Title: laws of distribution
Long Title: IUPAC Gold Book - laws of distribution
DOI: 10.1351/goldbook.L03487
Status: current

Definition
During the formation of a mixed crystal from a solution containing two components 'A' and 'B', the latter may be distributed according to the equation \[K_{\rm{A},\rm{B}}=\frac{b\ (a_{0}- a)}{a\ (b_{0}- b)}\] In this homogeneous distribution, \(a_{0}\) and \(b_{0}\) are the respective concentrations in the solution before crystallization and \(a\) and \(b\) are the respective concentrations in the solution after crystallization. \(K_{\rm{A},\rm{B}}\) is usually called the separation factor. The term homogeneous distribution coefficient is not recommended. Alternatively the distribution of the micro-component may follow the equation of Doerner and Hoskins \[\ln (\frac{a_{0}}{a}) = \lambda \ \ln (\frac{b_{0}}{b})\] (logarithmic distribution) where \(\lambda \) is usually called the logarithmic distribution coefficient, the meaning of the other symbols remaining the same. Exactly homogeneous or logarithmic distributions are extreme cases and very seldom encountered.

Related Terms
- crystallization: https://goldbook.iupac.org//terms/view/C01434
- distribution coefficient: https://goldbook.iupac.org//terms/view/D01812
- micro: https://goldbook.iupac.org//terms/view/M03894

Source
- Orange Book, 2nd ed., p. 85 (https://media.iupac.org/publications/analytical_compendium/)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/L03487/html
- json: https://goldbook.iupac.org/terms/view/L03487/json
- xml: https://goldbook.iupac.org/terms/view/L03487/xml

Citation: Citation: 'laws of distribution' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.L03487
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Accessed: 2026-08-01T17:06:38+00:00