Specific ion interaction theory

Last updated December 11, 2024

In theoretical chemistry, Specific ion Interaction Theory (SIT theory) is a theory used to estimate single-ion activity coefficients in electrolyte solutions at relatively high concentrations.^[1]^[2] It does so by taking into consideration interaction coefficients between the various ions present in solution. Interaction coefficients are determined from equilibrium constant values obtained with solutions at various ionic strengths. The determination of SIT interaction coefficients also yields the value of the equilibrium constant at infinite dilution.

Background

This theory arises from the need to derive activity coefficients of solutes when their concentrations are too high to be predicted accurately by the Debye–Hückel theory. Activity coefficients are needed because an equilibrium constant is defined in chemical thermodynamics as the ratio of activities but is usually measured using concentrations. The protonation of a monobasic acid will be used to simplify the presentation. The equilibrium for protonation of the conjugate base, A⁻ of the acid HA, may be written as:

{\ce {H+ + A- <=> HA}}

for which the association constant K is defined as:

K={\frac {{\ce {\{HA\}}}}{{\ce {\{H^+\}\{A^{-}\}}}}}

where {HA}, {H⁺}, and {A^–} represent the activity of the corresponding chemical species. The role of water in the association equilibrium is ignored as in all but the most concentrated solutions the activity of water is constant. K is defined here as an association constant, the reciprocal of an acid dissociation constant.

Each activity term { } can be expressed as the product of a concentration [ ] and an activity coefficient γ. For example,

\{HA\}=[HA]\times \gamma _{HA}

where the square brackets represent a concentration and γ is an activity coefficient. Thus the equilibrium constant can be expressed as a product of a concentration ratio and an activity coefficient ratio.

K={\frac {{\ce {[HA]}}}{{\ce {[H^+][A^{-}]}}}}\times {\frac {\gamma _{{\ce {HA}}}}{\gamma _{{\ce {H^+}}}\gamma _{{\ce {A^-}}}}}

Taking the logarithms:

\log K=\log K^{0}+\log \gamma _{{\ce {HA}}}-\log \gamma _{{\ce {H^+}}}-\log \gamma _{{\ce {A^{-}}}}

where:

K^{0}={\frac {{\ce {[HA]}}}{{\ce {[H^+][A^{-}]}}}}

at infinite dilution of the solution

K⁰ is the hypothetical value that the equilibrium constant K would have if the solution of the acid HA was infinitely diluted and that the activity coefficients of all the species in solution were equal to one.

It is a common practice to determine equilibrium constants in solutions containing an electrolyte at high ionic strength such that the activity coefficients are effectively constant. However, when the ionic strength is changed the measured equilibrium constant will also change, so there is a need to estimate individual (single ion) activity coefficients. Debye–Hückel theory provides a means to do this, but it is accurate only at very low concentrations. Hence the need for an extension to Debye–Hückel theory. Two main approaches have been used. SIT theory, discussed here and Pitzer equations.^[3]^[4]

Development

SIT theory was first proposed by Brønsted ^[5] in 1922 and was further developed by Guggenheim in 1955.^[1] Scatchard^[6] extended the theory in 1936 to allow the interaction coefficients to vary with ionic strength. The theory was mainly of theoretical interest until 1945 because of the difficulty of determining equilibrium constants before the glass electrode was invented. Subsequently, Ciavatta^[2] developed the theory further in 1980.

The activity coefficient of the jth ion in solution is written as γ_j when concentrations are on the molal concentration scale and as y_j when concentrations are on the molar concentration scale. (The molality scale is preferred in thermodynamics because molal concentrations are independent of temperature). The basic idea of SIT theory is that the activity coefficient can be expressed as

\log \gamma _{j}=-z_{j}^{2}{\frac {0.51{\sqrt {I}}}{1+1.5{\sqrt {I}}}}+\sum _{k}\epsilon _{jk}m_{k}

(molalities)

or

\log y_{j}=-z_{j}^{2}{\frac {0.51{\sqrt {I}}}{1+1.5{\sqrt {I}}}}+\sum _{k}b_{jk}c_{k}

(molar concentrations)

where z is the electrical charge on the ion, I is the ionic strength, ε and b are interaction coefficients and m and c are concentrations. The summation extends over the other ions present in solution, which includes the ions produced by the background electrolyte. The first term in these expressions comes from Debye–Hückel theory. The second term shows how the contributions from "interaction" are dependent on concentration. Thus, the interaction coefficients are used as corrections to Debye–Hückel theory when concentrations are higher than the region of validity of that theory.

The activity coefficient of a neutral species can be assumed to depend linearly on ionic strength, as in

\log \gamma =k_{m}I\,

where k_m is a Sechenov coefficient.^[7]

In the example of a monobasic acid HA, assuming that the background electrolyte is the salt NaNO₃, the interaction coefficients will be for interaction between H⁺ and NO₃⁻, and between A⁻ and Na⁺.

Determination and application

Firstly, equilibrium constants are determined at a number of different ionic strengths, at a chosen temperature and particular background electrolyte. The interaction coefficients are then determined by fitting to the observed equilibrium constant values. The procedure also provides the value of K at infinite dilution. It is not limited to monobasic acids.^[8] and can also be applied to metal complexes.^[9] The SIT and Pitzer approaches have been compared recently.^[10] The Bromley equation ^[11] has also been compared to both SIT and Pitzer equations.^[12] It has been shown that the SIT equation is a practical simplification of a more complicated hypothesis,^[13] that is rigorously applicable only at trace concentrations of reactant and product species immersed in a surrounding electrolyte medium.

Related Research Articles

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Wilhelm Ostwald’s dilution law is a relationship proposed in 1888 between the dissociation constant $K d$ and the degree of dissociation $α$ of a weak electrolyte. The law takes the form

In chemistry, an acid dissociation constant is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction

Solubility equilibrium is a type of dynamic equilibrium that exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation, or with chemical reaction with another constituent of the solution, such as acid or alkali. Each solubility equilibrium is characterized by a temperature-dependent solubility product which functions like an equilibrium constant. Solubility equilibria are important in pharmaceutical, environmental and many other scenarios.

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In physical chemistry, the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory explains the aggregation and kinetic stability of aqueous dispersions quantitatively and describes the force between charged surfaces interacting through a liquid medium. It combines the effects of the van der Waals attraction and the electrostatic repulsion due to the so-called double layer of counterions. The electrostatic part of the DLVO interaction is computed in the mean field approximation in the limit of low surface potentials - that is when the potential energy of an elementary charge on the surface is much smaller than the thermal energy scale, $. For two spheres of radius each having a charge separated by a center-to-center distance in a fluid of dielectric constant containing a concentration of monovalent ions, the electrostatic potential takes the form of a screened-Coulomb or Yukawa potential,$

In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same and, as a result, properties of the mixtures can be expressed directly in terms of simple concentrations or partial pressures of the substances present e.g. Raoult's law. Deviations from ideality are accommodated by modifying the concentration by an activity coefficient. Analogously, expressions involving gases can be adjusted for non-ideality by scaling partial pressures by a fugacity coefficient.

Dissociation in chemistry is a general process in which molecules (or ionic compounds such as salts, or complexes) separate or split into other things such as atoms, ions, or radicals, usually in a reversible manner. For instance, when an acid dissolves in water, a covalent bond between an electronegative atom and a hydrogen atom is broken by heterolytic fission, which gives a proton (H⁺) and a negative ion. Dissociation is the opposite of association or recombination.

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References

1 2 Guggenheim, E.A.; Turgeon, J.C. (1955). "Specific interaction of ions". Trans. Faraday Soc. 51: 747–761. doi:10.1039/TF9555100747.
1 2 Ciavatta, L. (1980). "The specific interaction theory in the evaluating ionic equilibria". Ann. Chim. (Rome). 70: 551–562.
↑ Pitzer, K.S. (1973). "Thermodynamics of electrolytes, I. Theoretical basis and general equations". J. Phys. Chem. 77 (2): 268–277. doi:10.1021/j100621a026.
↑ Pitzer, K.S. (1991). Activity coefficients in electrolyte solutions. Boca Raton, Fla: CRC Press. ISBN 0-8493-5415-3.
↑ Brønsted, J.N. (1922). "Studies on solubility IV. The principle of the specific interaction of ions". J. Am. Chem. Soc. 44 (5): 877–898. doi:10.1021/ja01426a001.
↑ Scatchard, G. (1936). "Concentrated solutions of strong electrolytes". Chem. Rev. 19 (3): 309–327. doi:10.1021/cr60064a008.
↑ Setchenow, I.M. (1892). "Action de l'acide carbonique sur les solutions des sels d'acides forts. Étude absorptiométrique". Ann. Chim. Phys. 25: 226–270.
↑ Crea, F.; De Stefano, C.; Foti, C.; Sammartano, S. (2007). "Sit parameters for the dependence of (poly)carboxylate activity coefficients on ionic strength ...". J. Chem. Eng. Data. 52: 2195–2203. doi:10.1021/je700223r.
↑ Ciavatta, L. (1990). "The specific interaction theory in equilibrium analysis. Some empirical rules for estimate interaction coefficients of metal ion complexes". Ann. Chim. (Rome). 80: 255–263.
↑ Elizalde, M. P.; Aparicio, J. L. (1995). "Current theories in the calculation of activity coefficients—II. Specific interaction theories applied to some equilibria studies in solution chemistry". Talanta. 42 (3): 395–400. doi:10.1016/0039-9140(95)01422-8. PMID 18966243.
↑ Bromley, L.A. (1973). "Thermodynamic properties of strong electrolytes in aqueous solutions". AIChE J. 19 (2): 313–320. doi:10.1002/aic.690190216.
↑ Foti, C.; Gianguzza, A.; Sammartano, S. (1997). "Comparison of equations for fitting protonation constants of carboxylic acids in aqueous tetramethylammonium chloride at various ionic strengths". Journal of Solution Chemistry. 26 (6): 631–648. doi:10.1007/BF02767633. S2CID 98355109.
↑ May, Peter M.; May, Eric (2024). "Ion Trios: Cause of Ion Specific Interactions in Aqueous Solutions and Path to a Better pH Definition". ACS Omega. 9 (46): 46373–46386. doi:10.1021/acsomega.4c07525.

External links

SIT program A PC program to correct stability constants for changes in ionic strength using SIT theory and to estimate SIT parameters with full statistics. Contains an editable database of published SIT parameters. It also provides routines to inter-convert MolaRities (c) and MolaLities (m), and lg K(c) and lg K(m).

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[G-1] 1 2 Guggenheim, E.A.; Turgeon, J.C. (1955). "Specific interaction of ions". Trans. Faraday Soc. 51: 747–761. doi:10.1039/TF9555100747.

[C-2] 1 2 Ciavatta, L. (1980). "The specific interaction theory in the evaluating ionic equilibria". Ann. Chim. (Rome). 70: 551–562.

[3] Pitzer, K.S. (1973). "Thermodynamics of electrolytes, I. Theoretical basis and general equations". J. Phys. Chem. 77 (2): 268–277. doi:10.1021/j100621a026.

[4] Pitzer, K.S. (1991). Activity coefficients in electrolyte solutions. Boca Raton, Fla: CRC Press. ISBN 0-8493-5415-3.

[5] Brønsted, J.N. (1922). "Studies on solubility IV. The principle of the specific interaction of ions". J. Am. Chem. Soc. 44 (5): 877–898. doi:10.1021/ja01426a001.

[6] Scatchard, G. (1936). "Concentrated solutions of strong electrolytes". Chem. Rev. 19 (3): 309–327. doi:10.1021/cr60064a008.

[7] Setchenow, I.M. (1892). "Action de l'acide carbonique sur les solutions des sels d'acides forts. Étude absorptiométrique". Ann. Chim. Phys. 25: 226–270.

[8] Crea, F.; De Stefano, C.; Foti, C.; Sammartano, S. (2007). "Sit parameters for the dependence of (poly)carboxylate activity coefficients on ionic strength ...". J. Chem. Eng. Data. 52: 2195–2203. doi:10.1021/je700223r.

[9] Ciavatta, L. (1990). "The specific interaction theory in equilibrium analysis. Some empirical rules for estimate interaction coefficients of metal ion complexes". Ann. Chim. (Rome). 80: 255–263.

[10] Elizalde, M. P.; Aparicio, J. L. (1995). "Current theories in the calculation of activity coefficients—II. Specific interaction theories applied to some equilibria studies in solution chemistry". Talanta. 42 (3): 395–400. doi:10.1016/0039-9140(95)01422-8. PMID 18966243.

[11] Bromley, L.A. (1973). "Thermodynamic properties of strong electrolytes in aqueous solutions". AIChE J. 19 (2): 313–320. doi:10.1002/aic.690190216.

[12] Foti, C.; Gianguzza, A.; Sammartano, S. (1997). "Comparison of equations for fitting protonation constants of carboxylic acids in aqueous tetramethylammonium chloride at various ionic strengths". Journal of Solution Chemistry. 26 (6): 631–648. doi:10.1007/BF02767633. S2CID 98355109.

[13] May, Peter M.; May, Eric (2024). "Ion Trios: Cause of Ion Specific Interactions in Aqueous Solutions and Path to a Better pH Definition". ACS Omega. 9 (46): 46373–46386. doi:10.1021/acsomega.4c07525.

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