7.2
Ionic Association
Strong electrolytes are often assumed to exist entirely as free ions in aqueous solution. In reality, oppositely charged ions can partially associate to form ion pairs, except in many 1:1 electrolytes, like NaCl or NaOH.
Bjerrum defined an ion pair as two oppositely charged ions close enough that their electrostatic attraction exceeds the thermal energy, quantified as 2kT, where k is Boltzmann’s constant, and T is the absolute temperature. When this condition is met, ion association becomes favorable.
Ion pairing increases with higher ionic charges, as in 2:1 or 2:2 electrolytes, leading to a significant fraction of ion pairs even at low concentrations. This prediction is experimentally supported. When the percentage of cations in ion pairs is plotted against molality, the results closely match Bjerrum’s theory.
It is also strongly influenced by the solvent: water’s high dielectric constant weakens electrostatic attraction and limits ion pairing, whereas solvents with lower dielectric constants enhance ion–ion attraction, making ion-pair formation significant even for 1:1 electrolytes.
The ionic association is the association of oppositely charged ions in an electrolyte solution to form ion pairs. Bjerrum defined ion pairs as two oppositely charged ions whose electrostatic attraction exceeds the thermal energy of the system, typically expressed as 2kT. Electrostatic attraction depends on ionic charge, separation distance, and the dielectric constant of the medium. Thermal energy, represented by kT, reflects the tendency of ions to move independently due to molecular motion. Ion pairing occurs when the attractive Coulombic interaction is strong enough to overcome this thermal agitation. The 2kT threshold is not arbitrary; it represents a practical benchmark at which attraction dominates over thermal escape.
According to Bjerrum’s theory, ion pairing in water is generally minimal for 1:1 electrolytes but increases significantly for ions with higher charges, even at low concentrations, due to stronger electrostatic interactions.
Water has a high dielectric constant because of its molecular polarity. This reduces electrostatic attraction between ions and limits ion-pair formation in aqueous solutions. In contrast, solvents with lower dielectric constants are less effective at stabilizing separated charges, leading to stronger electrostatic attraction and increased ion pairing. Ionic association reduces the electrical conductivity of a solution because ions form associated species, such as CaSO₄ and MgF₂. The extent of association can be estimated from conductivity measurements. Ionic association is usually negligible in dilute aqueous solutions but becomes significant in concentrated solutions. At infinite dilution, the degree of ionic association approaches zero. Temperature and molality also influence the extent of association.
Ion pairs differ from complex ions. Complex-ion formation commonly occurs in aqueous solutions of transition-metal salts and involves bonds with significant covalent character. In contrast, ion pairs are held together by electrostatic forces and often retain part of their solvent shells. Absorption spectroscopy can help distinguish between ion pairs and complex ions, and some solutions may contain both species. When ion-pair formation reduces the number of free ions in solution, the chemical potential of the ion pair equals the sum of the chemical potentials of the individual ions, allowing the Gibbs free energy change for the association reaction to be derived accordingly.
Strong electrolytes are often assumed to exist entirely as free ions in aqueous solution. In reality, oppositely charged ions can partially associate to form ion pairs, except in many 1:1 electrolytes, like NaCl or NaOH.
Bjerrum defined an ion pair as two oppositely charged ions close enough that their electrostatic attraction exceeds the thermal energy, quantified as 2kT, where k is Boltzmann’s constant, and T is the absolute temperature. When this condition is met, ion association becomes favorable.
Ion pairing increases with higher ionic charges, as in 2:1 or 2:2 electrolytes, leading to a significant fraction of ion pairs even at low concentrations. This prediction is experimentally supported. When the percentage of cations in ion pairs is plotted against molality, the results closely match Bjerrum’s theory.
It is also strongly influenced by the solvent: water’s high dielectric constant weakens electrostatic attraction and limits ion pairing, whereas solvents with lower dielectric constants enhance ion–ion attraction, making ion-pair formation significant even for 1:1 electrolytes.
From Chapter 7:
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7.2 : Ionic Association
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