Standard entropy activation

The standard entropy difference between the reactant(s) of a reaction and the activated complex of the transition state, at the same temperature and pressure. Entropy of activation is symbolized by either A5 or and is equal to (A// - AG )IT where A// is the enthalpy of activation, AG is the Gibbs free energy of activation, and T is the absolute temperature (provided that all rate constants other than first-order are expressed in temperature-independent concentration units such as molarity). Technically, this quantity is the entropy of activation at constant pressure, and from this value, the entropy of activation at constant volume can be deduced. See Transition-State Theory (Thermodynamics) Gibbs Free Energy of Activation Enthalpy of Activation Volume of Activation Entropy and Enthalpy of Activation (Enzymatic)... 

The total entropy of a substance in a state defined as standard. Thus, the standard states of a solid or a liquid are regarded as those of the pure solid or Ihe pure liquid, respectively, and at a stated temperature. The standard state of a gas is at 1 atmosphere pressure and specified temperature, and its standard entropy is the change of entropy accompanying its expansion to zero pressure, or its compression from zero pressure to 1 atmosphere. The standard entropy of an ion is defined in a solution of unit activity, by assuming that the standard entropy of the hydrogen ion is zero. 

The assumptions of the special model of a nonuniform surface were formulated above in terms of changes of the standard Gibbs energy, AG°, and the Gibbs activation energy, AG. It can be assumed that standard entropy, S°, of each kind of adsorbed particles and activated complexes on different sites of a nonuniform surface does not differ substantially in this case there can be given practically equivalent formulation of the model... 

AS = standard entropy change, i.e., standard entropy of activation. 

The standard entropy change, AS for the formation of the activated complex AIT from A and B is as follows ... 

If we assume that the activated complex is mobile on the surface and that the rotational and vibrational modes of the activated complex are the same as those of the gaseous species A, then the standard entropy change of adsorption is equal to... 

The activation energies for the dissociative adsorption of ethyl acetate and acetic acid were adjusted in the analysis. To be consistent with the DFT results shown in Table VIII, the activation energy for the dissociative adsorption of ethyl acetate was constrained to be less that the activation energy for the dissociative adsorption of acetic acid. The standard entropy changes for these steps were constrained such that the activated complexes were immobile species. The standard entropy and enthalpy changes to form the activated complex for step 2 were adjusted. 

Entropy of activation A S (standard entropy of activation A S ) (J mol-1 K-1) — The standard entropy difference between the -> transition state and the ground state of the reactants, at the same temperature and pressure. It is related to the - Gibbs energy of activation and - enthalpy of activation by the equations... 

Since we are concerned with the Arrenhius activation energy under equilibrium conditions, a further correction should be made for the TAS change with the system in equilibrium under standard conditions, i.e., considering the relative standard entropies for for Fe2+, Fe3+ equal to -137.7 and -315.9 J/mole-K,190 a difference of -178.2 J/mole-K. The... 

Values of the pre-exponential factor, A, activation energy, E, activation entropy, AS, and standard entropy AS°, for the addition of alkyl radicals to ethylene... 

We see that the difference in activation energies E — E2 is related to the standard heat of the reaction Aff, that the ratio of the frequency factors A1/A2 is related to the standard entropy change for the reaction AS while the difference in the constants C and C2 is equal to the difference in the mean heat capacities ACp of the reactants and products. If the accuracy of the data or the temperature range is sufficiently restricted that the approximate form of the Arrhenius equation may be used to represent the rate constants, it implies that ... 

In such a case there is a direct equality between the activation-energy difference and the standard heat of the reaction as well as between the logarithm of the ratio of the frequency factors and the standard entropy change. This gives a rationale for the nomenclature activation energy, which is used to designate the constant E in the rate equation. 

The entropy of activation would amount to about 10 cal/mole-°C, which is quite reasonable when compared with the over-all entropy change in the reaction of about 45 cal/mole- C (standard state 25 C, 1 atm pressure). The standard entropy change due to translation is 32.4 cal/mole-°C, which leaves 12.6 cal/mole-°C for rotation and vibrational changes, a figure that shoidd be compared with the 10 cal/molc- C entropy of activation. This would indicate that the transition-state complex is much more like two loosely bound NO2 molecules than it is like N2O4. 

Bywater and Roberts have made a detailed comparison of such reactions for a series of compounds from which the changes in entropy of activation can be considered in some detail. Table XII.3 lists the calculated standard (300°K, 1 atm) molar entropies of translation and rotation of complexes made of H or CH3 and RH and the standard entropy changes in the reactions H + HR H2R, CII3 + HR = CH4R (neglecting vibration) calculated by these authors. 

In these calculations the electronic contributions have been assumed to cancel, and vibrational assignments and internal rotation barriers were calculated according to Pitzer. Other assumptions have been discussed by the authcjrs. The vibrational contributions (not shown in table) nearly cancel each other near 300°K and can be neglected below 500°K in the calculation of AiS° for the reactions, so that the AaS° shown in the last two lines of Table XII.3, aside from symmetry changes, can be equated to the standard entropy of activation. 

Utilize the value of h from Problem 7 and of AH+ from Problem 8 to calculate the constant B of equation (27). Assuming c, the concentration of the species providing the protons in the discharge of hydrogen, to be 10 molecules per sq. cm., calculate the standard entropy of activation (A8 ) of the rate determining stage. 

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