Standard enthalpy activation

The solid product, BaO, was apparently amorphous and porous. Decomposition rate measurements were made between the phase transformation at 1422 K and 1550 K (the salt melts at 1620 K). The enthalpy and entropy of activation at 1500 K (575 13 kJ mole-1 and 200 8 J K"1 mole-1) are very similar to the standard enthalpy and entropy of decomposition at the same temperature (588 7 kJ and 257 5 J K-1, respectively, referred to 1 mole of BaS04). The simplest mechanistic explanation of the observations is that all steps in the reaction are in equilibrium except for desorption of the gaseous products, S02 and 02. Desorption occurs over an area equivalent to about 1.4% of the total exposed crystal surface. Other possible models are discussed. 

The Arrhenius activation energy,3 obtained from the temperature dependence of the three-halves-order rate constant, is Ea = 201 kJ mol-1. This is considerably less than the standard enthalpy change for the homolysis of acetaldehyde, determined by the usual thermodynamic methods. That is, reaction (8-5) has AH = 345 kJ mol-1. At first glance, this disparity makes it seem as if dissociation of acetaldehyde could not be a predecessor step. Actually, however, the agreement is excellent when properly interpreted. 

Ha Hi AHr AH m AH°fi AHS, AHvaP A I see Dimensionless Groups Henry s law constant for species Pa m3 mol-1, equation 9.2-8 enthalpy of reaction for reaction as written, J standard enthalpy of reaction, J standard enthalpy of combustion of species i J mol-1 standard enthalpy of formation of species i, J mol-1 standard molar enthalpy of reaction with respect to species i, J mol-1 enthalpy of vaporization, J mol-1 standard molar enthalpy of activation (TST), J mol-1 initiator (species) inhibitor, inert species... 

The choice of a given database as source of auxiliary values may not be straightforward, even for a thermochemist. Consistency is a very important criterion, but factors such as the publication year, the assignment of an uncertainty to each value, and even the scientific reputation of the authors or the origin of the database matter. For instance, it would not be sensible to use the old NBS Circular 500 [22] when the NBS Tables of Chemical Thermodynamic Properties [17], published in 1982, is available. If we need a value for the standard enthalpy of formation of an organic compound, such as ethanol, we will probably prefer Pedley s Thermodynamic Data and Structures of Organic Compounds [15], published in 1994, which reports the error bars. Finally, if we are looking for the standard enthalpy of formation of any particular substance, we should first check whether it is included in CODATA Key Values for Thermodynamics [16] or in the very recent Active Thermochemical Tables [23,24],... 

If we make the assumption that the reverse of reaction 15.5 is diffusion-controlled and assume that the activation enthalpy for the acyl radicals recombination is 8 kJ mol-1, the enthalpy of reaction 15.5 will be equal to (121 - 8) = 113 kJ mol-1. This conclusion helps us derive other useful data. Assuming that the thermal correction to 298.15 K is small and that the solvation enthalpies of the peroxide and the acyl radicals approximately cancel, we can accept that the enthalpy of reaction 15.5 in the gas phase is equal to 113 kJ mol-1 with an estimated uncertainty of, say, 15 kJ mol-1. Therefore, as the standard enthalpy of formation of gaseous PhC(0)00(0)CPh is available (-271.7 5.2 kJ mol-1 [59]), we can derive the standard enthalpy of formation of the acyl radical Af//°[PhC(0)0, g] -79 8 kJ mol-1. This value can finally be used, together with the standard enthalpy of formation of benzoic acid in the gas phase (-294.0 2.2 kJ mol-1 [59]), to obtain the O-H bond dissociation enthalpy in PhC(0)0H DH° [PhC(0)0-H] = 433 8 kJ mol-1. 

Table 13 Arrhenius activation energies and pre-exponential factors for thermal isomerization of tetraphenylethenes [42] and the standard enthalpy differences in benzene solution."...

The standard enthalpy difference between reactant(s) of a reaction and the activated complex in the transition state at the same temperature and pressure. It is symbolized by AH and is equal to (E - RT), where E is the energy of activation, R is the molar gas constant, and T is the absolute temperature (provided that all non-first-order rate constants are expressed in temperature-independent concentration units, such as molarity, and are measured at a fixed temperature and pressure). Formally, this quantity is the enthalpy of activation at constant pressure. See Transition-State Theory (Thermodynamics) Transition-State Theory Gibbs Free Energy of Activation Entropy of Activation Volume of Activation... 

As appears from the examination of the equations (giving the best fit to the rate data) in Table 21, no relation between the form of the kinetic equation and the type of catalyst can be found. It seems likely that the equations are really semi-empirical expressions and it is risky to draw any conclusion about the actual reaction mechanism from the kinetic model. In spite of the formalism of the reported studies, two observations should be mentioned. Maatman et al. [410] calculated from the rate coefficients for the esterification of acetic acid with 1-propanol on silica gel, the site density of the catalyst using a method reported previously [418]. They found a relatively high site density, which justifies the identification of active sites of silica gel with the surface silanol groups made by Fricke and Alpeter [411]. The same authors [411] also estimated the values of the standard enthalpy and entropy changes on adsorption of propanol from kinetic data from the relatively low values they presume that propanol is weakly adsorbed on the surface, retaining much of the character of the liquid alcohol. 

The proposed mechanism of the effect of water can be supported by two other findings (i) the calculations of Maatman et al. [410] revealed that the active sites could be identified with surface silanol groups [Sect. 4.1.2.(a)] and(ii) independent studies of other authors [424—426] showed that silica gel could actually adsorb two layers of water the first layer is strongly chemisorbed whereas the second is less strongly adsorbed and retains much of the character of free water. The standard enthalpy and entropy changes on adsorption determined from kinetic adsorption coefficients, Kr and Kr, for the first and second layer, respectively [411], are consistent with this observation. 

Enthalpy of activation A H (standard enthalpy of activation A H ) (kJ mol-1) — The standard enthalpy difference between the transition state and the ground state of the reactants at the same temperature and pressure. It is related to the temperature coefficient of the rate constant according to the equation ... 

Notice that equation (1.59) meets the commonly known rule that the apparent activation energy of a consecutive process equals the activation energy of the rate Hmiting step minus the sum of the heats (or plus sum of standard enthalpies, 2 AfH°) of the preceding stages, which are treated as being in equilibrium. 

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