Irreversible reactions, energy

Let us consider cases 1-3 in Fig. 4.4. In case 1, AG s for formation of the competing transition states A and B from the reactant R are much less than AG s for formation of A and B from A and B, respectively. If the latter two AG s are sufficiently large that the competitively formed products B and A do not return to R, the ratio of the products A and B at the end of the reaction will not depend on their relative stabilities, but only on their relative rates of formation. The formation of A and B is effectively irreversible in these circumstances. The reaction energy plot in case 1 corresponds to this situation and represents a case of kinetic control. The relative amounts of products A and B will depend on the heights of the activation barriers AG and G, not the relative stability of products A and B. 

Strictly speaking, the flow analogy is valid only for consecutive irreversible reactions, and it can be misleading if reverse reactions are significant. Even for irreversible reactions the rds concept has meaning only if one of the reactions is much slower than the others. For reversible reactions the free energy reaction coordinate diagram is a useful aid. In Fig. 5-10, for example, the intermediate 1 is unstable with respect to R and P, and its formation (the kf step) is the rds of the overall reaction. 

Rates observed at different temperatures but at the same initial and current compositions can also be used for evaluation of the activation energy. For a single irreversible reaction... 

Energy release and energy loss curves for an irreversible reaction in a flow reactor. 

Our knowledge of enzymes also tells us that under usual physiological conditions (i.e. at typical cellular concentrations of substrate) most metabolic reactions are reversible. Energetically irreversible reactions, i.e. those with a large positive free energy change, effectively act as one-way valves allowing substrate flow in the forward direction only. 

Remark 4- Eq.(13) is valid only for a first order irreversible reaction A B. So, it is the easiest form to writing the energy balance in the reactor. 

When one or more molecular entity(ies) participates in two or more parallel and irreversible reactions in which different products are formed, the faster-forming product will accumulate by the reaction having the lowest activation energy. Thus, kinetically controlled processes are those whose proportion of products is governed by the relative rates of the competing reactions. If the reac-... 

Tremaine, P.R. and Goldman, S., "Calculations of Gibbs Free Energies of Aqueous Electrolytes to 350°C from an Electrostatic Model for Ion Hydration", Jr. Phys. Chem., in press. Helgeson, H.C., "Evaluation of Irreversible Reactions in Geochemical Processes Involving Minerals and Aqueous Solutions - I Thermodynamic Relations", Geochimica et Cosmochimica Acta, (1968), 3, 853. 

Now, for a given feed temperature the intersection of the energy balance line with the S-shaped material balance line for the operating r gives the conditions within the reactor. Here three cases may be distinguished. These are shown in Fig. 9.14 for irreversible reactions. 

Figure 9.14 Three types of solutions to the energy and material balances for exothermic irreversible reactions.

The simplest sets of reactions involve series or parallel first-order irreversible reactions. We will first consider these cases because they have simple analytical solutions and are useful prototypes of more complicated reaction sets. These can be considered in the energy diagrams similar to those we discussed in the previous chapter for single reactions. 

In this chapter and in Chapter 6 we will usually solve these equations assuming a single first-order irreversible reaction, r = k T)C/. Other orders and multiple reactions could of course be considered, but the equations are much more difficult to solve mathematically, and the solutions are qualitatively the same. We will see that the solutions with these simple kinetics are sufficiently complicated that we do not want to consider more complicated kinetics and energy balances at the same time. 

Now we substitute this expression for X(T) into the energy-balance equation to yield a combined energy- and mass-balance equation for a first-order irreversible reaction in a CSTR,... 

On the other hand, the favored formation (and the yields) of N-acetylglucofuranosylamines were explained on the basis of steric considerations.24,26 The formation of N-acylglycosylamines is a kinetically controlled, irreversible reaction, and the prevalence of the furanose over the pyranose structure has been shown in many irreversible, cyclization reactions of carbohydrates.73 This preponderance, as well as the favoring of a determined anomeric configuration, would be the result of a balance of relative ffee-energies of the transition states in the cyclization step, which would have virtually the same geometry as the final, cyclic structure.74 The five-membered... 

There will be some parameters in the reaction rate expression, such as the order of an irreversible reaction or an activation energy EIRTf. The full process of getting the simplest set of equations for a set of independent reactions is covered in great detail in Chapter 2 of [I, Vol. 1]. 

This shows that for an irreversible process, the peak potential is shifted towards more negative (reduction reaction) or more positive (oxidation reaction) potentials by about 0.03 V per decade of increase in the scan rate. For a totally irreversible reaction, no return peak is observed due to the fact that the kinetics are so slow that the opposite reaction cannot occur. The activation energy, overcome by application of a potential, is so high that it is not possible to apply such a potential under experimental conditions. However, the absence of a return peak does not necessarily imply slow electron transfer, but can also be due to a fast following chemical reaction. 

In the case of an irreversible reaction, the rate constant (k) is determined by the difference in free energy (AF ) between the reactants and the transition state ... 

For a first order irreversible reaction, the energy balance is expressed in terms of the fractional conversion XA, where... 

Consider an exothermic irreversible reaction with first order kinetics in an adiabatic continuous flow stirred tank reactor. It is possible to determine the stable operating temperatures and conversions by combining both the mass and energy balance equations. For the mass balance equation at constant density and steady state condition,... 

By contrast, an irreversible reaction is one where the electrode reaction cannot be reversed. A high kinetic barrier has to be overcome, which is achieved by application of an extra potential (extra energy) called the overpotential, q, and in this case... 

However, when the view is restricted to simple, irreversible reactions obeying an nth order power rate law and, if additionally, isothermal conditions arc supposed, then—together with the results of Section 6.2.3—it can be easily understood how the effective activation energy and the effective reaction order will change during the transition from the kinetic regime to the diffusion controlled regime of the reaction. 

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