Waage and Guldberg

Guldberg and Waage (1867) clearly stated the Law of Mass Action (sometimes termed the Law of Chemical Equilibrium) in the form The velocity of a chemical reaction is proportional to the product of the active masses of the reacting substances . Active mass was interpreted as concentration and expressed in moles per litre. By applying the law to homogeneous systems, that is to systems in which all the reactants are present in one phase, for example in solution, we can arrive at a mathematical expression for the condition of equilibrium in a reversible reaction. 

We see that in determining the equilibrium the concentrations of the solids do not appear at all. This important result was first stated by Guldberg and Waage in 1867 in the form that the active mass of a solid is constant. It is true only when the solids are of unvarying composition. 

In the experiments reported in Table 9.1, five mixtures with different initial compositions of the three gases were prepared and allowed to reach equilibrium at 1000. I<. The compositions of the equilibrium mixtures and the total pressure P were then determined. At first, there seemed to be no pattern in the data. However, Guldberg and Waage noticed an extraordinary relation the value of the quantity... 

Within experimental error, Guldberg and Waage obtained the same value of K whatever the initial composition of the reaction mixture. This remarkable result shows that K is characteristic of the composition of the reaction mixture at equilibrium at a given temperature. It is known as the equilibrium constant for the reaction. The law of mass action summarizes this result it states that, at equilibrium, the composition of the reaction mixture can be expressed in terms of an equilibrium constant where, for any reaction between gases that can be treated as ideal,... 

It was shown by Guldberg and Waage that when solids are present in a system, their active masses may be taken as constant and included in the equilibrium constant, K. For example, in the reaction ... 

For reversible reactions one normally assumes that the observed rate can be expressed as a difference of two terms, one pertaining to the forward reaction and the other to the reverse reaction. Thermodynamics does not require that the rate expression be restricted to two terms or that one associate individual terms with intrinsic rates for forward and reverse reactions. This section is devoted to a discussion of the limitations that thermodynamics places on reaction rate expressions. The analysis is based on the idea that at equilibrium the net rate of reaction becomes zero, a concept that dates back to the historic studies of Guldberg and Waage (2) on the law of mass action. We will consider only cases where the net rate expression consists of two terms, one for the forward direction and one for the reverse direction. Cases where the net rate expression consists of a summation of several terms are usually viewed as corresponding to reactions with two or more parallel paths linking reactants and products. One may associate a pair of terms with each parallel path and use the technique outlined below to determine the thermodynamic restrictions on the form of the concentration dependence within each pair. This type of analysis is based on the principle of detailed balancing discussed in Section 4.1.5.4. 

Quantitative measurements of simple and enzyme-catalyzed reaction rates were under way by the 1850s. In that year Wilhelmy derived first order equations for acid-catalyzed hydrolysis of sucrose which he could follow by the inversion of rotation of plane polarized light. Berthellot (1862) derived second-order equations for the rates of ester formation and, shortly after, Harcourt observed that rates of reaction doubled for each 10 °C rise in temperature. Guldberg and Waage (1864-67) demonstrated that the equilibrium of the reaction was affected by the concentration ) of the reacting substance(s). By 1877 Arrhenius had derived the definition of the equilbrium constant for a reaction from the rate constants of the forward and backward reactions. Ostwald in 1884 showed that sucrose and ester hydrolyses were affected by H+ concentration (pH). 

Guldberg and Waage law See mass action law. gult berk and vag-3, 16 ) gum accroldes See acaroid resin. gam a kroi dez)... 

In 1862-1863 Berthelot and Pean de Sainte-Jille studied the equilibrium states in etherification reactions. In 1862-1867 Guldberg and Waage, on the basis of Berthelot and Pean de Sainte-Jille s experiments and their own data, suggested a primary formulation of the law of mass action. 

In 1879 Guldberg and Waage substituted the above formulation for the basic law of chemical reactions by its modem version in terms of the concept of mobile equilibrium. For the interaction between the initial substances A, B, C, taken in the stoichiometric ratio of a to to y, i.e. aA + / B + yC, the reaction rate, W, was expressed as... 

It should be noted that in their pioneering work in 1864 Guldberg and Waage used an expression whose form is close to the present-day dynamic formulation (w = kpaq r7) but in the further study "Investigations of chemical affinity (1867) they decided it would be enough to apply the equilibrium formula kpq = k p q. ... 

It was in 1879 that Guldberg and Waage s study with a dynamic formulation of l.m.a. was published. 

We do not completely understand with what this quotation is associated since the new value designated by Van t Hoff as concentration had previously been used by Guldberg and Waage ("amounts of these substances with respect to the same volume ) [17]. It can be repeated once again that the historic-scientific situation as well as the history itself cannot always be reconstructed. 

J. H. van t Hoff s classic text on chemical dynamics has been republished116 and his work on chemical dynamics,117 as well as that of Ostwald118 and Arrhenius,119 has been briefly discussed. There is a comprehensive narrative of the development of chemical kinetics from about the middle of the 19th century, which reconstructs Guldberg and Waage s work on chemical kinetics and compares their efforts to simultaneous work at Oxford by A. G. V. Harcourt (1834-1919) and W. Esson (1839-1916).120... 

P. 0hrstr0m, Guldberg and Waage on the influence of temperature on the rates of chemical reactions , Centaurus, 1985, 28, 277-287. 

Guldberg and Waage (1867) found the effect of reacting substances on a reversible reaction and gave a law known as the law of mass action. According to this law,... 

Looking at chemical kinetics from an historical viewpoint we find that the mass law proposed in 1867 by Guldberg and Waage was the first fundamental contribution to theory. According to this law, now thoroughly established by experiment, the speed of a chemical reaction is proportional to the active masses of the reacting substances, and, as a first approximation, concentrations may be substituted for the active masses. One of the earliest experimental researches in this field was that of Harcourt and Essen in 1880 on the reaction between oxalic acid and potassium permanganate. The several factors involved in this complex reaction were varied, one at a time, and the speed of the reaction was measured experimentally. 

The last equation, one of the most important physicochemical equations, expresses exactly the law of mass action, formulated for the first time by Guldberg and Waage in a less exact form. The equation enables the calculation of the equilibrium composition of a reaction mixture or determination of theoretically possible yields of chemical processes starting from the known value of the equilibrium constant K which can be determined by thermodynamic methods. 

Guldberg and Waage found that the equilibrium concentrations for every reaction system that they studied obeyed this relationship. That is, when the observed equilibrium concentrations are inserted into the equilibrium expression constructed from the law of mass action for a given reaction, the result is a constant (at a given temperature and assuming ideal behavior). Thus the value of the equilibrium constant for a given reaction system can be calculated from the measured concentrations of reactants and products present at equilibrium, a procedure illustrated in Example 6.1. 

The relation so obtained was, essentially, formulated by Guldberg and Waage In the exposition in question, the... 

Theory of esterification. As was mentioned on p. 298, the experiments of Berthelot and Pean de St. Giles led Guldberg and Waage to the discovery of the law of mass action. The recognition of this law is thus connected historically with the investigation of reactions in solutions. Using the experimental data of Berthelot and Pean de St. Giles to test the constancy of the expression... 

Chemical equilibria for many reactions have been studied. In each case it has been found that at equilibrium the concentrations of reactants and products remained constant. As long ago as 1864, Guldberg and Waage were working on equilibrium reactions they claimed that each chemical taking part had an active mass , which was the force that controlled the progress of a reaction. They concluded that the force was proportional to the masses of the chemicals involved. 

This simple equation, which interrelates the mole fractions of the components in the true equilibrium state, is essentially an expression of Guldberg and Waage s law of mass action. The quantity K T,p) is called the equilibrium constant of the reaction considered. 

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