Free enthalpy 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. 

The differentials of the energy functions are complete differentials with the property that the mixed second order differentials are equal to each other. This leads to important relations as exemplified for the free enthalpy by Eq. 3.38 as obtained from Eq. 3.37 ... 

The chemical potential is defined as an intensive energy function to represent the energy level of a chemical substance in terms of the partial molar quantity of free enthalpy of the substance. For open systems permeable to heat, work, and chemical substances, the chemical potential can be used more conveniently to describe the state of the systems than the usual extensive energy functions. This chapter discusses the characteristics of the chemical potential of substances in relation with various thermodynamic energy functions. In a mixture of substances the chemical potential of an individual constituent can be expressed in its unitary part and mixing part. 

These simple equations for the mixing terms of the molar free enthalpy and entropy are characteristic for perfect solutions and are identical with those for ideal gas mixtures. 

For a perfect binary solution the free enthalpy (Gibbs energy) of mixing per mole has been given in Eq. 8.7. We extend this equation 8.7 to a non-ideal binary solution by using the activity coefficients and y2 as shown in Eq. 8.17 ... 

We also see that the excess free enthalpy GE is differentiated with respect to the temperature and the number of moles of the solution to give the excess entropy SF and the partial molar excess free energy of mixing RTlnyi as follows ... 

A discrepancy in free enthalpy between the perfect solution and the non-ideal solution, if the reference system is symmetrical, is generally expressed by the excess free enthalpy GE, which consists of the enthalpy term HE and the entropy term -TSE i.e. GE = HE - TSE. Two situations arise accordingly in non-ideal solutions depending on which of the two terms, He and - TSE, is dominant The non-ideal solution is called regular, if its deviation from the perfect solution is caused mostly by the excess enthalpy (heat of mixing) HE ... 

If two pure liquids, one composed of only na moles of component a and the other of only rib moles of component b, are mixed and the total free enthalpy of the two liquids in separate initial states, Ga, is considered, then the enthalpy of the mixture Ge for an assumed ideal solution can be calculated. Because na + nb = n, na/n = xa and nbln = xb Eq. (4-8) results in ... 

The same result is obtained for mixtures of two perfect gases. Because there are no interactions between the individual particles of perfect gases (atoms or molecules) the decrease in the free enthalpy during mixing can be traced back to the increase in entropy. Mixing increases the disorder of the system. 

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 regular solutions [i , the partial free enthalpy (chemical potential) of substance B in solution, calculated with respect to the solid state, also contains the partial heat of mixing Au (the entropy is equal to that of the ideal case). From the expression for A U on p. 358 we have for the partial heat of mixing ... 

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... 

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