Quasi-equilibrium hypothesis

If reaction 2 is rate limiting, then from the quasi-equilibrium hypothesis... 

In the derivation of the rate equation, it is assumed that the surface reaction is irreversible and rate determining, whereas the adsorption steps of hydrogen and aldol are rapid enough for the quasi-equilibrium hypothesis to be applied. The desorption step of triol is assumed to be irreversible and very rapid (cr —>0). 

The use of the quasi-equilibrium hypothesis for the adsorption steps 1-1V implies that the concentrations of Aim, A2n, Mp and Mq are expressed by... 

The quasi-equilibrium hypothesis is applied on the adsorption steps. The surface coverage of hydrogen, formaldehyde and the aldol from the adsorption quasi-equilibria are inserted into the rate equations (10.108), after which the following expressions are obtained for the hydrogenation rates rf. 

The concentration of the intermediate A is obtained after applying the quasi-equilibrium hypothesis on the rapid step(6) ... 

For rapidly reacting intermediates, the quasi-steady-state hypothesis can be applied to eliminate the concentrations of the intermediates from the rate equations. For rapid reaction steps, the quasi-equilibrium hypothesis is used to eliminate the concentrations of the intermediates. 

Ri R2, the rates can be denoted by the vectors shown in Figure 2.2. The difference R+i — R-i = R+2 — R-2> where the indices -I- and — refer to the forward and backward rates of the elementary steps, respectively. However, since R+i and R i are large, their ratio approaches one, R+i/R-i 1, which implies that the quasi-equilibrium hypothesis can be applied R+i/R i = fc+iCA/fc-iCR = KiCa/cr = l,thatis,iTi = cr/ca, which is the well-known equilibrium expression for an elementary step. 

From the general solution obtained with the quasi-steady-state hypothesis, the solutions corresponding to the quasi-equilibrium hypothesis can be obtained as special cases. If step I is much more rapid than step II, fc i fc+2CB in Equation 2.27, the reaction rate becomes... 

Equations 2.50 and 2.51 could, of course, have been obtained directly by applying the quasi-equilibrium hypothesis in reaction steps 1 and 11, respectively. 

The quasi-equilibrium assumption is frequently used in the heterogeneous catalysis, since the surface reaction steps are often rate-Hmiting, while the adsorption steps are rapid. This is not necessarily true for large molecules. Here we consider the application of the quasi-equilibrium hypothesis on two kinds of reaction mechanisms, an Eley-Rideal mechanism and a Langmuir-Hinshelwood mechanism. The rate expressions obtained with this approach are referred to as Langmuir-Hinshelwood-Hougen-Watson (LHHW) equations in the literature, in honor of the pioneering researchers. 

The TST rate equation can be derived in various ways, and one of the most straightforward approaches which utilizes the quasi-equilibrium hypothesis will be chosen here. As an example, consider the plot of potential energy vs. the minimum-energy path representing the reaction coordinate for an exothermic gas-phase reaction, A + B C, as shown in Figure 6.1. 

Mass spectrometry measures the mass of fragment ions formed in a unimolecular dissociation of an energy-rich parent ion. To apply a transition state theory approach to the determination of flie branching into different products requires the assumption that after ionization there is a sufficient delay for the ion to distribute the excess energy over all the available modes. Mass spectrometrists refer to this assumption as the quasi-equilibrium hypothesis, and they are actively concerned about its validity. See Lifshitz (1989), Lorquet (1994, 2000). 

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