Ostwald–Freundlich equation
The Ostwald–Freundlich equation governs boundaries between two phases; specifically, it relates the surface tension of the boundary to its curvature, the ambient temperature, and the vapor pressure or chemical potential in the two phases. The Ostwald–Freundlich equation for a droplet or particle with radius formula_1 is: One consequence of this relation is that small liquid droplets (i.e., particles with a high surface curvature) exhibit a higher effective vapor pressure, since the surface is larger in comparison to the volume. Another notable example of this relation is Ostwald ripening, in which surface tension causes small precipitates  to dissolve and larger ones to grow. Ostwald ripening is thought to occur in the formation of orthoclase megacrysts in granites as a consequence of subsolidus growth. See rock microstructure for more. History. In 1871, Lord Kelvin (William Thomson) obtained the following relation governing a liquid-vapor interface: where: In his dissertation of 1885, Robert von Helmholtz (son of the German physicist Hermann von Helmholtz) derived the Ostwald–Freundlich equation and showed that Kelvin's equation could be transformed into the Ostwald–Freundlich equation. The German physical chemist Wilhelm Ostwald derived the equation apparently independently in 1900; however, his derivation  contained a minor error which the German chemist Herbert Freundlich corrected in 1909. Derivation from Kelvin's equation. According to Lord Kelvin's equation of 1871, If the particle is assumed to be spherical, then formula_23; hence, Note: Kelvin defined the surface tension formula_6 as the work that was performed per unit area "by" the interface rather than "on" the interface; hence his term containing formula_6 has a minus sign. In what follows, the surface tension will be defined so that the term containing formula_6 has a plus sign. Since formula_28, then formula_29; hence, Assuming that the vapor obeys the  ideal gas law, then where: Since formula_40 is the mass of one molecule of vapor or liquid, then Hence Thus Since then Since formula_48, then formula_49 . If formula_50, then formula_51. Hence Therefore which is the Ostwald–Freundlich equation.