Enthalpy change on mixing

j are the contact energies for each species. The energy of mixing Aiy can be replaced by if no volume change takes place on mixing, and for q new contacts formed in solution 

The number of contacts can be estimated from the lattice model by assuming that the probabihty of having a lattice cell occupied by a solvent molecule is simply the volume fraction ( ),. This means that each polymer molecule will be surrounded by (( )i rz) solvent molecules, and for Afj polymer molecules 

This equation is the van Laar expression derived for regular solutions and shows that this approach can be applied to polymer systems. To eliminate z, a dimensionless 

---

Now if you think about it some more, we have two expressions for the energy or enthalpy changes on mixing that are a result of interactions. If the various assumptions we have made (geometric mean, nearest neighbor interactions, pairwise additivity) are all good, then x must be related to solubility parameter differences. 

On this basis the enthalpy change on mixing is given by ... 

The first two terms on the right-hand side of Eq. (12-7) represent the interaction energies of the isolated components, and the last term is the change in internal energy AUm of the system when the species are mixed. If the contact energies can be assumed to be independent of temperature, the enthalpy change on mixing, AHm, is then... 

We are neglecting any enthalpy changes on mixing so that the partial molal enthalpies are equal to the molal enthalpies of the pure components. Tlie molal enthalpy of species i at a particular temperature and pressure, H , is usually expressed in terms of an enthalpy of formation of species i at some reference temperamre 7), plus the change in enthalpy that results when the tem-... 

Therefore, the isothermal volume change on mixing, AmixV, and the isothermal enthalpy change on mixing or the heat of mixing, A ,ix H, are... 

The enthalpy change on mixing, A7/m. is the difference in energy between the mixture F012 and the pure components oi and 02 and is given by... 

Ahm = enthalpy change on mixing pure liquids to give 1 mol of desired composition... 

AB[, AH z = latent heats of vaporization of the pure components at AHfnf AHl enthalpy changes on mixing pure vapors Cl, C2 = molal heat capacities of the pure vapors... 

---