Entropy change solution

Prediction of solubility for simple ionic compounds is difficult since we need to know not only values of hydration and lattice enthalpies but also entropy changes on solution before any informed prediction can be given. Even then kinetic factors must be considered. 

Consider the entropy change in forming one mole of solution at constant T from 4>m moles of 1 (of molar volume V ) and ni2 moles of 2 (of molar volume V2). In the pure state, the 0m 1 moles of 1 occupy (or have available) the volume 0mIF], and the 0m2 moles of 2 have available the volume 0m2 2- However, when the solution is formed, both the 0m 1 moles of 1 and the 0m2 moles of 2 have available to them the entire volume of the solution 0mi V +0m2 2- The entropy change experienced by component 1 due to this available volume change is... 

As known, SEC separates molecules and particles according to their hydro-dynamic volume in solution. In an ideal case, the SEC separation is based solely on entropy changes and is not accompanied with any enthalpic processes. In real systems, however, enthalpic interactions among components of the chromatographic system often play a nonnegligible role and affect the corresponding retention volumes (Vr) of samples. This is clearly evident from the elution behavior of small molecules, which depends rather strongly on their chemical nature and on the properties of eluent used. This is the case even for... 

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. 

Consider, for example, the saturated solution of a sparingly soluble crystal. Let AII>a, and AS, t denote the heat of solution and the entropy of solution when a few additional pairs are taken into the saturated solution. The condition for equilibrium between the solid and the solution. is, of course, that there shall be no change in the free energy in this process a saturated solution is one for which AF is zero. Hence we may write at once... 

Solutes in Methanol Solution. In Table 23 we have seen that for four solutes in methanol the viscosity //-coefficients are positive. This is the case even for KC1 and KBr, for which the coefficients are negative in aqueous solution. In Sec. 88 it was pointed out that it would be of interest to see whether this inversion is likewise accompanied by a change in sign for the ionic entropy. Although no accurate values for the entropy of solution of salts in methanol arc available, reliable estimates have been made for KC1, KBr, and NaCl.1 Since the /1-coefficients of KC1 and KBr have been determined both in methanol and in water, all the required data are available for these two solutes. The values of A/S" given in Table 29 have been taken from Table 34 in Chapter 12, where the method of derivation is explained. The cratie term included in each of these values is 14 cal/deg, as already mentioned in Sec. 90. 

The Number of Dipoles per Unit Volume. The Entropy Change Accompanying Proton Transfers. The Equilibrium between a Solid and Its Saturated Solution. Examples of Values of L and AF°. The Change of Solubility with Temperature. Uni-divalent and Other Solutes. Lithium Carbonate in Aqueous Solution. H2COj in Aqueous Solution. Comparison between HjCOj and Li2C03 in Aqueous Solution. Heats of Solution and the Conventional Free Energies and Entropies of Solution. 

Table III presents integral excess entropies of formation for some solid and liquid solutions obtained by means of equilibrium techniques. Except for the alloys marked by a letter b, the excess entropy can be taken as a measure of the effect of the change of the vibrational spectrum in the formation of the solution. The entropy change associated with the electrons, although a real effect as shown by Rayne s54 measurements of the electronic specific heat of a-brasses, is too small to be of importance in these numbers. Attention is directed to the very appreciable magnitude of the vibrational entropy contribution in many of these alloys, and to the fact that whether the alloy is solid or liquid is not of primary importance. It is difficult to relate even the sign of the excess entropy to the properties of the individual constituents.

Potassium nitrate dissolves readily in water, and its enthalpy of solution is +34.9 kj-niol. (a) Does the enthalpy of solution favor the dissolving process (b) Is the entropy change of the system likely to be positive or negative when the salt dissolves (c) Is the entropy change of the system primarily a result of changes in positional disorder or thermal disorder ... 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

The formation of the solution may be conceived to occur in two steps disorientation of the polymer molecules and mixing of the disoriented polymer with solvent. The separate entropy changes are readily obtained as follows The first is given by Eq. (8) with ni = 0, i.e. 

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. 

Solid ammonium nitrate is an orderly, crystalline substance, a state considerably less random than a solution of ions in water. In this case, the positive entropy change outweighs the enthalpy change. That is TAS > AH. The Gibbs free energy change is negative, so the process will proceed spontaneously. 

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