Any leaching process involves a solution, so the nature of the solution, especially the interaction of ions and molecules in the solution, has a significant impact on the leaching process. The molecules and ions that make up the aqueous solution interact with each other in a variety of ways, and the extent to which these effects occur and the resulting changes are extremely important in solution chemistry. In general, ions and molecules of a solute are solvated (hydrated) by water, and ions of opposite charges or ions interact with neutral molecules. There are two ways to describe this interaction or association:
(1) Debye-Huckel theory and its evolution. The original model of the Debye-Huckel equation is to treat ions simply as point charges and therefore only for extremely dilute electrolyte solutions. Subsequent corrections extend its scope of application.
(2) The interaction is treated as a chemical equilibrium. The experimentally measured equilibrium constants are used to describe the degree of equilibrium. The excess freeness of the system controls the value of these equilibrium constants.
Chemical equilibrium is described by the thermodynamic activity of the components involved in the reaction. Activity depends on the concentration of the component, but at higher concentrations it is usually not equal to the concentration because its behavior deviates from the ideal solution. This deviation is the source of excess Gibbs free energy and is included in a single coefficient, the activity coefficient.
The deviation of the actual solution from the ideal solution results from the interaction of ions and molecules in the solution. The deviation of the non-electrolyte solution is due to the short-range force, such as the effect of van der Waals force, and the deviation of the electrolyte solution is mainly the result of the long-range force.
I. Debye-Hickel theory
In the 1920s, Debye and Huckel proposed a theory that treats ions as a point charge and a solvent as a continuum with a specific dielectric constant. It is believed that each ion is surrounded by an ion group whose ion distribution is a spherically symmetric charge distribution called an ionic atmosphere. Therefore, Debye-Hickel theory is also called ionic atmosphere theory. They believe that the long-range force that causes the electrolyte solution to deviate from the ideal solution is the attraction between ions. The Boltzmann equation of classical statistical mechanics is used to describe the charge distribution of particles from the energy point of view. Poisson force using electrostatic theory. The process relates the potential at a point in space to the charge density. After proper simplification, the concept of ionic strength I is introduced:
I= 
(1)
The activity coefficient equation is derived
Lgγ i =-A i (2)
In the middle
A= (3)
Wherein, N A is the Avogadro number; e 0 is the electron charge; ε is the dielectric constant of the liquid, and the dielectric constant value of the water can be approximately taken for the dilute solution; R is the gas constant = 8.3143 J ∕ (mol· K). A is a constant for a solvent at a defined temperature and pressure. In water at 25 ° C, ε = 78.6, A = 0.509.
Individual ion activity and activity coefficients are not measurable and therefore have no thermodynamic significance, but can be correlated to measurable ion average activity. If one molecule of the binary electrolyte dissociates into a total of v, wherein v + cations, v - anions, the relationship between the average fitness coefficient γ ± and the individual ion activity coefficient is
(4)
Let the valence of the ions be z + and z - respectively , then
Lgγ ± =(z + lgγ ± +z - lgγ - )∕(z + +z - ) (5)
thus
-lgγ ± =Az + z - (6)
The Debye-Shocker theory and equations (2) and (6) are commonly referred to as Debye-Shocker's law of extremes and are suitable for very dilute solutions. It is believed that the extent to which an ion's behavior in a solvent deviates from the ideal state is determined by the solution charge density as reflected by the ionic strength, independent of the chemical nature of the ion.
Debye-Shocker's Extremely Limited Law gives a strong LDγ ± value for a strong electrolyte dilute solution with an ionic strength between 0 and 0.005, and it is also used as a semi-empirical experience for ionic strength or complex solution expansion. The basis of theory.
Second, the expansion of Debye-Heckel theory to concentrated solution
Debye-Heckel used the concepts of electrostatics, fluid mechanics and statistical mechanics to derive a theory describing the properties of electrolyte solutions dominated by the interaction between ions. Obviously, Debye-Shocker's extreme law applies only to extremely dilute electrolyte solutions. When the concentration of the strong electrolyte solution of the 1:1 type exceeds 10 -3 mol∕L or the ionic strength of other types of electrolyte solutions is similar, the application of the polar limit law begins to be difficult, and thus, after their theory, there have been repeated corrections. To extend it into a more concentrated solution. Most of the corrections were made by adding corrections to the Debye-Heckel equation. The Debye-Huckel equation reflects the long-range effects between ions, and the corrections reflect their short-range effects. These activity coefficient extension equations use empirical terms to fit the activity measurements of the experimental observations. For example, Bjerreum considers ion association, or more precisely, ion pairing to form an ion pair, which is modified to assume that the ions are in a paired state and are not centered on the ion due to the ionic atmosphere. The contribution of electrical energy. The degree of ion pair formation increases very rapidly as the ion spacing r value decreases, and the associated equilibrium constant can be calculated. Finally, the extended Debye-Hake equation
(7)
Where B is another constant. If the solution contains more than one electrolyte, the equation cannot be thermodynamically used to calculate the activity coefficient. In addition, the closest distance between ions is not known. In order to eliminate this quasi-basic parameter, the following form of equation is used.
(8)
Where z + = z - ; β is an empirical constant that can be selected for a particular system by fitting the data. Davies takes β=0.2 to get the equation
(9)
It is quite consistent with the measured value of the average activity coefficient of the dilute solution. For example, the average deviation of the 0.1 mol ∕L solution is only about 2%. This is an empirical equation based on published data. As long as there is enough experimental data about the salt γ ± so that the tunable parameters α and β can be accurately calculated, such equations can be used to calculate richer solutions, for low A 1:1 type simple electrolyte solution of valence can be calculated to a concentration of about 1 mol ∕L. In general, however, no equation is satisfactory.
3. Extension of Debye-Heckel theory to mixed electrolyte solutions
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
(10)
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 (11). The term "three ion" is included in the formula, but it is assumed that μ ijk is independent of ionic strength.
(11)
The equation for the activity coefficient can be written by appropriate derivation of G ex
(12)
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 (13). Using the parameter values ​​of simple electrolytes, the lnγ ± of 52 binary electrolyte mixtures with common ions is calculated, 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.
(13)
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
(14)
The value of the parameter Bm is given by Bromley, see the literature.
The basic equation of Meissner is
(15)
Where Г 12 is defined as Where γ 12 is the required electrolyte activity coefficient
B=0.75-0.65q
(16)
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:
(17)
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).
Fourth, the effect of temperature and complex on activity and activity coefficient
(1) Effect of temperature on activity and activity coefficient
The commonly given activity coefficient is the value at 25 ° C (298 K). For other activity coefficients, Meissner proposes the following equation to correct the q o value.
(18)
Where Δt = t-25; the values ​​of a and b are -0.0079 and -0.0029 for sulfates, and -0.005 and -0.0085 for other electrolytes. Furthermore, the value of Г in equation (19) must be changed to correct the Debye-Cocker parameter containing the temperature-dependent variable D.
(19)
(2) Effect of complex on activity and activity coefficient
1. Formation of complexes
The deviation of the Debye-Shocker's extreme law for strong electrolyte slags with concentrations greater than 10 -3 mol∕L indicates that in these solutions, the electrostatic attraction between ions no longer dominates the G ex value. In various attempts to extend the Debye-Hickel's extreme law, although short-range effects are considered in different ways, they all assume that no chemical bonds are formed by electron interaction between ions, and no new substances are formed. Since there is currently no way to calculate the effect of such inter-electron interactions on the G ex value, this assumption can only be made. For the new compounds formed between the components in the solution, whether between ions and ions or between ions and neutral molecules, the free energy of formation cannot be calculated. This type of reaction is very important for process chemistry and hydrometallurgy. To deal with these reactions, process chemistry and hydrometallurgists approach it from another perspective, treating them as chemical equilibrium, using experimentally measured equilibrium. Constants are used to quantitatively describe them.
Consider a z+ valence metal ion M z + in a solution containing a monovalent anion L − . When they act, it is assumed that L - is a ligand and the product is called a complex. The complex is formed hierarchically, and each stage is controlled by an equilibrium constant:
The maximum number n of L - ions forming a complex with M z + is called the coordination number of M z + . The total equilibrium constant β (called the instability constant) is
General form, cumulative instability constant
β n = K 1 K 2 K 3 ... Kn
If the ligand is an uncharged molecule, such as ammonia, and the equilibrium is treated in the same manner, the charge number of each complex is z+.
The factors controlling the absolute and relative amounts of each metal-containing component and free ligand in the solution are:
(1) the value of all equilibrium constants;
(2) total concentration of all forms of metal [M t ];
(3) total ligand concentration [Lt];
(4) the ratio of the above two concentrations;
(5) Activity coefficients of the components involved in the balance.
In the case where the total metal concentration in the dispersion is constant, as the total ligand concentration increases from zero, the complex ML is formed first and its concentration gradually increases, and begins to decrease when the complex ML 2 is produced. The concentration of the complex ML 2 is also gradually increased, and is decreased again when a higher-order complex is formed. The degree of formation of the complex MLm is defined by:
α MLm = [ML m ] / [M t ]
However, if a multinuclear complex is present, it contains more than one metal atom per ion or molecule, and the concentration is multiplied by the number of metal atoms contained in the calculation.
The average number of ligands is defined as
=([L t ]-[L])/[M t ]
That is, the concentration of the ligand bound in the complex divided by the total concentration of the metal, which is especially important when measuring the equilibrium constant.
When writing about a balanced chemical equation, solvation of the substances involved in the equilibrium is usually ignored. In fact, in aqueous solution, metal ions are strongly hydrated, and in many cases the ligand is considered to be a water molecule at a coordination position around the metal atom. For example, the Cu(NH 3 ) 4 2 + ion contains four amino groups arranged at four corners of a square centered on a copper atom. An amino group can be considered to replace a water molecule in the same position.
Like all other divalent and trivalent metal ions in the first transition series in the periodic table, the simple hydrated Cu 2 + ion has six coordinating water molecules arranged at the apex of the octahedron. However, due to the Jahn-Teller effect, the octahedron of Cu 2 + ions is distorted, so the metal ions are weakly combined with the fifth and sixth ligands, including hydrated water molecules. Therefore, the stepwise equilibrium constant (25 ° C) in the ammine is
lgK 1 lgK 2 lgK 3 lgK 4 lgK 5
4.15 3.50 2.89 2.13 -0.52
The Cu(NH 3 ) 5 2 + ion can be formed in a very concentrated aqueous ammonia solution, and the sixth ammonia molecule can only be combined in liquid ammonia.
Buyron explains why the K value decreases with the increase in the number of NH 3 groups bound to the Cu 2 + ions. He refers to the logarithm of the ratio of two adjacent equilibrium constants as the total effect, T (m -1 ), m and divides it into statistical effects S (m -1 ), m and ligand effect L (m -1 ), m two quantities. The tendency of the ligand L to be lost from the component ML m is proportional to the value of m, while the tendency of the component ML m in combination with the other ligand group L is proportional to the value of (n-m). The ratio of n consecutive stable constants will be
The ratio of two consecutive stable constants caused by statistical reasons alone is
therefore
This equation can be applied when each coordinating group occupies only one coordination position and the n coordination positions around the metal ion are identical. The first four constant K values ​​of the Cu II -NH 3 system are on the same order of magnitude, and the correction values ​​are adjusted in consideration of statistical factors, which are more evenly close:
lgK 1 (corr), 3.55 lgK 2 (corr), 3.32
lgK 3 (corr), 3.07 lgK 4 (corr), 2.73
Therefore, the difference between the test values ​​can be mainly attributed to the statistical effect.
Buyron divides the ligand effect itself into electrostatic effects and static effects. The electrostatic effect is caused by the charge between the ligand and the metal-containing component. The ligand ion L - is attracted to M 2 + or ML + but is repelled from ML 3 - . Buyron derived an equation to calculate the value of the electrostatic effect, and given the uncertainty of use, the static effect is only considered for uncharged ligands.
Certain types of ligands can occupy two coordination positions, which is a bidentate ligand. For example, ethylenediamine (en), H 2 N·CH 2 ·CH 2 ·H 2 N, carbonate, and many organic substances containing a neutral coordinating group and an acidic group, such as glycine, H 2 N· CH 2 ·COOH. It can be attached to a metal ion by its acid group, neutralizing a positive charge, or it can form a covalent bond with a metal by a nitrogen atom to form a chelate.
5. Influence of activity coefficient on formation of complexes
The formation of the complex changes the ionic strength of the solution, thereby also changing the activity coefficient of the ions. Let the ratio of the concentration of free metal ions in the solution to the total concentration of the metal be referred to as the total activity coefficient γ M (global activity coefficient) of the metal.
The commonly reported beta n is the value extrapolated to zero ionic strength, so a zero correction value is used. In the ammonia and ethylamine complex ion solution, the cumulative instability constant β n is not constant when the ionic strength changes. The above equations are not quite correct for ammonia solutions, and in fact it is possible to overestimate the γ M value. For example, when I=1, it may be overestimated by 2 times.
For negatively charged ligands, such as Cl - , CN and SO 4 2 - , the formation of complexes reduces the actual ionic strength, sometimes much lower than the value assumed to be completely dissociated. Meissner considered the effect of ordinary ion association in a binary electrolyte solution and corrected it by the choice of its q value. However, he did not give the q value of the chloride or cyanide of salts such as Cu + , Ag + , Au + , Au 3 + , Hg + and Pb 2 + which are known to form strong complexes. Solutions of these salts are very important in hydrometallurgy, but there is currently no good way to estimate the activity coefficients of these metal ions in chloride or cyanide solutions.
6. Effect of temperature on the equilibrium constant of complexes
The value of the equilibrium constant formed by the metal complex is a measure of the relative degree of stability of the simple hydrated metal ion in combination with the ligand molecule or ion in the solution. The strength of the chemical bond between the metal and the ligand acts to determine the stability of the complex, but other factors also have an effect.
The equilibrium constant is related to the standard free energy change ΔG å应 of the reaction:
△G Θ =-RTlnK
The change of standard free energy is determined by the changes of standard 焓 and standard entropy △H Θ and △S Θ
△G Θ =△H Θ -T△S Θ
Standard enthalpy is a measure of the degree of heat of the reactants and products at the time of formation of the complex, and is determined by the type of chemical bond formed between the metal ion and the ligand. In the case of single-charged monodentate ligand, each stage of △ H Θ value typically between + 20kJ / mol and -20kJ / mol, and when a strong covalent bond, △ H [Theta] values it possible high -80kJ ∕mol.
The standard enthalpy of complex formation is different from the enthalpy change, which is closely related to the structure of the complex environment. The standard entropy change ΔS Θ in the aqueous electrolyte solution is usually positive. This unexpected fact is due to the structural damage of the water around the complex. The positive entropy change caused by such structural failure is much larger than the negative entropy caused by the vibration and rotational entropy of the single metal and the translational entropy of the ligand. If the ligand is negatively charged, the neutralization of the charge during formation of the complex reduces the number of ions in the system and affects the entropy change. This causes a large positive entropy change, resulting in a more stable complex.
The association of metal ions with uncharged monodentate ligands does not reduce the number of ions present in the system, and there is no relocation of water molecules. In this case, only a small positive entropy change or even a negative entropy change occurs when the complex is formed. The value of ΔS 通常 is usually the single most important factor in controlling the stability of the complex. The higher the temperature, the more normal the standard entropy change in the solution will be, and the standard entropy of anion generation will be more negative. Therefore, in general, the higher the temperature, the more positive the entropy generated by the complex, and the more stable the complex.
The standard enthalpy change ΔH T å应 of the reaction when the temperature is not 25 ° C can be written as
(20)
Similarly, the standard entropy change can be written as
(twenty one)
In the formula, ΔC p Θ is the standard heat capacity when the pressure is constant. thus
(twenty two)
Introducing a Gibbs free energy function, which can be written as
(twenty three)
Substituting this formula into equation (23)
(twenty four)
and
(25)
As long as the free energy function of the reaction is known, that is, the standard change ΔC p Θ of the enthalpy under constant pressure is known, the equilibrium constant K T of the reaction at any temperature can be obtained from the equation (25).
Although the free energy function of many reactions can be found, the equilibrium reaction in most aqueous solutions is not known. Therefore, some assumptions need to be made in order to estimate the lgK T value of such a reaction in a system involved in hydrometallurgy.
If there is not enough heat capacity data, it is generally assumed that ΔC p Θ is a constant, and then equation (23) becomes
(26)
Points are sorted out
(27)
Substitute (6)
(28)
This also corresponds to a linear change in the ΔH å应 of the reaction with temperature.
The values ​​of ΔC p Θ , ΔH p Θ and ΔS p Θ for the complex reaction are now poorly known, and only a few cases know the equilibrium constant value in a small temperature range. Therefore, it can only be assumed that ΔH Θ varies with temperature to calculate ΔC p Θ . However, the values ​​thus obtained are very sensitive to errors with small equilibrium constants.
The equilibrium constant value is also related to the pressure, but the effect of the pressure below the critical pressure on the equilibrium constant in the aqueous solution is relatively small.
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