Standard chemical potential, solute

The chemical potential in the dyebath solution, is defined in equation 1 where is the standard chemical potential in the solution, R is the gas constant, Tis temperature in K, and a is activity. 

The standard electrode potentials , or the standard chemical potentials /X , may be used to calculate the free energy decrease —AG and the equilibrium constant /T of a corrosion reaction (see Appendix 20.2). Any corrosion reaction in aqueous solution must involve oxidation of the metal and reduction of a species in solution (an electron acceptor) with consequent electron transfer between the two reactants. Thus the corrosion of zinc ( In +zzn = —0-76 V) in a reducing acid of pH = 4 (a = 10 ) may be represented by the reaction ... 

In the case of ions in solution, and of gases, the chemical potential will depend upon concentration and pressure, respectively. For ions in solution the standard chemical potential of the hydrogen ion, at the temperature and pressure under consideration, is given an arbitrary value of zero at a specified concentration... 

For ions in solution the standard reference state is the hydrogen ion whose standard chemical potential at = 1 is given an arbitrary value of zero. Similarly for pure hydrogen at Phj = = 0- Thus for the... 

Example 2 Finely divided gold is agitated with an oxygen-saturated alkali-cyanide solution of pH = 12 containing 10 moldm of CN . Calculate the concentration of Au(CN)2 ions in solution at 25°C when the reaction is at equilibrium. The standard chemical potentials of the species involved (in kJ) are CN, 165 HjO, —237 Au(CN)f, 244 OH", —157. Assume that fl jo = 1, and take 2-303RT = 5710. 

The ions in solution are subject to two types of forces those of interaction with the solvent (solvation) and those of electrostatic interaction with other ions. The interionic forces decrease as the solution is made more dilute and the mean distance between the ions increases in highly dilute solutions their contribution is small. However, solvation occurs even in highly dilute solutions, since each ion is always surrounded by solvent molecules. This implies that the solvation energy, which to a first approximation is independent of concentration, is included in the standard chemical potential and has no influence on the activity. 

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, 5 (M+) and B X ), are related to the extraction constant the... 

In a general case of a mixture, no component takes preference and the standard state is that of the pure component. In solutions, however, one component, termed the solvent, is treated differently from the others, called solutes. Dilute solutions occupy a special position, as the solvent is present in a large excess. The quantities pertaining to the solvent are denoted by the subscript 0 and those of the solute by the subscript 1. For >0 and x0-+ 1, Po = Po and P — kxxx. Equation (1.1.5) is again valid for the chemical potentials of both components. The standard chemical potential of the solvent is defined in the same way as the standard chemical potential of the component of an ideal mixture, the standard state being that of the pure solvent. The standard chemical potential of the dissolved component jU is the chemical potential of that pure component in the physically unattainable state corresponding to linear extrapolation of the behaviour of this component according to Henry s law up to point xx = 1 at the temperature of the mixture T and at pressure p = kx, which is the proportionality constant of Henry s law. 

For a solution of a non-volatile substance (e.g. a solid) in a liquid the vapour pressure of the solute can be neglected. The reference state for such a substance is usually its very dilute solution—in the limiting case an infinitely dilute solution—which has identical properties with an ideal solution and is thus useful, especially for introducing activity coefficients (see Sections 1.1.4 and 1.3). The standard chemical potential of such a solute is defined as... 

The activity coefficient of the solvent remains close to unity up to quite high electrolyte concentrations e.g. the activity coefficient for water in an aqueous solution of 2 m KC1 at 25°C equals y0x = 1.004, while the value for potassium chloride in this solution is y tX = 0.614, indicating a quite large deviation from the ideal behaviour. Thus, the activity coefficient of the solvent is not a suitable characteristic of the real behaviour of solutions of electrolytes. If the deviation from ideal behaviour is to be expressed in terms of quantities connected with the solvent, then the osmotic coefficient is employed. The osmotic pressure of the system is denoted as jz and the hypothetical osmotic pressure of a solution with the same composition that would behave ideally as jt. The equations for the osmotic pressures jt and jt are obtained from the equilibrium condition of the pure solvent and of the solution. Under equilibrium conditions the chemical potential of the pure solvent, which is equal to the standard chemical potential at the pressure p, is equal to the chemical potential of the solvent in the solution under the osmotic pressure jt,... 

Conway et described the most convenient conditions defining standard chemical potentials for adsorption with solvent displacement. First, for n = 1, the conditions are the same as in binary solution thermo-... 

The state of unit activity of hydrated proton at the standard temperature 25X and pressure 1 atm. In elecfrodiemistry of aqueous solution, the scale of chemical potential for hydrated ions takes as the reference zero the standard chemical potential of hydrated protons at unit activity in addition the standard stable state energy of element atoms is set equal to zero. 

If we dehne the hrst two terms on the right-hand side of Equation (15.4) as p-2> the standard chemical potential of the solute in solution, then... 

We can define the standard chemical potential of the solute in solution as... 

For solutions obeying Henry s law, as for ideal solutions, and for solutions of ideal gases, the chemical potential is a linear function of the logarithm of the composition variable, and the standard chemical potential depends on the choice of composition variable. The chemical potential is, of course, independent of our choice of standard state and composition measure. 

Although we cannot determine its absolute value, the chemical potential of acomponent of a solution has a value that is independent of the choice of concentration scale and standard state. The standard chemical potential, the activity, and the activity coefficient have values that do depend on the choice of concentration scale and standard state. To complete the definitions we have given, we must define the standard states we wish to use. 

Solvent in Solution. We shall use the pure substance at the same temperature as the solution and at its equilibrium vapor pressure as the reference state for the component of a solution designated as the solvent. This choice of standard state is consistent with the limiting law for the activity of solvent given in Equation (16.2), where the limiting process leads to the solvent at its equilibrium vapor pressure. To relate the standard chemical potential of solvent in solution to the state that we defined for the pure liquid solvent, we need to use the relationship... 

In what follows we shall always write A, = fC. We assume that the ligand is provided from either an ideal gas phase or an ideal dilute solution. Hence, A, is related to the standard chemical potential and is independent of the concentration C. On the other hand, for the nonideal phase, A will in general depend on concentration C. A first-order dependence on C is discussed in Appendix D. Note also that A, is a dimensionless quantity. Therefore, any units used for concentration C must be the same as for (Aq) . 

Consider a dilute ideal solution of the solute B (which could be gaseous, liquid, or solid at the temperature in question) in the solvent A. Suppose that more concentrated solutions do not behave ideally and, in particular, the state of pure liquid B cannot be attained by going to more and more concentrated solutions (e.g., by removing A by volatilization). It is possible to define a standard chemical potential pertaining to a hypothetical standard state of the ideal infinitely dilute solution as the limit ... 

Although Pb tends to - °o as Xb tends to 0 (and In Xb also tends to - °o), the difference on the right-hand side of Eq. (2.18) tends to the finite quantity pi, the standard chemical potential of B. At infinite dilution (practically, at high dilution) of B in the solvent A, particles (molecules, ions) of B have in their surroundings only molecules of A, but not other particles of B, with which to interact. Their surroundings are thus a constant environment of A, independent of the actual concentration of B or of the eventual presence of other solutes, C, D, all at high dilution. The standard chemical potential of the solute in an ideal dilute solution thus describes the solute-solvent interactions exclusively. 

Solvation is a process in which solute particles (molecules or ions) in a solution interact with the solvent molecules surrounding them. Solvation in an aqueous solution is called hydration. The solvation energy is defined as the standard chemical potential of a solute in the solution referred to that in the gaseous state.11 The solvation of a solute has a significant influence on its dissolution and on the chemical reactions in which it participates. Conversely, the solvent effect on dissolution or on a chemical reaction can be predicted quantitatively from knowledge of the solvation energies of the relevant solutes. In this chapter, we mainly deal with the energetic aspects of ion solvation and its effects on the behavior of ions and electrolytes in solutions. 

Grunwald and Bacarella (16) have shown that the rate of change of the standard chemical potential Go of a solute with water mole fraction Z in a binary solvent mixture can be expressed by the relation ... 

In this case, the standard chemical potential corresponds to the standard free energy of formation of the species i in aqueous solution, that is ... 

The molar Gibbs energy of micelle formation is the Gibbs energy difference between a mole of monomers in micelles and the standard chemical potential in dilute solution ... 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

The difference between the two standard chemical potentials is determined in terms of the molar enthalpy of fusion by the methods developed in Section 10.12. For real solutions, the equation corresponding to Equation (11.162) is... 

The low solubility of hydrocarbons and other mainly apolar substances in water has been ascribed phenomenologically to the hydrophobic interaction. The hydro-phobic free energy can be defined4 as the difference between the standard chemical potentials of an apolar solute at infinite dilution in a hydrocarbon solvent juhc and in water... 

---