Specific ion interaction theory

Last updated May 21, 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]

Related Research Articles

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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.

The chemists Peter Debye and Erich Hückel noticed that solutions that contain ionic solutes do not behave ideally even at very low concentrations. So, while the concentration of the solutes is fundamental to the calculation of the dynamics of a solution, they theorized that an extra factor that they termed gamma is necessary to the calculation of the activities of the solution. Hence they developed the Debye–Hückel equation and Debye–Hückel limiting law. The activity is only proportional to the concentration and is altered by a factor known as the activity coefficient $. This factor takes into account the interaction energy of ions in solution.$

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The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes and plasmas. It is a linearized Poisson–Boltzmann model, which assumes an extremely simplified model of electrolyte solution but nevertheless gave accurate predictions of mean activity coefficients for ions in dilute solution. The Debye–Hückel equation provides a starting point for modern treatments of non-ideality of electrolyte solutions.

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The Bromley equation was developed in 1973 by Leroy A. Bromley with the objective of calculating activity coefficients for aqueous electrolyte solutions whose concentrations are above the range of validity of the Debye–Hückel equation. This equation, together with Specific ion interaction theory (SIT) and Pitzer equations is important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water.

Pitzer equations are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. They were first described by physical chemist Kenneth Pitzer. The parameters of the Pitzer equations are linear combinations of parameters, of a virial expansion of the excess Gibbs free energy, which characterise interactions amongst ions and solvent. The derivation is thermodynamically rigorous at a given level of expansion. The parameters may be derived from various experimental data such as the osmotic coefficient, mixed ion activity coefficients, and salt solubility. They can be used to calculate mixed ion activity coefficients and water activities in solutions of high ionic strength for which the Debye–Hückel theory is no longer adequate. They are more rigorous than the equations of specific ion interaction theory, but Pitzer parameters are more difficult to determine experimentally than SIT parameters.

Equilibrium chemistry is concerned with systems in chemical equilibrium. The unifying principle is that the free energy of a system at equilibrium is the minimum possible, so that the slope of the free energy with respect to the reaction coordinate is zero. This principle, applied to mixtures at equilibrium provides a definition of an equilibrium constant. Applications include acid–base, host–guest, metal–complex, solubility, partition, chromatography and redox equilibria.

Salting in refers to the effect where increasing the ionic strength of a solution increases the solubility of a solute, such as a protein. This effect tends to be observed at lower ionic strengths.

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.

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.

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