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Wilhelm Ostwald Friedrich Wilhelm Ostwald (; 4 April 1932) was a Baltic German chemist and philosopher. Ostwald is credited with being one of the founders of the field of physical chemistry, with Jacobus Henricus van 't Hoff, Walther Nernst, and Svante Arrh ...
’s dilution law is a relationship proposed in 1888 between the
dissociation constant In chemistry, biochemistry, and pharmacology, a dissociation constant (K_D) is a specific type of equilibrium constant that measures the propensity of a larger object to separate (dissociate) reversibly into smaller components, as when a complex ...
' and the degree of dissociation ' of a weak electrolyte. The law takes the form :K_d = \cfrac = \frac \cdot c_0 Where the square brackets denote concentration, and is the total concentration of electrolyte. Using \alpha=\Lambda_c/\Lambda_0, where \Lambda_c is the molar conductivity at concentration c and \Lambda_0 is the limiting value of molar conductivity extrapolated to zero concentration or infinite dilution, this results in the following relation: :K_d = \cfrac \cdot c_0


Derivation

Consider a binary electrolyte AB which dissociates reversibly into A+ and B ions. Ostwald noted that the
law of mass action In chemistry, the law of mass action is the proposition that the rate of the chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. It explains and predicts behaviors of solutions in dy ...
can be applied to such systems as dissociating electrolytes. The equilibrium state is represented by the equation: :AB <=> + B^- If ' is the fraction of dissociated electrolyte, then ' is the concentration of each ionic species. must, therefore be the fraction of ''undissociated'' electrolyte, and the concentration of same. The dissociation constant may therefore be given as :K_d = \cfrac = \cfrac = \cfrac \cdot c_0 For very weak electrolytes (however, neglecting 'α' for most weak electrolytes yields counterproductive result) , implying that . :K_d = \frac \cdot c_0 \approx \alpha^2 c_0 This gives the following results; :\alpha = \sqrt Thus, the degree of dissociation of a weak electrolyte is proportional to the inverse square root of the concentration, or the square root of the dilution. The concentration of any one ionic species is given by the root of the product of the dissociation constant and the concentration of the electrolyte. :\ce = \ce = \alpha c_0 = \sqrt


Limitations

The Ostwald law of dilution provides a satisfactory description of the concentration dependence of the conductivity of weak electrolytes like CH3COOH and NH4OH. The variation of molar conductivity is essentially due to the incomplete dissociation of weak electrolytes into ions. For strong electrolytes, however, Lewis and
Randall Randall may refer to the following: Places United States *Randall, California, former name of White Hall, California, an unincorporated community * Randall, Indiana, a former town *Randall, Iowa, a city *Randall, Kansas, a city *Randall, Minnesot ...
recognized that the law fails badly since the supposed equilibrium constant is actually far from constant. This is because the dissociation of strong electrolytes into ions is essentially complete below a concentration threshold value. The decrease in molar conductivity as a function of concentration is actually due to attraction between ions of opposite charge as expressed in the Debye-Hückel-Onsager equation and later revisions. Even for weak electrolytes the equation is not exact.
Chemical thermodynamics Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measureme ...
shows that the true equilibrium constant is a ratio of thermodynamic activities, and that each concentration must be multiplied by an activity coefficient. This correction is important for ionic solutions due to the strong forces between ionic charges. An estimate of their values is given by the Debye–Hückel theory at low concentrations.


See also

* Autosolvolysis * Osmotic coefficient * Activity coefficient *
Ion transport number In chemistry, ion transport number, also called the transference number, is the fraction of the total electric current carried in an electrolyte by a given ionic species : :t_i = \frac Differences in transport number arise from differences in ...
* Ion association * Molar conductivity Physical chemistry Enzyme kinetics


References

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