Standard entropy of solution

The study of thermodynamic properties of aqueous solutions of inert gases was the subject of my PhD thesis. In the early 1960s, not much was known about these systems. Experimental data were very scarce and inaccurate. Theory was highly speculative. Nevertheless, I chose this subject mainly for one reason I was fascinated by the hearsay that inert solute dissolved in water lowers the entropy of the system. Lowering the entropy meant increasing the structure of water. But why How can inert solutes cause an increase in structure and lower the entropy That was quite a mystery. I say it was hearsay because the experimental data on solubilities of inert solutes was very inaccurate. The entropy of solution was determined from the temperature dependence of the solubility. That renders the uncertainty of the values of the entropy of solution even larger than the uncertainty of the solubilities themselves. At that time I was not aware of the fact that the so-called standard entropy of solution was itself an uncertain measure of the entropy of solvation. 

The temperature dependence of the solubility is better expressed in terms of the standard entropy of solution. In Chapter 4, we introduced two definitions of the standard entropy of solutions corresponding to the processes I and II. The pertinent relations are... 

Fig. 7.5. Standard entropy of solution zl5s°(II) (in cal/mole deg) of methane as a function of mole fraction of ethanol at two temperatures.

It is very important to stress that the last equality holds only for these particular standard entropies of solution, which is why we have included the symbol II (see Section 4.11) in the notation. We also note that the quantities on the rhs of (8.121) are measurable, since and A/bt are usually measured as a function of temperature at constant pressure. Thus, (8.121) provides an approximate method of estimating the entropy change for the HI process. 

Equation (1) can be viewed in an over-simplistic manner and it might be assumed that it would be relatively easy to calculate the retention volume of a solute from the distribution coefficient, which, in turn, could be calculated from a knowledge of the standard enthalpy and standard entropy of distribution. Unfortunately, these properties of a distribution system are bulk properties. They represent, in a single measurement, the net effect of a large number of different types of molecular interactions which, individually, are almost impossible to separately identify and assess quantitatively. 

Different portions of the standard free energy of distribution can he allotted to different parts of a molecule and, thus, their contribution to solute retention can be disclosed. In addition, from the relative values of the standard enthalpy and standard entropy of each portion or group, the nianner in which the different groups interact with the stationary phase may also be revealed. 

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. 

When ammonium nitrate, NH jNOj, dissolves in water, it absorbs heat. Consequently, its standard enthalpy of solution must be positive. This means that the entropy change caused by ammonium nitrate going from solid to solution must increase for the process to proceed spontaneously. This is exactly what one would expect based on the concept of entropy as a measure of randomness or disorder. 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

If a2/ax = gim2lgxmx m2/mx (a = activity, g = molal activity coefficient, m = molality) if Henry s law is obeyed and a = gm, mh and m2 are the molal solubilities of the polymorphs, and if the standard molar enthalpies and standard molar entropies of solution are, respectively,... 

Fig. 5.3. Standard molar entropy of solution as a function of cation bonding strength. By convention the entropy of is taken as zero but H2O would be a more natural choice in this figure.

The total entropy of a substance in a state defined as standard. Thus, the standard states of a solid or a liquid are regarded as those of the pure solid or Ihe pure liquid, respectively, and at a stated temperature. The standard state of a gas is at 1 atmosphere pressure and specified temperature, and its standard entropy is the change of entropy accompanying its expansion to zero pressure, or its compression from zero pressure to 1 atmosphere. The standard entropy of an ion is defined in a solution of unit activity, by assuming that the standard entropy of the hydrogen ion is zero. 

Thus Af G ° for a species in aqueous solution can be determined calorimetrically. The standard entropy of formation of a species at 298.15 K is related to its standard molar entropy at 298.15 K by... 

Electroneutrality is required in all solutions thus, it is not possible to measure the properties of a single ion without influence from an ion of opposite charge. By convention, the standard enthalpy of formation and the standard entropy of the... 

Problem The standard heat of solution of 1 g. atom of potassium in dilute acid is found to be — 60.15 kcal. at 25 C. The standard oxidation potential of this metal is 2.924 volt at the same temperature the standard entropy of solid potassium is 15.2 e.u. g. atom and of gaseous hydrogen it is 31.21 e.u. mole. Calculate the standard entropy of the potassium ion in solution at 25 C. 

For anions, in particular, an entirely different procedure is adopted to determine the standard entropy of the ion in solution. Consider the solid salt Mp A, in equilibrium with its ions M+ and A in a saturated solution thus,... 

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