Enthalpy and Entropy Contributions

Given the partition function, the enthalpy and entropy terms may be calculated by carrying out the required differentiations in eq. (13.18). For one mole of molecules, the results for a non-linear system are (R being the gas constant) 

The rotational terms are slightly different for a linear molecule, and the vibrational terms will contain one vibrational contribution more. 

In order to calculate AG = Gts - Greactant, we need AH and AS. AHti is directly the difference in electronic energy between the TS and reactant. Except for complicated reactions involving several electronic states of different degeneracy (e.g. singlet molecules reacting via a triplet TS), A55ec is zero. 

For bimolecular reactions (i.e. where the reactant is two separate molecules) Afffrans and Affrot contribute a constant -4RT. The translational and rotational entropy changes are substantially negative, -30 to -50J/mol K, due to the fact that there are six translational and six rotational modes in the reactants but only three of each at the 

The six remaining degrees of freedom are transformed into the reaction coordinate and five new vibrations at the TS. These additional vibrations usually make AH, a few kJ/mol positive, and A5Jib positive by 5-lOJ/mol K For bimolecular reactions, the entropy typically raises the free energy barrier by 40-60 kJ/mol, relative to the electronic energy alone. 

The vibrational enthalpy consists of two parts, the first is a sum of hv/2 contributions, this is the zero-point energies. The second part depends on temperature, and is a contribution from molecules which are not in the vibrational ground state. This contribution goes toward zero as the temperature goes to zero when all molecules are in the ground state. Note also that the sum over vibrational frequencies runs over 3Ai — 6 for the reactant(s), but only 3A1 — 7 for the TS. At the TS, one of the normal vibrations has been transformed into the reaction coordinate, which formally has an imaginary frequency. 

The vibrational enthalpy consists of two parts, the first is a sum of hujl contributions, this is the zero-point energies. The second part depends on temperature, and is a contribution from molecules which are not in the vibrational ground state. This 

It should be noted that the experimental activation enthalpy for the Diels-Alder reaction is 33 kcal/mol (estimated from the reverse reaction and the experimental -reaction energy i.e. the MP2/6-31G(d) value is 14kcal/mol too low.-Similarly, the calculated reaction energy of —47 kcal/mol is in rather poor agreement with the 

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I.D. The data has been curve fitted to a linear function and thus the enthalpy and entropy contributions are extracted as the slope and intercept of each curve. 

The assumption that the energy can be written as a sum of terms implies that the partition function can be written as a product of terms. As the enthalpy and entropy contributions involve taking the logarithm of q, the product thus transforms into sums of enthalpy and entropy contributions. 

Enthalpy and entropy contributions (in kcal mol-1) to the binding of cations by 18-crown-6 [3] in water at 25°C ... 

For soft cations, such as Ag+ and Pb2+, covalent contributions are much more important, and consequently the observed order of complex stabilities is quite different from that for alkali cations NH > O > S for Pb2+ and NH, S > O for Ag+. Dissection of the overall effect into enthalpy and entropy contributions (Table 15) reveals the complicated nature of the heteroatom effect. For K+ and Ba2+, the more favourable entropy contribution for N and S ligands is more than offset by the unfavourable change in enthalpy of binding. 

Considerable information is available on the magnetic parameters associated with three different crystal structures of Fe which are b.c.c. and f.c.c. at ambient pressures and c.p.h. which is observed at high pressures. Table 6.5 gives the corresponding values of the maximum enthalpy and entropy contributions due to... 

As usual, AGr can be broken into enthalpy and entropy contributions ... 

Enthalpy and Entropy Contributions to the Free Energy of Vaporization... 

Table 3.15 Enthalpy and Entropy Contributions to Relative Free ...

Free energy, G = H — TS, is a state function that indicates whether a reaction is spontaneous or nonspontaneous. A reaction at constant temperature and pressure is spontaneous if AG < 0, nonspontaneous if AG > 0, and at equilibrium if AG = 0. In the equation AG = AH — TAS, temperature is a weighting factor that determines the relative importance of the enthalpy and entropy contributions to AG. 

The free-energy change (AG°mc) comprises enthalpy and entropy contribution according to the equation... 

Internal Magnetic Moment 238 12.3 Enthalpy and Entropy Contributions 303... 

Ghosh T, Garca AE, Garde S. Enthalpy and entropy contributions to the pressure dependence of hydrophobic interactions. J. Chem. Phys. 2002 116 2480-2486. 

Ligands which hind to metals through more than one donor atom show relatively high stability constants. Both enthalpy and entropy contribute to the magnitude of the stability constant and the balance between these contributions varies with ligand structure. 

A nanoparticle exposed to vacuum or a gas is less stable than a bulk coarse grained material. A surface free energy can be defined in terms of surface enthalpy and entropy contributions. 

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