Mixing entropy change

Equation (4.434) permits the calculation of mixing entropy (change of entropy at mixing of pure constituents to mixmre) defined as the difference between the entropy of the mixture and the sum of entropies of pure constituents molar mixing entropy (related to one mole of mixture, is therefore (using molar quantities in (4.434), (4.91), (4.292) at the same T, P of pure constituents and in mixture) ... 

Flory—Huggins calculated the mixing entropy change A5m ... 

By the standard methods of statistical thermodynamics it is possible to derive for certain entropy changes general formulas that cannot be derived from the zeroth, first, and second laws of classical thermodynamics. In particular one can obtain formulae for entropy changes in highly di.sperse systems, for those in very cold systems, and for those associated, with the mixing ofvery similar substances. 

Also of importance is the effect of temperature on the gas solubility. From this information it is possible to determine the enthalpy and entropy change experienced by the gas when it changes from the ideal gas state (/z and ) to the mixed liquid state ( andT,). 

Figure 2.13 Mixing of ideal gas A with ideal gas B at constant temperature and constant total pressure. The entropy change AS is given by equation (2.78).

The entropy changes ASa and ASB can be calculated from equation (2.69), which applies to the isothermal reversible expansion of ideal gas, since AS is independent of the path and the same result is obtained for the expansion during the spontaneous mixing process as during the controlled reversible expansion. Equation (2.69) gives... 

With the introduction of these relations into Eq. (41), the configurational entropy change (the entropy of mixing solvent and polymer excluded see Chap. XII) relative to the initial state ax = ay = az = l becomes... 

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. 

If the configurational entropy A>Sm is assumed to represent the total entropy change LSm on mixing, the free energy of mixing is simply obtained by combining Eqs. (10) and (20). That is,... 

Although entropy cannot be strictly localized, some contributing factors to the solvent entropy change induced by the solute are localized in the first solvent shell, and contributions to the entropy of mixing that are proportional to the number of solvent molecules in the first solvation shell might sometimes... 

Solution of long-chain molecules When two liquids mix to form a mixture, the entropy change is similar to that of the volume expansion, as long as the solute molecules have the same size as the solvent molecules and are randomly distributed. But when the solute forms long-chain molecules, the correct method of calculating the entropy was given by Flory. First consider a lattice model where the solvent and the solute molecules have the same volume. Let i and 2 be the number of solvent and... 

Further understanding of the kinetic of template polymerization needs consideration of the process entropy. Applying a well known lattice model, it is easy to see that entropy changes, AS, in free polymerization and the template polymerization, differs considerably. According to the principles of statistical thermodynamics, the entropy of mixing is given by the equation ... 

Here is Boltzmann s constant, or the gas constant per molecule, R/Nq, where No is Avogadro s number (or Na + Nb for one mole of solution) and va and are the volume fractions of solvent and polymer. Comparison of Eq. (2.76) with the entropy of mixing presented earlier in the chapter by Eq. (2.30) shows that they are similar in form, except that now the volume fractions of the components, va and vg, are found to be the most convenient way of expressing the entropy change for polymers, rather than the mole fraction used for most small molecules. This change arises from the differences in size between the large polymer molecules and the small solvent molecules which would normally mean mole fractions close to unity for the solvent, especially when dilute solutions are being studied. 

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