From Letters to the Editor

On the History of the Discovery of the Dissolution Equation

In foreign, and indeed also in domestic, literature there are statements that the dissolution equation was first derived by the American scientists A. Noyes and W. Whitney at the end of 1897, in an article printed in the Journal of the American Chemical Society, vol. 19, pp. 930–934 (1897), and also in Zeitschrift für Physikalische Chemie, vol. 23, pp. 689–692 (1897). Noyes and Whitney derived the equation for the rate of dissolution of a solid substance in its own solution from very limited experimental material, namely from the study of the dissolution of benzoic acid and lead chloride, relying on diffusion theory and Fick’s equation. According to their conclusions, the dissolution rate \(\frac{dx}{dt}\) depends only on the dissolution coefficient \(c\) and the degree of saturation \(s - x\):

\[ -\frac{dx}{dt} = c(s - x), \tag{1} \]

where \(s\) is the concentration of the saturated solution, \(x\) is the concentration of the given solution at time \(t\), \(c\) is the dissolution constant, and \(t\) is the dissolution time.

Upon a more careful study of this question in the Russian literature, we found that the first scientifically substantiated dissolution equation was derived by the Russian scientist, professor of the Kharkov Technological Institute Aleksandr Nikolaevich Shukarev. In the article “Distribution of Substances between Two Immiscible Solvents,” published in the Journal of the Russian Physico-Chemical Society for 1896 (vol. 28, pp. 604–614), he derived the dissolution equation.

On the basis of the study of considerable experimental material, A. N. Shukarev represented the rate of dissolution of a solid body in a solvent by the following equation:

\[ \frac{dc}{dt} = k\pi(a - c), \tag{2} \]

where \(k\) is the dissolution coefficient, \(c\) is the concentration of the solution at a given moment, \(a\) is the solubility limit, and \(\pi\) is the active surface of the solid body.

From the dissolution equation derived by Prof. A. N. Shukarev it is evident that the dissolution rate \(\frac{dc}{dt}\) depends on the dissolution coefficient

the value of \(k\), the degree of saturation \(a-c\), and also on the effective surface of the dissolving body \(\pi\). The error of Noyes and Whitney was corrected later, in 1900, by the works of Brunner and Toločko, who introduced into equation (1) a multiplier accounting for the effective surface \(F\). After correction, the Noyes–Whitney dissolution equation took the following form:

\[ -\frac{dx}{dt}=cF(s-x). \tag{3} \]

The equation of A. N. Shchukarev was printed in the April issue of the Journal of the Russian Physico-Chemical Society for 1896 and provoked a major scholarly discussion. A. A. Yakovkin and others spoke at the meeting of the Russian Physico-Chemical Society on 7/XI—1896 and in the pages of the journal against A. N. Shchukarev’s equation. In defense of A. N. Shchukarev’s equation A. A. Baikov spoke, pointing out the correctness of A. N. Shchukarev’s equation, except for the case when the dissolving substances interact chemically.

The dissolution equation of Noyes and Whitney, corrected by Brunner and Toločko, was extended by Nernst, by 1904, to all heterogeneous processes of dissolution and crystallization. Subsequently in the literature, the theory of dissolution and its equation were linked by various authors with the names of Nernst and Noyes. Later works on the study of the dissolution process showed the erroneousness of the Nernst–Noyes theory. Thus, already in 1904, Shchur, investigating readily soluble salts, derived a dissolution equation different from the Noyes–Whitney equation, namely:

\[ -\frac{dx}{dt}=k\lg\frac{s}{x}, \tag{4} \]

where the meanings of \(s\), \(x\), \(k\), and \(t\) are the same as in equations (1) and (3). Indications of the inconsistency of the Nernst–Noyes theory with the facts are found in the works of Erickson (1898), Auren (1901), Palmer (1906), Meyer-Wildermann (1909), Marc (1910), V. M. Fischer (1913), E. N. Gapon (1929), Drucker (1933), and others.

E. N. Gapon, in his work “Kinetics of the Precipitation of Salts from Supersaturated Solutions,” published in the Journal of the Russian Physico-Chemical Society, chemical part: 1929, vol. 61, issue 10, pp. 2319–2326, writes:

“Crystallization of a whole series of substances turned out not to obey the fundamental law of Nernst–Noyes: the rate of crystallization is proportional to the second power of supersaturation, not the first.” Consequently, the dissolution equation has the form:

\[ \frac{dc}{dt}=k\pi(a-c)^3, \tag{5} \]

where the designations \(c\), \(a\), \(k\), \(\pi\), and \(t\) are the same as in equation (2).

Thus, the work of Noyes and Whitney appeared more than a year after the publication of the work of Prof. A. N. Shchukarev, after the controversy that had taken place in the scholarly circles of the Russian public and in the pages of Russian journals around the dissolution equation. Despite such fame of A. N. Shchukarev’s dissolution equation, neither Noyes and Whitney, nor Nernst and others, when expounding the same question and giving an analogous equation, although a less perfect one, mention in the list of literature used the work of Prof. A. N. Shchukarev.

The suppression of discoveries made by Russian scientists, and the attribution of their works, even without mention in the list of cited literature, is characteristic in many cases of scholars of capitalist countries.

The priority for the discovery of the dissolution equation must belong only to the one who first derived and substantiated it—to the Russian scientist Professor A. N. Shchukarev.

M. S. Nichik