Rate constants, adsorption process

By analyzing the variation of peak position as a function of a scan rate, it is possible to gain an estimate for the electron transfer rate constants. Adsorption processes on electrode surface can be distinguished from charge transfer processes, as in former case cyclic voltammogram is symmetrical around potential axes. 

Basically, the effect of composition of the reaction mixture on the hydrogenation process may be characterized by the reaction rates, rate constants, adsorption coefficients, or selectivities of competitive reactions. All these characteristics have been used in various studies. 

Derive Eq. XI-IS, assuming a Langmuir adsorption process described in Eq. XI-2, where ka and kd are the adsorption and desorption rate constants. Treat the solution... 

The quantitative solution of the problem, i.e. simultaneous determination of both the sequence of surface chemical steps and the ratios of the rate constants of adsorption-desorption processes to the rate constants of surface reactions from experimental kinetic data, is extraordinarily difficult. The attempt made by Smith and Prater 82) in a study of cyclohexane-cyclohexene-benzene interconversion, using elegant mathematic procedures based on the previous theoretical treatment 28), has met with only partial success. Nevertheless, their work is an example of how a sophisticated approach to the quantitative solution of a coupled heterogeneous catalytic system should be employed if the system is studied as a whole. 

As in a monolayer adsorption process, we consider that the rate of filling of sites by TCP molecules follows first-order kinetics. If No represents the total number of free sites per unit area at time t = 0, and N(t) is the number of sites available at time t, then dN(t)ldt = -kN(t), where k is the rate constant of the adsorption process. Therefore, N(t) decreases as No exp(-kt), and the number of sites occupied by TCP molecules at t becomes [No -N(t)], a quantity that determines directly the parameter (t) in Eq. (25). So Wo(t) can be written as... 

There are three approaches that may be used in deriving mathematical expressions for an adsorption isotherm. The first utilizes kinetic expressions for the rates of adsorption and desorption. At equilibrium these two rates must be equal. A second approach involves the use of statistical thermodynamics to obtain a pseudo equilibrium constant for the process in terms of the partition functions of vacant sites, adsorbed molecules, and gas phase molecules. A third approach using classical thermodynamics is also possible. Because it provides a useful physical picture of the molecular processes involved, we will adopt the kinetic approach in our derivations. 

It is interesting to note that, although the intrinsic rate of desorption is slower than that of adsorption, both rates were found to be sufficiently fast under our experimental conditions so that the adsorption-desorption process on the Pt surface can be assumed to rapidly equilibrate at all times that is, even a ten-fold increase in both the adsorption and desorption rate constants (while keeping their ratio constant) did not significantly change the predicted step responses. With the assumption of chemisorption equilibrium, Equations (1) and (4) can be combined into the form (35)... 

The rate constant of adsorption is and the rate constant characterizing the way sites lose adsorbate is kd. From simple kinetics (see Chapter 8), the rate of adsorption depends on the number of sites available N(l - 0), the rate constant of the process fca, and the amount of adsorbate wanting to adsorb, which is proportional to pressure p. Overall, the rate of adsorption is N x (1 — 9) x ka x p. 

Once adsorbed, we assume that M is internalised following a first-order kinetic process in each of the sites, with internalisation rate constants k and k2 respectively [9,16-18], For each kind of adsorption site, we have an uptake flux given by ... 

As seen above (equation (5)), the basis of the simple bioaccumulation models is that the metal forms a complex with a carrier or channel protein at the surface of the biological membrane prior to internalisation. In the case of trace metals, it is extremely difficult to determine thermodynamic stability or kinetic rate constants for the adsorption, since for living cells it is nearly impossible to experimentally isolate adsorption to the membrane internalisation sites (equation (3)) from the other processes occurring simultaneously (e.g. mass transport complexation adsorption to other nonspecific sites, Seen, (equation (31)) internalisation). 

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). 

The extent to which ions, etc. adsorb or experience an electrostatic ( coulombic ) attraction with the surface of an electrode is determined by the material from which the electrode is made (the substrate), the chemical nature of the materials adsorbed (the adsorbate) and the potential of the electrode to which they adhere. Adsorption is not a static process, but is dynamic, and so ions etc. stick to the electrode (adsorb) and leave its surface (desorb) all the time. At equilibrium, the rate of adsorption is the same as the rate of desorption, thus ensuring that the fraction of the electrode surface covered with adsorbed material is constant. The double-layer is important because faradaic charge - the useful component of the overall charge - represents the passage of electrons through the double-layer to effect redox changes to the material in solution. 

The decomposition behavior of formic acid on the close-packed Ru(lOTO) surface parallels the reaction on nickel, except that the autocatalytic process was not observed (lOJ). Water was desorbed at 183 K by apparent second-order kinetics following adsorption of HCOOH at 100 K. Subsequent desorption of Hj, COj, and CO suggested the formation of the surface anhydride. The rate constant for decomposition was 2.6 x 10 sec exp —26.9 kcal/mol// r. ... 

The homogeneity of the surface should be such that the free-energy changes and the adsorption-desorption rate constants associated with the chromatographic process on the molecular level fall within a narrow range. 

The cadmium electrodeposition on the solid cadmium electrode from the sulfate medium was investigated [217]. The following kinetic parameters were obtained cathodic transfer coefficient a = 0.65, exchange current density Iq = 3.41 mA cm , and standard rate constant kg = 8.98 X 10 cm s . The electrochemical deposition of cadmium is a complex process due to the coexistence of the adsorption and nucleation process involving Cd(II) species in the adsorbed state. 

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