Free energy conventions used

In the following section, the micellization model and the free-energy expression used in ref 6 are described. In section ID, the cmc and C t are calculated numerically for various values of o. Because the numerical calculations for a complete parametric study would be too lengthy, approximate, analytical relations for the two concentrations are developed in section IV. Computations based on these relations show that, of all the parameters, a is the only one which drastically affects the ratio between cmc and Cme The last section emphasizes again that Ccrit has a value close to the conventional cmc as long as the expression used for the free energy is a physically acceptable one. 

Expressing equation (21) in thermodynamic terms using the conventional terms for the standard free energy. 

A note on good practice Notice that by using the molar convention, the units match RT is a molar energy (kilojoules per mole), and so too are the two Gibbs free energy terms. 

A note on good practice Always write Eq. 8 with the standard state sign. Note too that, for the units to match on both sides, we have to use the molar convention for the standard Gibbs free energy. 

So far, we have only considered perturbations in the forward direction. As in conventional free energy calculations, powerful relations can be derived if forward and backward perturbations are combined. With the free energy being a state function, we can reverse the path direction. This leads to several useful relations derived originally by Crooks [16, 18, 19], In particular, we obtain immediately... 

The standard free energy of the reaction, AG° = E — °, is fixed for each reactant couple as soon as the electrode potential is fixed. For simplicity we have written above that AG° is equal to E — E° rather than the usual relationship AG° = F(E — E°). This convention, which is used throughout the book, implies that when potentials are expressed in volts, energies are expressed in electron volts. The term driving force will be used frequently to designate —AG°, in line with the expectation that an increase in the driving force usually speeds up the reaction. 

Concentrations of aqueous electrolyte solutions are conventionally expressed using the aquamolality scale (L = moles salt per 55.508 mol solvent (l,000g for H20)). Some typical solubilities (298.15K) are listed in Table 5.13. Almost all salts are less soluble in D20 than in H20. For those salts whose solubility increases with temperature, which is the ordinary behaviour, the isotope effects decrease with temperature. Writing the standard state partial molar free energy of pure solid salt as Pxsalt) and its standard state in solution as p, (HorD) we have on comparing the saturated solutions in H20 and D20,... 

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