Guldberg-Waage rate expressions

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. 

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... 

Concentration of reactants. In 1864, Cato Guldberg and Peter Waage recognized that at constant temperature the rate of a homogeneous reaction is usually proportional to some power of the concentration of each reactant. The concentration is expressed in moles of... 

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