True heat of activation

In whichever of these ways the chemical transformation comes about, all the information about the nature of chemical change which has been derived from the study of reactions in the gaseous phase justifies the conclusion that the molecules must be activated by the acquisition of thermal energy considerably above the mean. This energy we may call the true heat of activation. 

We are now in a position to see the difference between the true and apparent heats of activation. The true heat of activation, Q, is given by... 

The quantitative results must be regarded as of an approximate character only, since it is far from certain that the true heat of activation is ever accurately extricable but in a general way it seems clear that the main argument is supported by experiment. 

In order to estimate the true heat of activation, AH° for reaction (2) has to be evaluated by non-thermodynamic calculations [5]. Since AH cannot be directly evaluated, the true pre-exponential factors, and hence true entropies of activation, from eqn. (101) cannot be measured. Weaver... 

When a or is a function of temperature, or b is given by Eq. (17), the simple additive relation between A and AH given in Eq. (53) does not arise. The case where a is linear in 7, namely a(T) = yT, as found for a number of processes experimentally, is of special interest with regard to evaluation of the true heat of activation, AW°. ... 

By applying this approach to rates measured at a series of overpotentials, the potential dependence of what we have referred to above as the true heat of activation and the entropy of activation, A5 at constant potential, , was evaluated for proton discharge from the above two media. The important conclusion that was reached from the results is that A5 (or equivalently A5 (since these A5 functions differ only by a constant quantity) is dependent on potential for the h.e.r. at Hg, as shown in Fig. 23. 

This conclusion was based only upon a supposed increase in the heat of activation with temperature, which was interpreted as proof that the wall reaction which predominates at lower temperatures is superseded by a true gas reaction. Hinshelwood and Topley f found, by varying the ratio surface/ volume, that the reaction taking place in a silica vessel was predominantly heterogeneous up to 1,044° abs. at least. Since the total velocity as measured in these experiments was actually rather less than that in the experiments of Trautz and Bhandarkar, it seems clear that the reaction measured by the latter observers must have been heterogeneous also. Re-examination of their experimental data, moreover, fails to substantiate the conclusion that there is any real increase in the heat of activation with temperature. 

Thus the only correlation which may reasonably be sought is one between the heat of activation and the velocity constant expressed, not as a fraction of the total number of molecules, but as a fraction of the number actually adsorbed at any moment. If k0bs. is the observed velocity constant, calculated in terms of the total gas, and a is the fraction of the total gas which is actually adsorbed, then the true velocity constant would be 0bs. divided by a. This we may represent by the letter x ... 

Relation between the true and apparent heats of activation. 

When the products of reaction exert no retarding influence, the apparent heat of activation is less than the true value by an amount A, which determines the variation with temperature of the adsorption. 

There is one important special case in which the apparent heat of activation becomes equal to the true value. This is when the surface is completely covered with the reactant over the whole range of temperature, and there is no retardation due to the presence of the products of reaction, cr has the constant value unity, and the variation of the observed reaction velocity is due entirely to the changing rate of the actual chemical transformation. 

The natural line of inquiry is to study the progress of a given reaction on various catalytic surfaces, to determine the relative numbers of molecules adsorbed on each surface, and to seek a correlation between the heat of activation, using provisionally the apparent value as a sufficiently good approximation to the true value, and the velocity of change referred to equal numbers of adsorbed molecules. Unfortunately, no example has hitherto been found suitable for experimental investigation, in which both the adsorptions and the reaction velocities can be measured. Thus no really valid test can be made. The existence of centres of varying activity would still further complicate the interpretation even of direct measurements of adsorption. 

The relation between the true and apparent heats of activation is given by the equation... 

The decomposition of ammonia on the surface of platinum takes place at a speed which is inversely proportional to the pressure of the hydrogen present. The combined influence of the two terms E and A produces an apparent heat of activation of more than 100,000 calories. This is in striking contrast with the value of E true, 39,000 calories for the unretarded reaction on the surface of tungsten. The decomposition of ammonia on molybdenum is of zero order, but retarded by nitrogen the value of E according to Burk is 53,200 calories. Kunsman finds 32,000 calories Trans. Faraday Soc., 1922, 17, 621. 

Adkins and Nissen appear to think that because the heat of activation is dependent upon the method of preparation of the catalyst it can have no connexion with the stability of the molecule (this is quite apart from any distinction between true and apparent heat of activation). This is of course a complete misunderstanding, for the stability of the molecule is also a function of the nature of the surface upon which it is adsorbed. Otherwise catalysis would not exist. 

In any practical electrochemical experiment the absolute, but unknown, metal/solution p.d. at the reference electrode must normally vary with temperature on account of the single interface reaction entropy change. This leads to the now well-known situation that measurements of or io as a function of temperature can never give the true or real heat of activation for the electrode process. This was first pointed out by Temkin who showed that... 

The application of the theory of absolute reaction rates (36) to catalysis turns out to be closest to the multiplet theory. The former was applied for the first time by Temkin (58) with a simplifying assumption that the sum of the partition functions of the particles on the surface equals unity. Let us note the results (36) that are near to the multiplet theory. The theory of absolute reaction rates, based on quantum mechanics and statistics, proved that in the case of adsorption, the attraction of the two-atom molecules (of hydrogen) to two atoms of the catalyst (carbon or nickel) is energetically more favorable than to one atom. It demonstrates that on solid surfaces the true energy of activation must be small and that for the endothermic process it must be nearly equal to the heat of the latter. As in the multiplet theory, the theory considers the new bonds as beginning to be formed before the old ones are broken. The theory deals with the real arrangement of atoms and with the mutual energy of their valence electrons. 

We can easily verify the validity of this statement if we compare (1.45) with (1.23) and (1.24) and take into account the fact that AH = TAS° = -q for a zero potential drop, and that the term corresponds to a transition from the true (at a constant a g ) to the apparent (a B " const) activation energy. Note that tne alue of Wq depends on the true heat of an elementary act and hence on the heat of adsorption of the initial reagents and products (AH g,... 

Just as the surface and apparent kinetics are related through the adsorption isotherm, the surface or true activation energy and the apparent activation energy are related through the heat of adsorption. The apparent rate constant k in these equations contains two temperature-dependent quantities, the true rate constant k and the parameter b. Thus... 

Although it is not universally true that the activation energies of reactions parallel their heats of reaction, this is approximately true for the kind of addition reaction we are discussing. Accordingly, we can estimate E = k AH, with k an appropriate proportionality constant. If we consider the difference between two activation energies by combining this idea with Eq. (7.21), the contribution of the nonstabilized reference reaction drops out of Eq. (7.21) and we obtain... 

Based on the experimental data kinetic parameters (reaction orders, activation energies, and preexponential factors) as well as heats of reaction can be estimated. As the kinetic models might not be strictly related to the true reaction mechanism, an optimum found will probably not be the same as the real optimum. Therefore, an iterative procedure, i.e. optimization-model updating-optimization, is used, which lets us approach the real process optimum reasonably well. To provide the initial set of data, two-level factorial design can be used. 

Activated Adsorption. Activated adsorption—that is, adsorption with a measurable rate of adsorption and a measurable temperature coefficient of rate of adsorption—is a type of chemisorption which is, for instance, found in the adsorption of nitrogen on certain metals at elevated temperatures. The difficulties of deciding whether or not true van der Waal s adsorption exists in cases where the heats of adsorption exceed considerably the heats of condensation will become apparent later in the text. 

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