Jacobus H. van 't Hoff

Physical chemistry. In 1884 van’t Hoff published Études de dynamique chimique, which dealt not only with reaction rates but also with the theory of equilibrium and the theory of affinity based on free energy. In the first section of the book he classified reaction velocities as unimolecular, bimolecular, and multimolecular. He started from the observation (accidentally discovered during his stereochemical researches) that dibromosuccinic acid decomposes at 100°C., a process that he classified as a unimolecular (first-order) reaction. As an example of a bimolecular (second-order) reaction he used the saponification of the sodium salt of monochloric acid, which he had studied in 1883 with his pupil L. C. Schwab: CH₂CLCOOH + NaOH → NaCl + CH₂OHCOONa.
Van’t Hoff recognized the positive-salt effect of the sodium chloride and explained deviations in more concentrated solutions as the variations in volume of the molecules. He also determined the order of chemical reaction for many compounds, for example, the first-order decomposition of arsenic hydride. When arsine is heated, one would expect the chemical equation of its decomposition, to indicate a quadrimolecular reaction . But after having determined the velocity of decomposition, van’t Hoff found that the reaction is of the first order. Thus he discovered that the order may differ from the molecularity, that is, the number of molecules shown in the ordinary chemical reaction equation. Moreover, van’t Hoff found that his researches were complicated by activity factors, reaction milieus, and the movements of the molecules.
Van’t Hoff’s experiments on the influence of temperature on reaction velocity culminated in his famous thermodynamic relationship between the absolute temperature T and the velocity constant K:
where A and B are factors dependent on the temperature, and A is now called the activation energy. To make the relation plausible, van’t Hoff adopted the notion (first used by Leopold von Pfaundler) of chemical equilibrium as the result of two opposite reactions; but van’t Hoff was the first to introduce the double-arrow symbol (still universally used) to indicate the dynamic nature of chemical equilibrium.
After investigating the inflammation temperature at which the reaction takes place, van’t Hoff derived the law of mass action on the basis of reaction velocities—the velocities of the forward and reverse reactions being equal at equilibrium. He also established the general equation for the effect of the absolute temperature T on the equilibrium constant K:
in which q is the heat of reaction at constant volume. The derivation of this equation is not given in the Études. In 1886 van’t Hoff showed that the Clausius-Clapeyron equation (in the form given by Horstmann), which related the temperature coefficient of the vapor pressure to the heat of reaction and volume change, can be generalized in terms of the equilibrium constant, as given above. Since K=k₁/k₂, where k₁ and k₂ are the reaction velocities of the forward and reverse directions, so that
From this so-called van’t Hoff isochor it follows that the increase or decrease of the equilibrium constant with the absolute temperature depends upon the sign of the reaction heat q at constant volume. Van’t Hoff applied his relation to both homogeneous and heterogeneous equilibriums, to condensed systems (in which no component has a variable concentration), and to physical equilibriums, that is, changes of state.
Van’t Hoff formulated his principle of mobile equilibrium in the limited sense that at constant volume the equilibrium will tend to shift in such a direction as to oppose the temperature change that is imposed upon the system: “Every equilibrium at constant volume between two systems is displaced by fall of temperature in the direction of that system in the production of which heat is developed.“In 1884 Le Châtelier cast the principle in a general form and extended it to include compensation, by change of volume, for imposed pressure changes. This principle is known as the van’t Hoff–Le Châtelier principle.
In the fifth section of his Études, which dealt with affinity, van’t Hoff defined the work of chemical affinity A as the heat q produced in the transformation, divided by the absolute temperature P of the transition point and multiplied by the difference between p and the given temperature T:
The quantity A is now called the maximum external work of the system. By differentiating the equation in respect to T, we find the Gibbs-Helmholtz relation for the dependence of the absolute temperature T on the electromotive force at a constant volume:
Van’t Hoff also established a simple thermodynamic relationship between the osmotic pressure D of the solution and the vapor pressures of pure water S_e and of the solution S_z : D = 10.5 T log S_e / S_z.
At first the the études received little attention. It was neither a textbook nor a purely scientific treatise; it included many new formulas that were presented and applied without derivation. Although the same subjects were discussed in his Vorlesungen über theoretische und physikalische Chemie, the latter work was better arranged and included the results of subsequent research–and thus became a valuable textbook. The proper derivations of the equations in the études appeared in a number of publications. In “L’équilibre chimique dans les systèmes gazeux, ou dissous à l’état dilué” (1886) van’t Hoff showed from quantitative experiments on osmosis that dilute solutions of cane sugar obey the laws of Boyle, Gay-Lussac, and particularly Avogadro.
In his study of solutions, van’t Hoff also investigated their properties in the presence of semipermeable barriers. He extended the quantitative investigation of the botanist Wilhelm Pfeffer (1877), who had contained solutions of cane sugar, and of other substances, within membranes of hexacyanocopper II ferrate, which he formed in the pores of earthenware pots by soaking them first in a solution of copper sulfate and then of potassium ferrocyanide. Van’t Hoff showed that the osmotic pressure P of a solution inside such a vessel immersed in the pure solvent is in apparently direct proportion to the concentration of the solute and in inverse proportion to the volume V of the solution at a given temperature. At a given concentration, P is proportional to the absolute temperature T. The relation serves the general gas law pV = kT.
Van’t Hoff then applied this law thermodynamically to various solutions. He found that the laws of Gay-Lussac, Boyle, and Avogadro are valid only for ideal solutions, that is, those solutions that are diluted to such an extent that they behave like “ideal“gases and in which both the reciprocal actions of the dissolved molecules and the space occupied by these molecules compared with the volume of the solution itself can be neglected.
To the analogy that exists between gases and solutions vam’t Hoff gave the general expression pV = iRT, in which the coefficient i expresses the ratio of the actual osmotic effect produced by an electrolyte to the effect that would be produced if it behaved like a nonelectrolyte. He also arrived at the important generalization that the osmotic pressure that the dissolved substance would exercise in the gaseous state if it occupied a volume is equal to the volume of the solution. Thus he applied Avogadro’s law to dilute solutions. Van’t Hoff determined that the coefficient i has a value of nearly one for dilute solutions and exactly one for gases. He reached this value by various methods, including the vapor pressure and Raoult’s results on the lowering of the freezing point. For dilute solutions of binary electrolytes, such as sodium chloride and potassium nitrate, he found values ranging from 1.7 to 1.9. Hugo de Vries’s experiments with plant cells and Donders’ and Hartog Jacob Hamburger’s experiments with red blood corpuscles produced isotonic coefficients that agreed with van’t Hoff’s.
Thus van’t Hoff was able to prove that the laws of thermodynamics are valid not only for gases but also for dilute solutions. His pressure law gave general validity to the electrolytic theory of Arrhenius, who recognized in the values of i the magnitude that he had deduced, from experiments on electrical conductance, as the number of ions in which electrolytes are divided in solution. Consequently, van’t Hoff became an adherent of the theory of electrolytic dissociation.
In “Lois de l’équilibre chimique dan’s l’état dilué, gazeux ou dissous” (1886) van’t Hoff showed that for many substances the value of i was one, thus validating the relation pV = RT for osmotic pressure. It then became possible to calculate the osmotic pressure of a dissolved substance from its chemical formula and, conversely, the molecular weight of a substance from the osmotic pressure. In “Conditions électriques de l’équilibre chimique” (1886), van’t Hoff gave a fundamental relation between the chemical equilibrium constant and the electromotive force (the free energy) of a chemical process:
in which K is the chemical equilibrium constant, E is the electromotive force of a reversible galvanic cell, and T is the absolute temperature.
While at Amsterdam, van’t Hoff worked on physicochemical problems with a number of his pupils (Johan Eykman, Pieter Frowein, Arnold Holleman, Cohen, and Willem Jorissen) and with foreign chemists who came to Amsterdam to study under him (Arrhenius and Wilhelm Meyerhoffer). Besides his fundamental contributions to thermodynamics of chemical reactions, van’t Hoff also studied solid solutions and double salts. In an important paper on solid solutions, “Ueber feste Lösungen und Molekulargewichtsbestimmung an festen Körpern“(1890), he determined, with the aid of his laws, the molecular weights of the dissolved substance–a solution of carbon in iron or a solution of hydrogen in palladium.
In Vorlesungen über Bildung und Spaltung von Doppelsalzen (1897) van’t Hoff outlined the theoretical and practical treatment of the formation, separation, and conversion of many double salts, especially the tartrates of sodium, ammonium, and potassium. The book also gave a survey of the work in this field by van’t Hoff and by a number of his pupils in the laboratory at Amsterdam.
At Berlin, van’t Hoff studied the origin of oceanic deposits and the conditions of the formation of oceanic salt deposits, particularly those at Stassfurt, from the point of view of Gibbs’s phase rule. He investigated phase equilibriums that form when various quantities of individual salts from the Stassfurt minerals are placed in water that is evaporated at a constant temperature. He also studied the form, order, and quantities of these equilibriums and the effect on them of time, temperature, and pressure. This important theoretical study was of special benefit to the German potash industry. Van’t Hoff’s method generally consisted in determining the fundamental nonvariant equilibriums (consisting of vapor, solution, and three solid phases) that characterize a four-component system at each particular temperature. In this study he was assisted chiefly by Meyerhoffer. Their results were published in the Sitzungsberichte of the Prussian Academy of Sciences and were summarized in van’t Hoff’s two-volume Zur Bildung der ozeanischen Salzablagerungen.
Chemistry is indebted to van’t Hoff for his fundamental contributions to the unification of chemical kinetics, thermodynamics, and physical measurements. He was instrumental in founding physical chemistry as an independent discipline.