Energy of solution

ITlie free energy of solution of a given substance from its normal standard state as a sohd, liquid, or gas to the hyj)othetical one molal state in aqueous solution may he calculated in a manner similar to that described in footnote for calculating the heat of solution. 

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

There seem to be no large-scale uses for HI outside the laboratory, where it is used in various iodination reactions (lecture bottles containing 400 g HI are available). Commercial solutions contain 40-55 wt% of HI (cf. azeotrope at 56.9% HI, p. 815) and these solutions are thermodynamically much more stable than pure HI as indicated by the large negative free energy of solution. 

Free energy of solution, containing chain molecules of a definite length (before the beginning of degradation), can be written as follows ... 

Free energy of solution formation, consisting of the same amount of solvent and degradated molecules, is presented as follows ... 

Heat of Precipitation. Entropy of Solution and Partial Molal Entropy. The Unitary Part of the Entropy. Equilibrium in Proton Transfers. Equilibrium in Any Process. The Unitary Part of a Free Energy Change. The Conventional Standard Free Energy Change. Proton Transfers Involving a Solvent Molecule. The Conventional Standard Free Energy of Solution. The Disparity of a Solution. The E.M.F. of Galvanic Cells. 

Entropy of Solution and Partial Molal Entropy. If the heat of solution of a solute is known, and the free energy of solution is known at some low concentration, then the entropy of solution AS at the same concentration can at once be found from the relation... 

The Conventional Standard Free Energy of Solution. Returning now to the solution of a crystalline solid, let us consider the free energy of solution. Taking a uni-univalent substance let AF denote the change in free energy per mole when additional ions are added to a solution at temperature T where the solute has the mole fraction x and let us fix attention on the quantity... 

The left-hand side of (97) is just the usual standard free energy of solution AF°. We see that... 

In agreement with (98), the left-hand side is just the standard free energy of solution AF°. Here y, as defined by (106), is the usual activity coefficient on the molality scale. In particular, when the solid is in contact with its saturated solution, there is no change in the free energy when additional ions are taken into solution. In this case, if in (108) we write m, t and y,at, the values of m and y in the saturated solution, we may set AF equal to zero. This will be discussed in Sec. 100. 

The Conventional and the Unitary Entropy of Solution. In Sec. 55 we discussed the free energy of solution, by considering the quantity (AF — 2RT In x). Again taking a uni-univalent solute, let us now fix attention on the quantity... 

Turning next to the conventional free energy of solution of the same substance, we have... 

The conventional free energy of solution is greater than this by the amount 3RT In M adding this quantity, we obtain... 

The heat of solution tends at extreme dilution to the value +4207 cal/mole. Calculate the conventional free energy of solution at 25°C and the conventional entropy of solution. 

The saturated solution of potassium iodate in water at 25°C has a molality equal to 0.43. Taking the activity coefficient y in this saturated solution to be 0.52, find the conventional free energy of solution at 25°C, and calculate in electron-volts per ion pair the value of L for the removal of tho ions K+ and (IOs) into water at 25°C. 

Lead, excess entropy of solution of noble metals in, 133 Lead-thalium, solid solution, 126 Lead-tin, system, energy of solution, 143 solution, enthalpy of formation, 143 Lead-zinc, alloy (Pb8Zn2), calculation of thermodynamic quantities, 136 Legendre expansion in total ground state wave function of helium, 294 Lennard-Jones 6-12 potential, in analy-... 

Silver-copper, energy of solutions, 142 Silver-gold, excess entropy, 132, 136 excess free energy, 136 Silver-lead, alloy (AgsPb5), calculation of thermodynamic quantities, 136 Silver-zinc, alloy (Ag5Zn5), 129... 

AGg (X) can be removed by assuming that it is equivalent to the polar contribution to the free energy of solution of solute X in a nonpolar hydrocarbon solvent, such as squalane. A second reason for using a reference hydrocarbon solvent is to correct, at least partially, for the fact that the hardcore van der Haals volume is a poor estimate of the size of the cavity and its accessible surface for solvent interactions for aromatic and cyclic solutes. The solvent accessible surface area would logically be the preferred parameter for the cavity term but is very difficult to calculate while the van der Haals volume is readily accessible. With the above approximations the solvent interaction term for... 

---