Mixing process Gibbs-energy change

The thermodynamic quantities associated with the mixing of pure liquids to form a solution are important in assessing solution properties. Suppose a moles of component A are combined with b moles of component B to form a solution. The Gibbs energy change associated with this process is given by... 

For construction of the trajectory the process duration Tj, was initially divided into 5 segments. For the considered elementary example the composition of reaction mix and Gibbs energy at the final point of the process coincided with the same characteristics of x , that were obtained from a one-stage calculation with an accuracy to the fraction of percent. Increase in the number of calculation periods did not change anyhow the calculation results. 

A solution is a single-phase mixture of more than one compound, and the driving force for its spontaneous formation from the pure compounds at constant T and p is the negative Gibbs free energy change of the mixing process, —AG, as... 

In Appendix H, we have examined processes involving mixing and assimilation in ideal-gas systems. We have seen that mixing in itself does not contribute anything to the thermodynamics of the process, whereas assimilation and deassimilation do. We now examine similar processes in nonideal systems where intermolecular interactions exist. We shall examine the change in the Gibbs energy, rather than the entropy. But the conclusions are the same. 

Symmetrical ideal solution. Let A and B be similar particles, in the sense discussed in chapter 5. We perform the same process III as in figure 1.3. The corresponding change in Gibbs energy is (1.5). If we perform the same process, but under the same pressure before and after the mixing, we have for the chemical potentials of A and B, in the final states... 

For both idealities, when material is added, the volume must expand to keep P constant and we must add heat to keep T constant. If we mole-fraction average the work given in (6.3.1), we obtain the change in Gibbs energy on mixing, g , which is the reversible isothermal-isobaric work involved in forming a mixture from its pure components cf. 3.7.4 in which we consider the reverse process. 

Another approach stems from a consideration of the Gibbs free energy change AG for a dissolution process, which in general may be expressed in terms of the enthalpy and entropy changes associated with the mixing process ... 

Notice, for instance, that this reaction statement could perfectly well correspond to a process of mixing and m2 moles of reactant substances and R2, respectively, to produce = Ml and fi2 = 2 of product substances and P2, respectively. The change in the Gibbs energy for the general reaction process can be obtained by adding and subtracting the chemical potentials for products and reactants. 

In order for mixing and solution to occur, it is essential that the change in free energy, AG, which is the driving force in the solution process, decrease to below zero. A/f and AG are equal to the change in enthalpy and change in entropy, and for constant temperature the relationship is the classical Gibbs equation ... 

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