The molar reaction Gibbs energy

Applying the general definition of a molar differential reaction quantity (Eq. 11.2.15) to the Gibbs energy, we obtain the definition of the molar reaction Gibbs energy or molar Gibbs 

Equation 11.2.16 shows that this quantity is also given by the partial derivative 

The total differential of G in a closed system with T, p, and taken as the independent variables is then 

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Isothermal galvanic cells with only one known cell reaction can be calculated from the molar reaction Gibbs energy, A,G, and the number of electrons exchanged in the reaction, z ie,... 

In short, in an equilibrium state each phase has the same temperature and the same pressure, each species has the same chemical potential in the phases in which it is present, and the molar reaction Gibbs energy of each phase is zero. 

When equilibrium exists between the liquid and solid phases, the temperature is the freezing point Tf of the liquid. At equilibrium, the molar reaction Gibbs energy defined by ArG = J2iViiii is zero ... 

This book will denote the molar reaction Gibbs energy of a cell reaction by ArGceii, rather than AfG, in order to emphasize that the cell reaction takes place in a galvanic cell with its advancement tied to an electric current. This quantity is defined by... 

The first two terms on the left side of Eq. 14.3.4 are sums over aU the reactants and produets of the cell reaction. From Eq. 14.3.1, we recognize the sum of these terms as the molar reaction Gibbs energy of the cell reaction ... 

The question now arises whether ttie molar reaction Gibbs energy ArGceii of the cell reaction is equal to the molar reaction Gibbs energy ArG of the direct reaction. Both ArGceii and ArG are defined by the sum Both reactions have the same values of v,, but... 

Consider first a cell without a Uquid junction. This kind of ceU has a single electrolyte solution, and all of the reactant and product ions of the ceU reaction are in this solution phase. The same solution phase is present in the reaction vessel during the direct reaction. When all ions are in the same phase, the value of v,- /r,- is independent of the electric potentials of any of the phases (see the comment following Eq. 11.8.4 on page 350), so that the molar reaction Gibbs energies are the same for the cell reaction and the direct reaction ... 

ArG° is the molar reaction Gibbs energy when each reactant and product is at unit activity and, if it is an ion, is in a phase of zero electric potential. Since AfG° is equal to —/ Tin A" (Eq. 11.8.10), we can write... 

A distinguishing aspect in electrode kinetics is that the heterogeneous rate constants, kred and kox, can be controlled externally by the difference between the inner potential in the metal electrode (V/>M) and in solution (7/>so1) that is, through the interfacial potential difference E = electrode setup (typically, a three-electrode arrangement and a potentiostat), the E-value can be varied in order to distort the electrochemical equilibrium and favor the electro-oxidation or electro-reduction reactions. Thus, the molar electrochemical Gibbs energy of reaction Scheme (l.IV), as derived from the electrochemical potentials of the reactant and product species, can be written as (see Eqs. 1.32 and 1.33 with n = 1)... 

The first term on the right side of Eq. 11.8.2 is the standard molar reaction Gibbs energy, or standard molar Gibbs energy of reaction ... 

Substituting the equilibrium conditions ArG=Oand Qrxn=K inEq. 11.8.8 gives an important relation between the standard molar reaction Gibbs energy and the thermodynamic equilibrium constant ... 

The relation K = exp (—ArG°/RT) (Eq. 11.8.11) gives us a way to evaluate the thermodynamic equilibrium constant K oi a. reaction at a given temperature from the value of the standard molar reaction Gibbs energy AfG° at that temperature. If we know the value of AfG°, we can calculate the value of K. 

One method is to calculate AfG° from values of the standard molar Gibbs energy of formation AfG° of each reactant and product. These values are the standard molar reaction Gibbs energies for the formation reactions of the substances. To relate AfG° to measurable quantities, we make the substitution im = Hi — TSi (Eq. 9.2.46) in ArG = iVifXi to give ArG = - T or... 

The thermodynamic equilibrium constant K, for a given reaction equation and a given choice of reactant and product standard states, is a function of T and only of T. By equating two expressions for the standard molar reaction Gibbs energy, AfG° = lA ArG° = —RT nK (Eqs. 11.8.3 and 11.8.10), we obtain... 

Some of the most useful experimentally-derived data for thermodynamic calculations are values of standard molar reaction enthalpies, standard molar reaction Gibbs energies, and standard molar reaction entropies. The values of these quantities for a given reaction are related, as we know (Eq. 11.8.21), by... 

In this hypothetical cell, ArGceii is equal to the standard molar reaction Gibbs energy AfG°. From Eq. 14.3.13, or Eq. 14.3.14 with Ej assumed equal to zero, we have... 

For example, the standard reaction Gibbs energy for reaction A is the difference between the molar Gibbs energies of fructose-6-phosphate and glucose-6-phosphate in solution at 1 mol dm and 1 bar. 

Practically in every general chemistry textbook, one can find a table presenting the Standard (Reduction) Potentials in aqueous solution at 25 °C, sometimes in two parts, indicating the reaction condition acidic solution and basic solution. In most cases, there is another table titled Standard Chemical Thermodynamic Properties (or Selected Thermodynamic Values). The former table is referred to in a chapter devoted to Electrochemistry (or Oxidation - Reduction Reactions), while a reference to the latter one can be found in a chapter dealing with Chemical Thermodynamics (or Chemical Equilibria). It is seldom indicated that the two types of tables contain redundant information since the standard potential values of a cell reaction ( n) can be calculated from the standard molar free (Gibbs) energy change (AG" for the same reaction with a simple relationship... 

In reality, the enthalpy of reaction is strongly temperature-dependent. When the temperature dependence of the standard enthalpy of reaction with the help of the molar heat capacities is taken into account (see Eq. 12.6), the following values for the enthalpies of reaction, Gibbs energies of reaction, and equilibrium constants are obtained (see Example 12.8) ... 

If a chemical process takes place at constant temperature while each reactant and product remains in its standard state of unit activity, the molar reaction quantity Af.Y is called the standard molar reaction quantity and is denoted by ArZ°. For instance, AyapH° is a standard molar enthalpy of vaporization (already discussed in Sec. 8.3.3), and ArG° is the standard molar Gibbs energy of a reaction. 

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)... 

We have seen that standard reaction Gibbs energy, AjG, is defined as the difference in standard molar Gibbs energies of the products and the reactants weighted by the stoichiometric coefficients, v, in the chemical equation... 

The standard potential of a cell reaction (E n) values can be calculated from the standard molar free (Gibbs) energy change (AG" ") for the same reaction with a simple relationship ... 

Previously we have said little about g° other than that it was a function of temperature only and that each species had its own value of g°. We discussed standard states in Chapters 7, 8, and 9. A standard state is some state of matter that we will all agree upon as a suitable basis for constructing tables of properties. For most chemical reaction purposes we choose the standard state of some substance as the pure substance in its normal state (solid, liquid, or gas) at F = 1 atm or 1 bar, and an arbitrarily chosen T, normally = 25°C = 298.15 K for the tables of interest in this chapter. Alas, there are other standard states that are much more convenient for some problems, as discussed previously for vapor-liquid equilibrium calculations. However, if we put off for the moment saying what our standard state is, we can use the symbol ° to indicate a property in the standard state, and then say that, for any pure chemical element or compound (pure species) the partial molar Gibbs energy is the same as the pure species Gibbs energy, and in its standard state... 

The thermodynamic function used as the criterion of spontaneity for a chemical reaction is the Gibbs free energy of reaction, AG (which is commonly referred to as the reaction free energy ). This quantity is defined as the difference in molar Gibbs free energies, Gm, of the products and the reactants ... 

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