Consider a binary electrolyte AB with a concentration ‘c’ that reversibly dissociates into its constituent ions. The degree of this dissociation is represented by ⍺. This means that the equilibrium concentration of each ionic species can be expressed as ⍺c. As well as this, the fraction of the electrolyte that remains undissociated at equilibrium is given by (1−⍺). The corresponding equilibrium concentration for this undissociated portion is then calculated as (1−⍺)c. For such solutions, Ostwald’s dilution law can be expressed through the equilibrium constant K, also known as the electrolyte’s dissociation constant. At equilibrium, K is defined as the ratio of the concentration of products raised to their stoichiometric coefficients divided by the concentration of reactants raised to their stoichiometric coefficients.
K = (cα)(cα)/c(1–α) = cα2/1–α
For very weak electrolytes, α is much less than 1, so 1–α can be approximated as 1. This means that the equilibrium constant simplifies to K ≈ cα2.
However, it has been found that Ostwald’s dilution law can be applied only to weak electrolytes, and it does not hold for strong electrolytes like HCl and NaF. In the case of strong electrolytes like NaF and NaCl, X-ray analysis shows that their crystals are made solely of ions, not molecules; these compounds, known as electrovalent compounds, are formed by the transfer of electrons from a metal to a non-metal atom. When electrovalent compounds are melted or dissolved in water, the ions gain mobility and can conduct electricity. The strength of the electrostatic forces, and as a result, the conductivity, is also affected by the dielectric constant of the medium, according to Coulomb’s law.
Based on Arrhenius' theory of electrolytic dissociation, Ostwald’s dilution law explains the equilibrium in aqueous electrolyte solutions.
Consider an electrolyte AB at a concentration ‘c’ mol per liter, which dissociates reversibly into ions.
If α is the degree of dissociation, each ion has an equilibrium concentration of cα, while the undissociated fraction (1 − α) has a concentration of c(1 − α). These terms define the equilibrium constant K, called the dissociation constant.
Ostwald’s dilution law applies only to weak electrolytes like acetic acid and NH₄OH.
Strong electrolytes like HCl and NaF are almost completely dissociated, with α close to one. Under these conditions, (1 − α) approaches zero, making the law mathematically invalid.
The failure of the law for strong electrolytes arises because, on dissolution, water’s high dielectric constant weakens electrostatic forces, leading to near-complete dissociation. As a result, no ion–molecule equilibrium exists, and Ostwald’s dilution law becomes inapplicable.
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