Konovalov’s Thought Experiment

Dmitiri Konovalov (1856-1929) was a Russian chemist who made important contributions to the theory of solutions. He studied the vapor pressure of solutions of liquids in liquids and in 1884 published a book on the subject which gave a scientific foundation to the distillation of solutions and led to the development of industrial distillation processes.

On the subject of partially miscible liquids forming conjugate solutions, Konovalov in 1881 established the following fact: “If two liquid solutions are in equilibrium with each other, their vapor pressures, and the partial pressures of the components in the vapor, are equal.”

J. Willard Gibbs in America had already developed the concept of chemical potential to explain the behavior of coexistent phases in his monumental treatise On the Equilibrium of Heterogeneous Substances (1875-1878). Konovalov was unaware of this work, and independently found a proof on the basis of this astutely reasoned thought experiment:

«Consider Figure 77 shown above. Two liquid layers α and β in coexistent equilibrium are contained in a ring-shaped tube, and above them is vapor. If the pressure of either component in the vapor were greater over α than over β, diffusion of vapor would cause that part lying over β to have a higher partial pressure of the given component than is compatible with equilibrium. Condensation occurs and β is enriched in the specified component. By reason of the changed composition of β however, the equilibrium across the interface of the liquid layers is disturbed and the component deposited by the vapor will pass into the liquid α. The whole process now commences anew and the result is a never-ending circulation of matter round the tube i.e. a perpetual motion, which is impossible. Hence the partial pressures of both components are equal over α and β and therefore also their sum i.e. the total vapor pressure.»

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Equivalence of vapor pressure and chemical potential

Konovalov showed that the condition of equilibrium in coexistent phases was equality of vapor pressure p for each component. This is consistent with the concept of ‘generalized forces’, a set of intensive variables which drive a thermodynamic system spontaneously from one state to another in the direction of equilibrium. Vapor pressure is one such variable, and chemical potential is another. Hence Gibbs showed that chemical potential μ is a driver of compositional change between coexistent phases and that equilibrium is reached when the chemical potential of each component in each phase is equal. In shorthand the equilibrium position for partially miscible liquids containing components 1 and 2 in coexistent phases α, β and vapor can be stated as:

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P Mander, July 2020

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