Gibbs free standard energy approximation

The Gibbs free energy (computed in the harmonic approximation) were converted from the 1 atm standard state into the standard state of molar concentration (ideal mixture at 1 molL-1 and 1 atm). 

From the preceding it follows that the half-wave potential measured in DCP will only in rare cases approximately equal the standard potential. The requirements for this are (i) no side reactions (equilibria) of the reduced or oxidized form (esp. no protonation reactions), (ii) no amalgamation, or a dissolution in mercury with negligible Gibbs free energy of amalgamation, and (iii) no strong deviation of the activity coefficient ratio from unity. 

The standard Gibbs free energy of formation, AG°, for any oxide can be read directly off the vertical axis of the graph. For example, at 1000°C, the standard Gibbs free energy of formation of NiO is approximately -250 kJ for two moles of NiO. 

ZPE and thermal and entropic corrections at the appropriate experimental temperatures can be calculated using the frequencies in conjimction with the standard textbook formulas for the statistical thermodynamics of an ideal gas under the harmonic oscillator/rigid rotor approximation. Equations (4) and (5) relates the rate constant and equilibrium constant with the Gibbs free energy, which can be described in terms of the enthalpy (H) and the entropy (S) in the following equation ... 

Since activities are commonly assumed to be close to concentrations, Eq. 3.18 reduces to the more familar Eq. 3.20, where Q = [B] / [A]. This equation is simply another (and approximate) way of expressing Eq. 3.18. It gives the driving force that exists for a reaction to occur when the concentrations of B and Ado not reflect the difference in the intrinsic Gibbs free energies of their respective solutions at standard states (AGrxn°)-... 

These expressions contain the differences between the Gibbs free energies of the liquid and the sohd phases in their pure standard states, i.e. these are the free energies of melting of the pure substances. They are, however, needed for temperatures other than T j, the equilibrium melting points of the pure substances. An approximate equation can be obtained in the following way. 

The standard entropy of small gas-phase molecules, such as or CO, is of the order of 2meV/K. Their entropic contribution to the Gibbs free energy at room tan-perature (and at Ibar) is therefore approximately -0.6eV/molecule and increases with temperature to about -1 eV at 500 K. Most smaller molecules involved in heterogeneous catalysis have entropies of this order of magnimde one important exception is having a standard entropy of only 1.35 meV/K. Note that, for example,... 

It is a serious drawback that it is not possible to determine the transfer activity coefficient of the proton (or of any other single-ion species) directly by thermodynamic methods, because only the values for both the proton and its counterion are obtained. Therefore, approximation methods are used to separate the medium effect on the proton. One is based on the simple sphere-in-continuum model of Born, calculating the electrostatic contribution of the Gibb s free energy of transfer. This approach is clearly too weak, because it does not consider solvation effects. Different ex-trathermodynamic approximation methods, unfortunately, lead not only to different values of the medium effect but also to different signs in some cases. Some examples are given in the following log yH+ for methanol -1-1.7 (standard deviation 0.4) ethanol -1-2.5 (1.8), n-butanol -t-2.3 (2.0), dimethyl sulfoxide -3.6 (2.0), acetonitrile -1-4.3 (1.5), formic acid -1-7.9 (1.7), NH3 -16. From these data, it can be seen that methanol has about the same basicity as water the other alcohols are less basic, as is acetonitrile. Di-... 

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