The principle of microscopic reversibility or detailed balance

It might be thought that since chemisorption equilibrium was discussed in Section XVIII-3 and chemisorption rates in Section XVIII-4B, the matter of desorption rates is determined by the principle of microscopic reversibility (or, detailed balancing) and, indeed, this principle is used (see Ref. 127 for... 

The principle of microscopic reversibility or detailed balance is used in thermodynamics to place limitations on the nature of transitions between different quantum or other states. It applies also to chemical and enzymatic reactions each chemical intermediate or conformation is considered as a state. The principle requires that the transitions between any two states take place with equal frequency in either direction at equilibrium.52 That is, the process A — B is exactly balanced by B — A, so equilibrium cannot be maintained by a cyclic process, with the reaction being A — B in one direction and B — > C — A in the opposite. A useful way of restating the principle for reaction kinetics is that the reaction pathway for the reverse of a reaction at equilibrium is the exact opposite of the pathway for the forward direction. In other words, the transition states for the forward and reverse reactions are identical. This also holds for (nonchain) reactions in the steady state, under a given set of reaction conditions.53... 

There is a useful application of the Principle of Microscopic Reversibility (or Detailed Balancing) in the study of surface processes. This is a principle that requires that, when carried out under identical conditions, the reverse of any process should proceed by exactly the same route as the forward process thus whatever energy input is needed for the chemisorption of a hydrogen molecule will be recovered and released when the two atoms recombine and desorb. Measurement of the relaxation of the vibrational and translational energy of the desorbing molecule therefore provides information on the needs in dissociation, and values of S can also be derived. ... 

S is symmetric. This basic property leads to the quantum mechanical principle of microscopic reversibility or detailed balancing. 

In a system of connected reversible reactions at equilibrium, each reversible reaction is individually at equilibrium. This is the principle of microscopic reversibility or its corollary, the principle of detailed balance. 

The principle that at equilibrium each elementary process is exactly balanced by its reverse reaction is known as the principle of microscopic reversibility or the principle of detailed balancing. "... 

Both Newton s equation of motion for a classical system and Schrodinger s equation for a quantum system are unchanged by time reversal, i.e., when the sign of the time is changed. Due to this symmetry under time reversal, the transition probability for a forward and the reverse reaction is the same, and consequently a definite relationship exists between the cross-sections for forward and reverse reactions. This relationship, based on the reversibility of the equations of motion, is known as the principle of microscopic reversibility, sometimes also referred to as the reciprocity theorem. The statistical relationship between rate constants for forward and reverse reactions at equilibrium is known as the principle of detailed balance, and we will show that this principle is a consequence of microscopic reversibility. These relations are very useful for obtaining information about reverse reactions once the forward rate constants or cross-sections are known. Let us begin with a discussion of microscopic reversibility. 

The principle of microscopic reversibility can be used to check a set of postulated rate coefficients for self-consistency or to calculate the still unknown value of one rate coefficient from those of all others. To this end, most texts on kinetics prescribe a procedure called detailed balancing. However, a much simpler rule will do ... 

Setting the rate of formation of the outer-sphere complex equal to its rate of conversion is known as the steady-state approximation and the outer-sphere complex is a reactive intermediate under such conditions. A steady state occurs when only a single or some of the elementary reactions in a mechanism arc at equilibrium. Complete equilibrium requires that the rates of forward and reverse reactions must be equal for all the elementary reactions and that all species must be at steady state. This is the principle of detailed balancing and is a consequence of the theory of microscopic reversibility that requires that forward and reverse reactions in an elementary process follow the same path. 

The principle we have applied here is called microscopic reversibility or principle of detailed balancing. It shows that there is a link between kinetic rate constants and thermodynamic equilibrium constants. Obviously, equilibrium is not characterized by the cessation of processes at equilibrium the rates of forward and reverse microscopic processes are equal for every elementary reaction step. The microscopic reversibility (which is routinely used in homogeneous solution kinetics) applies also to heterogeneous reactions (adsorption, desorption dissolution, precipitation). 

This equation shows that the phenomenological coefficients are related to the reaction rates at equilibrium. The principle of detailed balance or microscopic reversibility is incorporated into Jr3f =. /r3b = Jr3f and hence the... 

The principle of detailed balance or microscopic reversibility is now invoked. It states that at equilibrium each elementary process proceeds as readily in one direction as in the other. According to this principle, one must demand that x - tojj - a>in - 0 note that this enlarges on requirement... 

The principle of detailed balance is a consequence of microscopic reversibility—the fact that the fundamental equations governing molecular motion (i.e., Newton s laws or the Schrodinger equation) have the same form when time t is replaced with t and the sign of all velocities (or momenta) are also reversed. 

William Thomson and others regarded the reciprocal relations only as conjectures. A well-founded theoretical explanation for these relations was developed by Lars Onsager (1903-1976) in 1931 [3]. Onsager s theory is based on the principle of detailed balance or microscopic reversibility that is valid for systems at equilibrium. 

The principle of detailed balance or microscopic reversibility is formulated using the general thermodynamic theory of equilibrium fluctuations that we discussed in section 14.2. A summary of the main results of this section is as follows. 

In this section we shall look at the meaning of linear phenomenological laws in the context of chemical reactions. In a formalism in which the principle of detailed balance or microscopic reversibility is incorporated through the condition that forward rates of every elementary step balance the corresponding reverse rate, the Onsager reciprocity is implicit. No additional relations can be derived for the reaction rates if it is assumed that at equilibrium each elementary step is balanced by its reverse. Therefore, the main task in this section will be to relate the Onsager coefficients Ly and the experimentally measured reaction rates. In our formalism the Onsager reciprocal relations will be automatically valid. 

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