Free enthalpy of mixing

Figure 8. Free enthalpy of mixing G of binary solid solutions (regular) Ca,. (PO ) OH F as a function of x at W/2.303 RT = 1.4.

Similar to the entropic contribution, one can also express the free enthalpy of mixing per unit volume. 

According to the Hildebrand concept, the free enthalpy of mixing AH is given by [79]... 

Fig. 4. Vectorial representation of solubility parameters used to calculate the free enthalpy of mixing as a function of conversion, q...

Figure 52. The free enthalpy of mixing of the fast ion conductor Nasicon (Nai+ ZiyPsyM/tiJ (y= x/3) obtained from emf measurements as a function of composition.272 The shape of the curves indicates the stability of a thermodynamic two phase system at T< 615 K. Reprinted from U. Warhus, J. Maier, and A. Rabenau, J. Solid St Chem., 72 (1988) 113-125. Copyright 1988 with permission from Elsevier.

For instance, separating a two-gas mixture requires a minimum amount of energy equal to their free enthalpy of mixing therefore for separating N moles of two gases with an x molar fraction for the first gas we have, assuming a mixture of two ideal gases ... 

This can be done using high concentrated HC1 because this lowers HC1 free enthalpy of mixing with H20 close to zero and also increases the solubility of CuCl and therefore the variation of the free enthalpy of mixing of CuCl with the HC1/H20 solution (Fritz, 1982). However under such conditions the purity of the hydrogen needs to be checked. 

According to Eq. (14) three effects contribute to the excess free enthalpy of mixing ... 

In view of thermodynamics the ceiling temperature looks like a melting point. Below and above this temperature the system consists of 100% polymer and of 100% monomer, respectively. This is shown in Fig. 20.2. If, however, the polymer is soluble in its monomer, then the free enthalpy of mixing also plays a role and the result will be that the "melting point" is not as sharp as shown there will be a gradual change (i.e. the dashed line) from 100% polymer to 100% monomer. The ceiling temperature is in this case defined as the temperature where the amount of monomer equals the amount of polymer (i.e. at 50%) and equal to (see, e.g. Ivin, 2000) ... 

For gaseous samples the enrichment is determined by the free enthalpies of condensation and mixing. The free enthalpy of mixing is mainly a function of the polymer. Thus for some polymers very useful relations exists which derive the enrichment factors of various substances from their boiling points (Table 6.5-3). 

Here, AG is the free enthalpy of mixing, u. is the chemical potential of component i, and X. is its mole fraction. ... 

The layered structure cannot be refined indefinitely by deformation due to the increasing hardness with decreasing crystallite size (for details see Sect. 3.3.2). The main alloying, therefore, occurs by an interdiffusion reaction at the created clean interfaces, if a thermodynamic driving force (negative free enthalpy of mixing) exists for this diffusion couple. The required temperature rise is provided by the heat released during the ball collisions (Sect. 3.3.2). 

Flory and Rehner have proposed that the free enthalpy change during swelling depends on two contributions, the free enthalpy of mixing network and solvent AG and a contribution from elasticity, the free enthalpy of elastic deformation... 

Figure 52. The free enthalpy of mixing of the fast ion conductor Nasicon (Nai+ r2P3 jSi/)i2)...

For polymers the contribution of the entropy of mixing ASm to the free enthalpy of mixing AGm is small. According to the lattice model of Flory/Huggins (Sperling 1986), AGm is assumed to be... 

For strictly binary systems, appropriate differentiation of the free enthalpy of mixing leads to... 

Using the rules of regular solution theory [26] we derive the free enthalpy of mixing two monodisperse copolymers P and find [27]... 

The separation of substances which mix spontaneously can be accoiiqrlished either via a demon or some device which consumes energy supplied in the form of heat or mechanical work. The basic principle of any separation process is that a certain amount of energy is required to accomplish the separation. Hence, two substances A and 5 will mix spontaneously when the free entMpy of the product (the mixture) is smaller than the sum of the free enthalpies of the pure substances. The minimum amount of energy (W, necessary to accomplish complete separation is at least equal to or larger than the free enthalpy of mixing. 

Whether or not a certain process, i.e. chemical reaction, mixing of components etc, is spontaneous depends upon AH and T AS. For the mixing of two or more components the free enthalpy of mixing (AG ) with the subscript m for mixing, is given by. 

The change in the free enthalpy- of mixing aG which occurs on mixing n, mol of component 1 with n, mol of component 2 at constant P and T is now given by... 

The number of moles may be replaced by mole fraction and this lead to the general expression for the free enthalpy of mixing per mole for an ideal solution. 

Suppose that the temperature is decreased from T to T2. The composition A at temperature T2 lies inside the demixing gap and is not stable thermodynamically. The curve of AGn, at temperature T2 is also given in figure III - 24. At temperature T2 all compositions between and ( ) can reduce their free enthalpies of mixing by demixing into two phases with of compositions respectively (see figure III - 22). These two phases are in equilibrium with each other since they lie on the same tangent to the AG- curve, i.e., the chemical potential in phase 0 must be equal to that of phase <() . ... 

Figure III - 27. Schematic drawing of the free enthalpy of mixing (AG ,) as a function of the...

One of the main variables in the immersion precipitation process is the choice of the solvent/nonsolvent system. In order to prepare a membrane from a polymer by phase inversion the polymer must be soluble. Although one or more solvents may be suitable for the chosen polymer, the solvent and nonsolvent must be completely miscible. Water is frequently used as a nonsolvent but other nonsolvents can also be used. Some solvents for cellulose acetate and polysulfone which are miscible with water are listed in table III.6. The solubility of these organic solvents with water must be considered further. As described in the previous section, the miscibility of components of all kind is determined by the free enthalpy of mixing... 

---