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In chemistry, J. H. van't Hoff (1884) [4] came up with the idea that equilibrium has dynamical nature and is a result of the balance between the forward and backward reaction rates. He did not study reaction mechanisms with many elementary reactions and could not formulate the principle of detailed balance for complex reactions.
Equality of forward and backward reaction rates, however, is a necessary condition for chemical equilibrium, though it is not sufficient to explain why equilibrium occurs. Despite the limitations of this derivation, the equilibrium constant for a reaction is indeed a constant, independent of the activities of the various species involved ...
If both reactions are elementary reactions, then the rate of reaction is given by [3] [] = [] + [] where k f is the rate constant for the forward reaction and k b is the rate constant for the backward reaction and the square brackets, […], denote concentration.
Guldberg and Waage also recognized that chemical equilibrium is a dynamic process in which rates of reaction for the forward and backward reactions must be equal at chemical equilibrium. In order to derive the expression of the equilibrium constant appealing to kinetics, the expression of the rate equation must be used.
A reversible reaction is a reaction in which the conversion of reactants to products and the conversion of products to reactants occur simultaneously. [1]+ + A and B can react to form C and D or, in the reverse reaction, C and D can react to form A and B.
Informally, the Kolmogorov forward equation addresses the following problem. We have information about the state x of the system at time t (namely a probability distribution p t ( x ) {\displaystyle p_{t}(x)} ); we want to know the probability distribution of the state at a later time s > t {\displaystyle s>t} .
Chemical equilibrium is a dynamic state in which forward and backward reactions proceed at such rates that the macroscopic composition of the mixture is constant. Thus, equilibrium sign ⇌ symbolizes the fact that reactions occur in both forward ⇀ {\displaystyle \rightharpoonup } and backward ↽ {\displaystyle \leftharpoondown } directions.
Under kinetic reaction control, one or both forward reactions leading to the possible products is significantly faster than the equilibration between the products. After reaction time t, the product ratio is the ratio of rate constants k and thus a function of the difference in activation energies E a or ΔG ‡: