Enthalpy of a solute

In general, the enthalpy of a solution containing r moles H20/mole solute is for reference states of pure solute and solvent at 25°C and 1 atm... 

In order to describe the collapse of a long-chain polymer in a poor solvent, Flory developed a nice and simple theory in terms of entropy and enthalpy of a solution of the polymer in water [14]. In order to obtain these two competing thermodynamic functions, he employed a lattice model which can be justified by the much larger size of the polymer than the solvent molecules. The polymer chains are represented as random walks on a lattice, each site being occupied either by one chain monomer or by a solvent molecule, as shown in Figure 15.8. The fraction of sites occupied by monomers of the polymer can be denoted as 0, which is related to the concentration c, i.e., the number of monomers per cm by 0 = ca, where is the volume of the unit cell in the cubic lattice. Though the lattice model is rather abstract, the essential features of the problem are largely preserved here. This theory provides a convenient framework to describe solutions of all concentrations. 

Fig. 3. The enthalpy of a solution of chlorine in nickel silicides as a function of the molar fraction of silicon.

In other words L is the difference between the total enthalpy of a solution and the total enthalpy of the same amount of pure water. Differentiating Equation (10.67) with respect to 2 we get a familiar expression for L2,... 

The continuous passage from water to a normal solvent is exemplified in Figs. 7.4-7.6, where the free energy, the entropy, and the enthalpy of a solution of methane are plotted as a function of the mole fraction of ethanol. Note that the anomalously low entropy and enthalpy of solution are confined to the water-rich region of the water-ethanol mixtures. 

Perhaps it is appropriate at this junction to pause and reflect on the usefulness of using a two-structure model for understanding the properties of aqueous solutions. Consider for concreteness the enthalpy of a solution of a solute S in the specific model considered above (i.e., Nq = I and -> 0). The intuitive expectation is that the enthalpy of solution should be dominated by the interaction energy of S with the cavity, Eg. A measurement may show that Hg is much more negative [note that the second term in (7.87) is negative, since we chose + PVi < 0]. We would... 

Some care must be exercised in the interpretation of this statement. We saw in Section 7.7 that part of the structural changes (defined in a very broad sense) can be absorbed in the static part of the partial molar entropies and enthalpies of a solute. The above statement applies to any particular definition of the structure which has been adopted for the present purpose. 

The approach for enthalpy involves a more classical thermodynamic treatment. The enthalpy of a solution is composed of contributions from each constituent species in the solution. Each species contributes a pure component enthalpy term and an "excess enthalpy" term. This latter term is based upon the derivative of the species activity coefficient with respect to temperature. 

The slope of the curve at sol=0 is Aso H°°, the molar enthalpy of solution at infinite dilution. If the measurements are made at the standard pressure, AsoiH° is the same as the standard molar enthalpy of solution, Asoi-H °, because the standard molar enthalpy of a solute is the molar enthalpy at p=p° and infinite dilution. 

The relative partial molar enthalpy of a solute is dehned by... 

In the gaseous state, molecules are so far apart that there are virtually no intermolecular forces of attraction between them. Therefore, the solute-solute interaction has little effect on the enthalpy of a solution of a gas. Energy is released when a gas dissolves in a liquid because attraction between solute gas and solvent molecules outweighs the energy needed to separate solvent molecules. 

K12 Kizhnyaev, V.N., Gorkovenko, O.P., Bazhenov, D.N., and Smirnov, A.I., The solubilities and enthalpies of a solution of polyvinyltetrazoles in organic solvents (Russ.), Vysokomol. 

An ideal solute has no effect on the enthalpy of a solution in the sense that the enthalpy of mixing is zero. However, it does affect the entropy, and we found in eqn 3.21 that AS > 0 when a solute dissolves in a solvent to give an ideal solution. We can therefore expect a solute to modify the physical properties of the solution. Apart from lowering the vapor pressure of the solvent, which we have aheady considered, a nonvolatile solute has three main effects it raises the boiling point of a solution, it lowers the freezing point, and it gives rise to an osmotic pressure. 

By definition, the molar enthalpy change on mixing is the difference between the molar enthalpy of a solution and the sum of the molar enthalpies of the components which make it up, all at the same temperature and pressure as the solution, in iheir actual state (see Eq. (74)) weighted by their mole fractions Zj. Consequently to this definition, can be expressed in terms of residual molar enthalpies ... 

Example 6.10 Estimate the enthalpy of a solution of 60 wt% H2SO4 balance water at 200°E, from the partial mass enthalpies computed in Example 6.7. 

Equation (34) would describe the partial molar enthalpy, of a solute in a real solution. From the discussion above, it was shown that for an ideal solution,... 

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