Law of Microscopic Reversibility

The subsequent chain mechanism proposed by Rosenkrans violated the law of microscopic reversibility. 

Can you see the answer now at a glance Is there a second way to get the same result Does it make sense Use the law of microscopic reversibility to check alternatives on reversible steps. Is the assumed causality correct ... 

The probability of stimulated emission by an excited molecule, Bpv, is the same as that of the reverse process, absorption by the ground-state molecule. This is a consequence of the law of microscopic reversibility if the number of excited molecules Nm is equal to the number of ground-state molecules N , then the rates of stimulated absorption and emission must be equal. If by some means a population inversion can be produced, Nm > Nn, the net effect of interaction with electromagnetic radiation of frequency v will be stimulated emission (Figure 2.4). This is the operating principle of the loser. LASER is an acronym for light amplification by stimulated emission of radiation (Section 3.1). 

The law of microscopic reversibility tells us that all chemical reactions must be reversible. A basic requirement that must be satisfied if a reaction is to be of practical value is that it should be faster than the corresponding reverse reaction, because otherwise the products will be converted back into the reactants faster than they are formed. It is also necessary that the rate of the forward reaction should be reasonable. For the moment, we will be concerned only with the effect of reversibility. The rates of reactions will be considered in the next chapter. 

The law of microscopic reversibility is a consequence of the special theory of relativity which states that the equations of motion of a mechanical system must be invariant for a change in the sign of the time variable. This means that the mechanisms of the forward and reverse reactions in a closed chemical system must be identical. 

The simple use of a chemically irreversible chemical reaction step representing a chemical process is physically unrealistic, because the law of microscopic reversibility or detailed balance [94] is violated. More realistic is the use of an reaction scheme (Eq. 11.1.22, Fig. 11.1.21b). Even for the relatively simple reaction scheme, interesting additional consequences arise when the possibility of reversibility of the chemical step is considered. In Fig. II. 1.2lb, cyclic voltammograms for the case of a reversible electron transfer process coupled to a chemical process with kf = 10 s and fcb = 10 s" are shown. At a scan rate of 10 mV s a well-defined electrochemically and chemically reversible voltammetric wave is found with a shift in the reversible half-wave potential E1/2 from Ef being evident due to the presence of the fast equilibrium step. The shift is AEi/2 = RT/F ln(X) = -177 mV at 298 K in the example considered. At faster scan rates the voltammetric response departs from chemical reversibility since equilibrium can no longer be maintained. The reason for this is associated with the back reaction rate of ky, = 10 s or, correspondingly, the reaction layer, Reaction = = 32 pm. At Sufficiently fast scan rates, the product B is irre-... 

The law of microscopic reversibility stipulates that reactions taking place in the forward and backward direction must follow the same path or, more precisely, must cross the same Gibbs energy of activation barrier. Admittedly, this is not a universal law, and there can be situations under which it does not apply, but such situations are rare, so that it can be assumed to apply, unless proven otherwise. We shall not go into the fine details of this law, except to note that it is implicitly assumed to apply whenever one writes the common relationship. 

Thus, the standard Gibbs energy of a reaction is equal to the difference between the standard Gibbs energies of activation of the forward and backward reactions, which only applies when the reaction crosses the same energy barrier in both directions, namely, when the law of microscopic reversibility applies. 

Here is where the law of microscopic reversibility comes in. If we accept that in metal dissolution the charge must be carried across the interface by the metal cations, this law immediately forces us to accept that the same applies to metal deposition ... 

Since most natural waters are near saturation this reversal of the rate law would appear to be in line with the concept of microscopic reversibility of the forward and backward reaction steps. Some data are given in Fig. 8.3. 

The principle of microscopic reversibility, required by the laws of thermodynamics, specifies that there must be a reverse for every microscopic process. It is therefore strictly speaking incorrect to omit reverse steps, and doing so is justified only when the omitted reverse step is occurring so slowly as to have no observable effect on the reaction during the time it will be under observation. 

The power-law formalism was used by Savageau [27] to examine the implications of fractal kinetics in a simple pathway of reversible reactions. Starting with elementary chemical kinetics, that author proceeded to characterize the equilibrium behavior of a simple bimolecular reaction, then derived a generalized set of conditions for microscopic reversibility, and finally developed the fractal kinetic rate law for a reversible Michaelis-Menten mechanism. By means of this fractal kinetic framework, the results showed that the equilibrium ratio is a function of the amount of material in a closed system, and that the principle of microscopic reversibility has a more general manifestation that imposes new constraints on the set of fractal kinetic orders. So, Savageau concluded that fractal kinetics provide a novel means to achieve important features of pathway design. 

A local thermodynamic state is determined as elementary volumes at individual points for a nonequilibrium system. These volumes are small such that the substance in them can be treated as homogeneous and contain a sufficient number of molecules for the phenomenological laws to be apphcable. This local state shows microscopic reversibility that is the symmetry of all mechanical equations of motion of individual particles with respect to time. In the case of microscopic reversibility for a chemical system, when there are two alternative paths for a simple reversible reaction, and one of these paths is preferred for the backward reaction, the same path must also be preferred for the forward reaction. Onsager s derivation of the reciprocal rules is based on the assumption of microscopic reversibility. 

At equilibrium, the affinities vanish (A] = 0,A2 = 0). Therefore, Jrl - Jt3 = 0 and. /r2. Jr3 0 and the thermodynamic equilibrium does not require that all the reaction velocities vanish they all become equal. Under equilibrium conditions, then, the reaction system may circulate indefinitely without producing entropy and without violating any of the thermodynamic laws. However, according to the principle of detailed balance, the individual reaction velocities for every reaction should also vanish, as well as the independent flows (velocities). This concept is closely related to the principle of microscopic reversibility, which states that under equilibrium, any molecular process and the reverse of that process take place, on average, at the same rate. 

This shows that Ln = L2. This simple analysis suggests that a matrix obeying the general law of symmetric crosscoefficients could be derived from the principle of microscopic reversibility by applying the methods of statistical mechanics. 

The slow oxidation by CI2 has been described by Mazumdar and Pisharody (45, 46). Unfortunately, neither the presentation of the data nor its interpretation is clear. The rate law is incorrectly derived from the proposed mechanism, which in turn violates the principle of microscopic reversibility. 

Onsager assumed that the variables and the rate laws were the same on the macroscopic and the microscopic level this is the so-called regression hypothesis. Also using the assumption of microscopic reversibility, he proved the reciprocal relations ... 

Mkrosoopic Reversibility and Detailed- Babmoe. —The prindpie of microscopic reversibility arises from the invariance of the laws of motion - quantal as well as dassical - under time revosal. Because of this the probability of a transition between fully specified states pa unit time is independoit of the direction in vriiidi time is chosen to move, i.e. 

Onsager reciprocity relation is based on (i) principle of microscopic reversibility, (ii) fluctuation theory and (iii) the assumption that decay of fluctuations follows ordinary macroscopic laws. We give below a brief account of its derivation. 

Equation (2.22) involves the concept of microscopic reversibility. If we assume that decay of fluctuations follows ordinary macroscopic laws, we can write Eq. (2.18) in a form where Jf = 8a /8r and is the force. Substituting Eq. (2.18) into Eq. (2.22) we obtain... 

In principle, the results based on fluctuation theory and principle of microscopic reversibility would only be true for systems close to equilibrium. This will also be true for the assumption of linear relation between fluxes and forces. One has to understand also the serious limitation of phenomenological linear laws. The condition is that the magnitude of t should satisfy the inequality,... 

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. 

In conclusion to this introduction it may be remarked that a new branch of thermodynamics has developed during the past few decades which is not limited in its applications to systems at equilibrium. This is based on the use of the principle of microscopic reversibility as an auxiliary to the information contained in the laws of classical thermodynamics. It gives useful and interesting results when applied to non-equilibrium systems in which there are coupled transport processes, as in the thermo-electric effect and in thermal diffusion. It does not have significant applications in the study of chemical reaction or phase change and for this reason is not included in the present volume.f... 

The principle of detailed balancing can be derived from the principle of microscopic reversibility (see Chapter 18), which says that Newton s laws of motion for the collisions between atoms and molecules arc symmetrical in time— they would look the same if time ran backward. The proof of detailed balance from microscopic reversibility is given in [3]. Detailed balance is helpful in understanding the mechanisms of chemical reactions, the molecular steps from reactants to products. 

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