Molar Gibb’s free energy

The total partial molar Gibb s free energy of sorption (aG°t = aG°s) is directly related to Kp by... 

It s the molar Gibb s free energy and it s intensive. Conceptually, chemical potential is to Gibb s free energy what specific heat capacity is to heat capacity in the former it s per mole and the latter is typically per mass unit. 

From the thermodynamic viewpoint, miscibility is determined by the molar Gibb s free energy of mixing (AG ) which in turn is governed by the combinatorial molar entropy of mixing and molar enthalpy of mixing as shown in... 

Measurements of the potentials of galvanic cells at open circuit give information about the thermodynamics of cells and cell reactions. For example, the potential of the cell in Figure 1, when the solution concentrations are 1 molar (1 M) at 25°C, is 1.10 V. This is called the standard potential of the cell and is represented by E°. The available energy (the Gibb s free energy AG°) of the cell reaction given in equation (3) is related to E° by... 

Clearly, this state can be attained by transferring a volume vxic of pure solvent from the particular volume concerned to the rest of the solution. To that end we must transfer vx/eVo moles of solvent, if lA represents the molar volume of the solvent. Now, if go is the molar potential of the solvent, the increase in Gibb s free energy when vdxjcVo moles of solvent are transferred from a volume in which the concentration is c -f JC to another volume in which the concentration is c, is given by... 

Very similar conventions may be introduced to characterize the entropies and Gibbs free energies of ionic species. Here one adopts the convention that at T = 298.15 K and at 1 bar S°(H+) = 0 and AG°(H+) = 0, for water as solvent. Tabulations of molar entropies and free energies may then be constructed as outlined earlier. These are also of the same rather limited applicability as the comparable enthalpies for ions. As an example, one may determine the equilibrium constant for a given ionic reaction at infinite dilution through the relation, ACjj = —RT In Kion, for which the left hand side is first established by looking up the relevant data from the tabulations. 

G = Gibbs molar free energy S = molar entropy F = Helmholtz free molar energy H = molar enthalpy U = molar internal energy... 

Gibbs free energy or Gibbs molar free energy molar flow of gas phase acceleration of gravity enthalpy, molar enthalpy, weight enthalpy Henry s constant Planck s constant height horsepower radiation intensity molar flux... 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

Before leaving our discussion of partial molar properties, we want to emphasize that only the partial molar Gibbs free energy is equal to n,-. The chemical potential can be written as (cM/<9 ,)rv or (dH/dnj)s p H partial molar quantities for fi, into equations such as those given above. 

Let us consider a rock at temperature T whose chemical composition q (recipe) is expressed as the vector of all the molar fractions x0 of s elements or oxides. It is assumed that it can be made by an arbitrarily large number p s of mineral phases exclusive of solid solution. B is the component matrix of these minerals for the selected set of elements or oxides. Let nj be the number of moles of mineral j and gj its Gibbs free energy of formation AGf T estimated when formed from either the elements or the oxides. The function to be minimized is the Gibbs free energy G given by... 

The molar Gibbs free energy of the phase at P and T of interest is obtained by combining equations 2.94, 2.95, and 2.96 for known values of molar enthalpy and molar entropy at 2) and P reference conditions H% p and S% respectively). 

The standard enthalpy difference between reactant(s) of a reaction and the activated complex in the transition state at the same temperature and pressure. It is symbolized by AH and is equal to (E - RT), where E is the energy of activation, R is the molar gas constant, and T is the absolute temperature (provided that all non-first-order rate constants are expressed in temperature-independent concentration units, such as molarity, and are measured at a fixed temperature and pressure). Formally, this quantity is the enthalpy of activation at constant pressure. See Transition-State Theory (Thermodynamics) Transition-State Theory Gibbs Free Energy of Activation Entropy of Activation Volume of Activation... 

The differences in solvation of the reactants and the products constitute in general the major difference between the driving force for the equilibrium reaction in solution and that in the gas phase. The molar Gibbs free energy of solvation for any species I that participates in the equilibrium in a given solvent S can be written as... 

Another expression for the total standard partial molar Gibbs free energy is obtained from Henry s law. Henry s law may be written... 

The last member of Equation (2) shows that n, is the partial molar quantity associated with the Gibbs free energy, G. Euler s theorem gives then... 

We will follow the IUPAC recommendation that surface properties per unit surface area be represented by the lower case (g = Gibbs free energy, u = energy, h = enthalpy, etc.) with a superscript.s designating that the property is for the surface. The quantities gs,us,hs... for the surface are in many ways comparable to molar properties (or partial molar properties for mixtures) in the bulk phase. 

The compilation (Lias et al. 1988) is also the source of most of the data for the gas phase acidity, AGa in kJ mol 1 at 298 K. This is the standard molar Gibbs free energy of proton dissociation according to S(H) — S + H+ in the gas phase. Again, the equilibrium constant of a competition reaction,... 

T absolute temperature R molar ideal gas constant Cp mean molar heat capacity area of surface or interface T thickness of interfacial layer Q heat (extensive) q heat per mole of adsorbate U internal energy H enthalpy S entropy G Gibbs free energy y surface tension... 

---