Molar entropy of mixing

The excess molar entropy of mixing is the real entropy of mixing minus the ideal entropy of mixing. Using a binary A-B solution as an example, Ae xSm s... 

The molar entropy of mixing for the ideal solution follows as... 

Figure 9.6 (a) Molar entropy of mixing of ideal polymer solutions for r = 10, 100 and 1000 plotted as a function of the mole fraction of polymer compared with the entropy of mixing of two atoms of similar size, r = 1. (b) Activity of the two components for the same conditions. 

The ideal molar entropy of mixing is then given by... 

Generally, the chemical potential of a constituent substance i in a mixture consists of a unitary part, which is inherent to the pure substance i and independent of its concentration, and a communal part, which depends on the concentration of constituent i [Ref. 3.]. The communal part of the chemical potential of a constituent i in a mixture arises from the entropy of mixing of i For an ideal mixture the molar entropy of mixing of i, s,M, is given from Eq. 3.51 by = -j ln x, and hence the communal part of the chemical potential is expressed by p 4 = -TsM = RT nx, at constant temperature, where x, is the molar fraction of... 

The molar entropy of mixing of the ideal solution is thus not equal to zero. This is due to the fact that the mixing of pure components proceeds spontaneously and is connected with rearrangement of the melt and thus with an increase in entropy. 

If 1 mole of exchange sites is being considered, then S is equal to Avogadro s number and the gas constant, R, can replace kS to give the molar entropy of mixing ... 

Since any impure crystal has at least the entropy of mixing at the absolute zero, its entropy cannot be zero such a substance does not follow the third law of thermodynamics. Some substances that are chemically pure do not fulfill the requirement that the crystal be perfectly ordered at the absolute zero of temperature. Carbon monoxide, CO, and nitric oxide, NO, are classic examples. In the crystals of CO and NO, some molecules are oriented differently than others. In a perfect crystal of CO, all the molecules should be lined up with the oxygen pointing north and the carbon pointing south, for example. In the actual crystal, the two ends of the molecule are oriented randomly it is as if two kinds of carbon monoxide were mixed, half and half. The molar entropy of mixing would be... 

Construct a graph of the molar entropy of mixing AS IR vs. volume fraction for a polymer solution where the polymer degree of polymerization Zj = 10 and 1000. You should do this by plotting AS IR values starting... 

From the thermodynamic viewpoint, miscibility is determined by the molar Gibb s free energy of mixing (AG ) which in turn is governed by the combinatorial molar entropy of mixing and molar enthalpy of mixing as shown in... 

Although the molar entropy of mixing to form an ideal mixture is positive, this is not true for some nonideal mixtures. McGlashan cites the negative value A5m(mix) = —8.8 J mol for an equimolar mixture of diethylamine and water at 322 K. 

Molar entropy of mixing of the ideal solution By using relation [3.18] we obtain ... 

The excess molar entropies of mixing water with cosolvents are obtained from the corresponding enthalpies and Gibbs energies, (x) = [// (Xs)-G (jCs)]/r, from the data in Table 3.13 (provided the same temperature is employed for both enthalpies and Gibbs energies). 

According to Eq.(7.20), the integral molar entropy of mixing is given as... 

The partial molar entropy of mixing of gold in solid Au-Cu alloys, determined at 500°C (773 K) over the complete solution range, is tabulated below. 

Calculate the partial molar entropy of mixing of copper and integral molar entropy of mixing of the solution containing 40 atomX copper. 

The partial molar entropy of mixing of zinc in the Cd-Zn alloy can be calculated from Eq.(8.10) and is given by... 

By comparing this expression with the general formula for the molar entropy of mixing of a solution ... 

The solid curve in Figure 7.6 represents the sum of the two terms in Eq. 7.28 the difference between these curves shows the molar entropy of mixing for ideal solutions. The maximum entropy increase on mixing, for an ideal solution, corresponds to Xa = Xh, = 0.5, for which... 

One model that has found applicability in the lipids area is the regular solution theory developed by Hildebrand and Scott [9] and Scatchard [10]. Incorporating a partial molar entropy of mixing term [11-14] into the regular solution theory yields the following expression for the activity of a component in a liquid mixture ... 

The same principles can also be applied to mixtures of two amorphous polymers 1 and 2 or to a ternary polymer-polymer-solvent system. The presence of polymer 1 reduces the possible arrangements of monomeric units of polymer 2 the molar entropy of mixing can never become as positive as in polymer-solvent systems. The resulting entropy term is only slightly negative and can no longer compensate the positive enthalpy term... 

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