Molar standard-state free-energy change

The molar standard-state free-energy change of a reaction (AG°) is a function of the equilibrium constant K) and is related to changes in the molar standard-state enthalpy (AH°) and entropy (A5°), as described by the Gibbs-Helmholtz equation ... 

One identifies the stoichiometric-coefficient-weighted sum of pure-component chemical potentials in the reference states, at unit fugacity, with the standard-state free-energy change for chemical reaction, since [pi, pure(/ )l° is equivalent to the molar Gibbs free energy of pure component i in this reference state. Hence,... 

AG° = the molar standard state Gibbs free energy (the change in free energy of a reaction when the products and reactants are maintained at standard conditions)... 

To calculate the total free energy change of a reaction, AG, it is necessary to know the standard molar free energy of formation, AG°, of each component involved, i.e. the energy required to form one mole of a substance from its stable elements under standard conditions. For a solid, the standard state refers to a pure substance in its most stable form under reference conditions of pressure and temperature, usually 0.1 MPa and25°C (298.15 K). 

In thermodynamic considerations of A-B binary solution, if the standard state of B is clanged from the Raoultian standard state to the Henrian standard state, the standard molar free energy changes accordingly. 

The free energy content of a system depends on temperature and pressure (and, for mixtures, on concentrations). The value of AG for a process depends on the states and the concentrations of the various substances involved. It also depends strongly on temperature, because the equation AG = A// — T AS includes temperature. Just as for other thermodynamic variables, we choose some set of conditions as a standard state reference. The standard state for AG is the same as for AH —1 atm and the specified temperature, usually 25°C (298 K). Values of standard molar free energy of formation, AG , for many substances are tabulated in Appendix K. For elements in their standard states, AG = 0. The values of AG may be used to calculate the standard free energy change of a reaction at 298 K by using the following relationship. 

Recognizing that the lumped standard-state chemical potential terms represent the standard-state molar free-energy change for the reaction, AG°, the equation can be simplified to a final form ... 

Gibbs free-energy change when 1 mole of a compound is synthesized from its elements in their standard states. (8.4) standard melting point. The melting point of a substance at 1 bar pressure. (5.2) standard molar enthalpy of formation (Aff J). The enthalpy change that results when 1 mole of a compound in its standard state is formed from its elements in their standard states. 

The change in Gibbs free energy of a system, when reactants in their standard states are converted to products in their standard states, is called the molar standard free energy change (AG ) for the reaction. The superscript zero to the G indicates the standard state and the overbar indicates that the molar amounts of the reactants and products given by the numerical coefficients in the balanced chemical equation for the reaction are involved. For the forward reaction of the general chemical reaction (1.5)... 

This AF° was estimated as follows For the reaction in question, aH may be taken as — 11.3 kcal/mole = —11300 cal/mole (Table V, data of Durell et al., 1962). The total entropy change was estimated as — 2.5 — 16.5 = — 19.0 entropy units. Therefore, AF° = AH - rAS = —11300—300 (—19) =-11300-1-5700=-5600 cal/mole. This molar free-energy change and others designated here by the superscript apply to a standard state with all reactants and products at a concentration of IM, with other conditions as defined above. If the standard state is taken as one in which the hy-dronium ion is at a concentration of 10 , as at pH 7.0, then the superscript will be used. 

Table 23.2 Standard molar Gibbs free energy changes of some solids, liquids, gases and aqueous ions. The states are shown as state symbols after each substance.

A concentration scale for solutes in aqueous solutions, equal to moles of solute/55.51 mol water. It is frequently used in studies of solvent isotope effects. As pointed out by Schowen and Schowen the choice of standard states can change the sign for the free energy of transfer of a species from one solvent to another, even from HOH and DOD. The commonly used concentration scales are molarity, mole fraction, aquamolality, and molality. Free energies tend to be nearly the same on all but the molality scale, on which they are about 63 cal mol more positive at 298 K than on the first three scales. The interested reader should consult Table I of Schowen and Schowen ... 

Just as we can define a standard enthalpy of formation (AH°f) and a standard free energy of formation (AG°f), we can define an analogous standard entropy of formation (AS°f) as being the entropy change for formation of a substance in its standard state from its constituent elements in their standard states. Use the standard molar entropies given in Appendix B to calculate AS°f for the following substances ... 

Gj -G° is the change in molar free energy of / due to the change in state from the standard state to the state of solution of a particular composition. This is called the partial molar free energy of mixing or relative partial molar free energy of i and is designated... 

Calculate the change of the standard molar free energy of silicon for the change of the standard state from Raoultian to Henrian. 

---