Entropy and Enthalpy Corrections

With temperature, entropy, and enthalpy correction, they obtained free energy change AG°. The reversible electrochemical potential was calculated by the equation... 

In the previous examples we only considered electronic energy changes and approximated the entropy as all or nothing. In essence, we assumed that gas-phase species have 100% of their standard state entropy and surface species possess no entropy at all. These assumptions can certainly be improved and in order to construct thermodynamically consistent microkinetic models this is not just optional, but absolutely necessary. Entropy and enthalpy corrections for surface species can be calculated using statistical thermodynamics from knowledge of the vibrational frequencies, and the translational and rotational degrees of freedom (DOF). In contrast to gas-phase molecules, adsorbates cannot freely rotate and move across the surface, but the translational and rotational DOF are frustrated within the potential energy well imposed by the surface. In the harmonic limit the frustrated translational and rotational DOF can conveniently be described as vibrational modes, which in turn means that any surface adsorbate will have iN vibrational DOFs that are all treated equally. 

In this equation m denotes the mass of the particle and Cs is the number of sites per unit area, which is roughly 10 sites cm for transition metal surfaces. Experience has shown that the entropy and enthalpy corrections do not vary appreciably across different transition metal surfaces and for computational screening it is commonly assumed that these contributions are constant. 

Care must be taken to use or determine the correct change of state to which the change of entropy and enthalpy refers. The difficulty arises when one or more equilibrium reactions are present in addition to those used in determining the cell reaction. Such conditions occur when two or more phases are in equilibrium for example, the electrolytic solution may be saturated with a solid phase, or one of the electrodes may consist actually of a liquid solution that is saturated with a solid solution or with another liquid solution. Such equilibria do not alter the change of the Gibbs energy or the emf. Let the cell reaction be represented as v,Bj and an equilibrium reaction as... 

Table 3 contains the enthalpies, zero point energies, entropies and free enthalpies of the activation and reaction steps (3)—(5). The enthalpies are the pure differences of the enthalpies of formation calculated by MINDO/3 at T = 298 K in the gas phase. The free enthalpies were calculated with the help of enthalpies corrected by the zero point energies and of the entropies given in Table 3. 

We are at a loss to explain the discrepancy in the BF3 enthalpies of interaction with the sulfur donors. Steric effects may be operative, but this is far from the whole story for the BCI3 interaction is much larger than BF3 with these donors. Furthermore, using the tentative ( 113)3 parameters to estimate those of ( 2115)3 , we calculate an enthalpy from E and of 11.1 k.cal mole- for the BF3-P( 2H6)3 adduct compared to a measured value of 9.5 k.cal mole i. The authors report much difficulty with the sulfur donor system, but their error estimates could not possibly account for the difference between our calculated and the observed result. The behavior of ( 2115)35 compared to ( 2115)3 is clearly inconsistent with the behavior of these two donors toward ( 2H5)sAl where both enthalpies are correctly predicted with our parameters. It may be that the BF3-( 2115)25 system has an even lower equilibrium constant than reported and is completely dissociated over the temperature range studied. (This would require a very different entropy if the — AH predicted by E and were correct.) A slight impurity (reported to be less than 0.1%) or decomposition product could interact appreciably with BF3 and changing pressure contributions from this adduct with temperature could be attributed incorrectly to the sulfur donor adduct. The actual BF3-sulfur donor adduct would then be a very common example of an adduct which cannot be studied by the vapor pressure technique because it is completely dissociated at the temperatures at which one of the components has appreciable vapor pressure. We have examined the reaction of BF3 ( 2Hs) 2O with large excess of ( H2) 4S in dichloroethane solution at 25 ° and have found the equilibrium constant to be too low to be measured calorimetrically. 

There are two central questions in chemical kinetics (1) How fast can the fastest chemical reactions be (2) Why are many chemical reactions slow We will try to provide some elementary insights when answering these questions. Kinetics has several levels. First, there is a level of correct stoichiometry for a reaction. Second, there is a level of energetic characterization of a reaction, that is, free energy, enthalpy, entropy, and volume changes of reaction (see Section 2.4 and Table 2.6). Third, there is a level of experimental study of reaction rates and the formulation of rate laws that correctly describe the observed rates. Finally, there is the level of mechanism, where elementary reaction steps are proposed, verified experimentally, and used to predict rate expressions, which are then compared with observation. 

There are now several ways to proceed. The most correct is to use the steam tables, and to use either the energy balance or the entropy balance and do the integrals numerically (since the internal energy, enthalpy, entropy, and the changes on vaporization depend on temperature. This is the method we will use first. Then a simpler method will be considered. 

Figure 13 Thermodynamic parameters for the interaction between glucose oxidase and n-dodecyltrimethylammonium bromide (DTAB) as a function of the number of moles of DTAB bound per glucose oxidase molecule (v). AG- ( ), AH (A), and ASp (V) are the Gibbs energy, enthalpy, and entropy per mole of DTAB bound. The symbols and correspond to AG , and TASV corrected for statistical effects. (Data taken from Ref. 88.)...

These arguments lend some support to the claim that enthalpy estimates are correct to within 2 kcal./mole and entropy estimates are correct to within 6 cal./mole deg. In fact, even deviations of these magnitudes appear to be unlikely. 

AG°o,v(Ar) and AG°oiv(Ar ) are the free energies of solvation of the neutral molecule and the radical cation, respectively, and F is the Faraday constant. It should be noted that the ionization potential is the enthalpy of ionization at 0 K thus, the ionization entropy and the temperature correction are neglected in equation (3). However, these corrections are assumed to be fairly small. 

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