice offers a number of activity coefficients for a single electrolyte that does not associate, and these electrolytes have one or both ions that are monovalent. The basis of the method for calculating the activity coefficient is the Debye-Huckel equation (3). The parameter values ​​of simple electrolytes are used to calculate the lnγ ± of 52 binary electrolyte mixtures with common ions, and the calculated value of lnγ + and lnγ are obtained. The difference between the values. From these differences, θ and ψ are obtained. The θ and ψ values ​​are then used as additional curve fitting parameters for the mixed electrolyte solution. A similar calculation was performed for the other 11 binary mixed electrolytes without common ions. Confirm that all θ and ψ values ​​are small.
(3)
Most of the calculations have been reported, and the two additional terms E θ and E θ' are included in the fitting equation. In some systems, the improvement in the degree of improvement is significant, and the improvement is significant in the HCl-SrCl; HCl-BaCl 2 and HCl-MnCl 2 systems, and the introduction of additional items in the HCl-AlCl 3 system is important. It was determined in these systems that the activity of HCl was dispersed and used for calculation.
Some particularly important in practice a single substance and solution properties such as sulfuric acid phosphoric acid, sodium oxide and sodium sulfate may also be represented by Equation Spitzer additional items. The complete analysis of the published NaCl-H 2 O extends to 300 ° C and 100 MPa pressure, requiring 28 parameters, including parameters for the standard state of the aqueous solution. Another set of 20 parameters is required below 100 °C. The temperature dependence of the activity coefficient is related to the enthalpy of the material involved in deviating from the ideal behavior. It is convenient to use the temperature coefficient as a parameter when using the Pete equation.
The equations derived by Pice have the long-range force term and the short-range force term between ions, and assume that there is an interaction between the electrons in the ion. Thus the general form of the Pete equation cannot be used to describe the behavior of systems involving nonionic species. However, it can be used to treat the vapor-liquid equilibrium of weak electrolyte systems such as NH 3 -CO 2 -H 2 O, NH 3 -SO 2 -H 2 O and NH 3 -H 2 S-H 2 O. Edwards et al. extended the Pete equation to correct the concentration to 20 mol ∕ kg and temperature 0 to 170 ° C. For these weak electrolytes, the concentration corresponds to an ionic strength of about 6 mol ∕L.
For equation hydrometallurgical also important proposed by Meissner and Bromley. The equation proposed by Bromley is
(4)
The value of the parameter Bm is given by Bromley, see the literature.
The basic equation of Meissner is
(5)
Where Г 12 is defined as Where γ 12 is the required electrolyte activity coefficient
B=0.75-0.65q
C=1+0.55qexp(-0.023I 3 )
A γ = 0.5107 (25 ° C aqueous solution)
q is the Meissner experience parameter. As long as the mixture of salts does not change, the same value is maintained for all ionic strengths q.
Meissner provides equations for the q values ​​of 121 binary electrolytes and the calculation of q values:
Where I i , I j - only the ionic strength of the ion i or j;
- the q value of pure electrolyte i2;
- the q value of the pure electrolyte Ij;
Ij-cation and anion (i=odd, j=even).
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