Energy change

Franck-Condon principle According to this principle the time required for an electronic transition in a molecule is very much less than the period of vibration of the constituent nuclei of the molecule. Consequently, it may be assumed that during the electronic transition the nuclei do not change their positions or momenta. This principle is of great importance in discussing the energy changes and spectra of molecules. 

Gibbs-Helmholtz equation This equation relates the heats and free energy changes which occur during a chemical reaction. For a reaction carried out at constant pressure... 

First, the films separately are allowed to expand to some low pressure, t, and by Eq. IV-48 the free energy change is... 

We now consider briefly the matter of electrode potentials. The familiar Nemst equation was at one time treated in terms of the solution pressure of the metal in the electrode, but it is better to consider directly the net chemical change accompanying the flow of 1 faraday (7 ), and to equate the electrical work to the free energy change. Thus, for the cell... 

D. Dependence of Other Physical Properties on Surface Energy Changes at a Solid Interface... 

B. Surface Energy and Free Energy Changes from Adsorption Studies... 

Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

If the contact angle is zero, as in Fig. XIII-8e, there should be no tendency to adhere to a flat surface. Leja and Poling [63] point out, however, that, as shown in Fig. XIII-8/, if the surface is formed in a hemispherical cup of the same radius as the bubble, then for step la, the free energy change of attachment is... 

Vibrational energy states are too well separated to contribute much to the entropy or the energy of small molecules at ordinary temperatures, but for higher temperatures this may not be so, and both internal entropy and energy changes may occur due to changes in vibrational levels on adsoiption. From a somewhat different point of view, it is clear that even in physical adsorption, adsorbate molecules should be polarized on the surface (see Section VI-8), and in chemisorption more drastic perturbations should occur. Thus internal bond energies of adsorbed molecules may be affected. 

If we consider the case of a gas in adsorption equilibrium with a surface, there must be no net free energy change on transporting a small amount from one region to the other. Therefore, since the potential represents the work done by the adsorption forces when adsorbate is brought up to a distance x from the surface, there must be a compensating compressional increase in the free energy of the adsorbate. Thus... 

If the process is carried out at constant volume, the heat evolved Qi will be equal to an energy change AE2 or, per mole of adsorbate, qi = Ae2 (small capital letters will be used to denote mean molar quantities). Alternatively, the process may be... 

Thus for isobaric processes a new fimction, the enthalpy H, has been introduced and its change A// is more directly related to the heat that must have been absorbed than is the energy change At/. The same reservations about the meanmg of heat absorbed apply in this process as in the constant-volume process. 

The enthalpy, entropy and free energy changes for an isothennal reaction near 0 K caimot be measured directly because of the impossibility of carrying out the reaction reversibly in a reasonable time. One can, however, by a suitable combination of measured values, calculate them indirectly. In particular, if the value of... 

Figure A2.3.20 Free energy change in the transfomiation of CFt OFl to CFt CFt (after [92]).

The difference in the free energy change when L is replaced by L2 is... 

We assume for simplicity that the adsorbed phase has the same entropy as the solid so that only an energy change is associated with the transfer of material from the bnlk to the adsorbed phase, then ... 

The first law of thennodynamics relates the energy change m a system at constant volume to the work done on the system and the heat added to the system q. 

Values of COT) can be derived from a constant volume calorimeter by measuring AU for small values of Tj - TO and evaluating AU/(T2 - T ) as a fiinction of temperature. The energy change AU can be derived from a knowledge of tlie amount of electrical energy required to change the temperature of the sample + container... 

Solution calorimetry covers the measurement of the energy changes that occur when a compound or a mixture (solid, liquid or gas) is mixed, dissolved or adsorbed in a solvent or a solution. In addition it includes the measurement of the heat capacity of the resultant solution. Solution calorimeters are usually subdivided by the method in which the components are mixed, namely, batch, titration and flow. 

Batch calorimeters are instmments where there is no flow of matter in or out of the calorimeter during the time the energy change is being measured. Batch calorimeters differ in the way the reactants are mixed and in the method used to detennine the enthalpy change. Enthalpy changes can be measured by the various methods... 

Lynden-Bell R M, van Duijneveldt J S and Frenkel D 1993 Free-energy changes on freezing and melting ductile metals Mol. Phys. 80 801-14... 

---