Reaction thermodynamics concentration, dependence

First law of thermodynamics The statement that the change in energy, AE, of a system, is the sum of the heat flow into the system, q, and the work done on the system, w, 214-217,223q First order reaction A reaction whose rate depends upon reactant concentration raised to the first power, 292-295, 316-317q... 

Second law of thermodynamics A basic law of nature, one form of which states that all spontaneous processes occur with an increase in entropy, 457 Second order reaction A reaction whose rate depends on the second power of reactant concentration, 289,317q gas-phase, 300t... 

The simplest case to be analyzed is the process in which the rate of one of the adsorption or desorption steps is so slow that it becomes itself rate determining in overall transformation. The composition of the reaction mixture in the course of the reaction is then not determined by kinetic, but by thermodynamic factors, i.e. by equilibria of the fast steps, surface chemical reactions, and the other adsorption and desorption processes. Concentration dependencies of several types of consecutive and parallel (branched) catalytic reactions 52, 53) were calculated, corresponding to schemes (Ila) and (lib), assuming that they are controlled by the rate of adsorption of either of the reactants A and X, desorption of any of the products B, C, and Y, or by simultaneous desorption of compounds B and C. 

We have noted previously that the forward and reverse rates are equal at equilibrium. It seems, then, that one could use this equality to deduce the form of the rate law for the reverse reactions (by which is meant the concentration dependences), seeing that the form of the equilibrium constant is defined by the condition for thermodynamic equilibrium. By and large, this method works, but it is not rigorously correct, since the coefficients in the equilibrium condition are only relative, whereas those in the rate law are absolute.19 Thus, if we have this net reaction and rate law for the forward direction,... 

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 addition to its constraints on the concentration dependent portions of the rate expression thermodynamics requires that the activation energies of the forward and reverse reactions be related to the enthalpy change accompanying reaction. In generalized logarithmic form equation 5.1.69 can be written as... 

The general features discussed so far can explain the complexity of these reactions alone. However, thermodynamic and kinetic couplings between the redox steps, the complex equilibria of the metal ion and/or the proton transfer reactions of the substrate(s) lead to further complications and composite concentration dependencies of the reaction rate. The speciation in these systems is determined by the absolute concentrations and the concentration ratios of the reactants as well as by the pH which is often controlled separately using appropriately selected buffers. Perhaps, the most intriguing task is to identify the active form of the catalyst which can be a minor, undetectable species. When the protolytic and complex-formation reactions are relatively fast, they can be handled as rapidly established pre-equilibria (thermodynamic coupling), but in any other case kinetic coupling between the redox reactions and other steps needs to be considered in the interpretation of the kinetics and mechanism of the autoxidation process. This may require the use of comprehensive evaluation techniques. 

To be thermodynamically correct, the tendencies for half-reactions to occur depend on the activities of the chemical species involved, not the concentrations. See Chapter 5 (Section 5.2.12) for a brief discussion of activity. 

A representation of all of the elementary reactions that lead to the overall chemical change being investigated. This representation would include a detailed analysis of the kinetics, thermodynamics, stereochemistry, solvent and electrostatic effects, and, when possible, the quantum mechanical considerations of the system under study. Among many items, this representation should be consistent with the reaction rate s dependence on concentration, the overall stoichiometry, the stereochemical course, presence and structure of intermediate, the structure of the transition state, effect of temperature and other variables, etc. See Chemical Kinetics... 

Fluorescence quantum yield and emission maximum determinations as a function of peptide concentration may also permit the detection of peptide self-aggregation at concentrations below 10-4 M, because the peptide fluorophore is likely to be located in a different environment in the peptide aggregate. For example, the concentration-dependent changes in the tryptophan fluorescence emission maximum of mellitin were monitored to determine the equilibrium dissociation constant and thermodynamic parameters of the monomer-tetramer self-association reaction of this peptide. 25 Similarly, measurement of the changes in the tryptophan fluorescence intensity of gramicidin A as a function of its concentration permitted the determination of an average monomer-dimer equilibrium con-stant. 26 ... 

The first steps towards molecular complexity must have been based on spontaneous reactions - reactions that occurred because they were under thermodynamic control. As we have learned in Chapter 1, this does not mean that there is a causal chain of thermodynamic events leading to life, since a given thermodynamic output depends on the initial conditions (as is always the case in thermodynamics) these are often determined by the laws of contingency - the given temperature or pressure or concentration for that particular process. Thermodynamic control means, however, that if the same reaction is repeated under the same initial conditions, the same results are obtained - as exemplified by Miller s reaction in the famous flask under simulated reducing atmospheric conditions. 

According to the second law, the dissipation function must be positive if not zero, which of course is to be expected here, since we are dealing with a spontaneously occurring passive process. The thermodynamic force A/x+, which contains both a concentration-dependent component and an electrical component, is the sole cause of the flow J+. In a system in which more than one process occurs, each process gives rise to a term in the dissipation function consisting of the product of an appropriate force and its conjugate flow. In the case of active transport of the cation, as found, for example, in certain epithelial tissues, the cation flux is coupled to a metabolic reaction. If we represent the flow or velocity of the reaction per unit area of membrane by Jr, the appropriate force driving the reaction is... 

Type IT. When Ed > ER and AG < 0, the reaction should be possible thermodynamically but may not occur because of a high energy of activation AG. The role of photoexcitation in this case is to provide an easier route for the reaction. These are called photocatalyzed reactions. The photoreduction of methylene blue by EDTA or other electron donors like stannous chloride fall in this category. The reaction is pH and concentration dependent and the reductunt is consumed during the reaction. Dyes in the reduced state can act as very powerful reducing agents. 

When Tm is concentration dependent, an additional method" can be used to determine the thermodynamic quantities associated with melting. For example, consider the dissociation of a duplex that is formed from a self-complementary bimolecular process. The reverse reactions to those given in reactions (16.23) or (16.24) are specific examples of such processes. As Table 16.2 shows, the equilibrium constant for such a dissociation process is given by... 

As with enthalpies, AS and AG for reactions do not depend on the reaction pathway taken and so can be estimated from thermodynamic cycles like that of Fig. 1. They depend even more strongly than AH on concentration and pressure. Tabulated standard entropies may be used to estimate changes in a reaction from... 

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