Spontaneity escaping tendency

In Chapter 5, we considered systems in which composition becomes a variable, and defined and described the chemical potential. We showed that the chemical potential provides the condition for spontaneity or equilibrium. It is the potential that drives the flow of mass in a chemical process, A useful quantity related to the chemical potential is the fugacity. It can also be thought of as a measure of the flow of mass in a chemical process, and can be used to determine the point of equilibrium. It is often known as the escaping tendency since it can be used to describe the ease with which mass flows from one phase to another, particularly the flow from a solid or liquid phase to a gas phase. 

Thus, we may say that the escaping tendency of the iodine is greater in the water than in the carbon tetrachloride phase, and the chemical potentials in the two phases describe the spontaneous direction of transport from one phase to the other. 

Thus, for a spontaneous reaction, we can say that the sum of the escaping tendencies for the reactants is greater than the sum of the escaping tendencies for the products. 

The condition of Equation (13.7) can be met only if p,j = p,n, which is the condition of transfer equilibrium between phases. Or, to put the argument differently, if the chemical potentials (escaping tendencies) of a substance in two phases differ, spontaneous transfer will occur from the phase of higher chemical potential to the phase of lower chemical potential, with a decrease in the Gibbs function of the system, until the chemical potentials are equal (see Section 10.5). For each component present in aU p phases, (p 1) equations of the form of Equation (13.7) provide constraints at transfer equilibrium. Furthermore, an equation of the form of Equation (13.7) can be written for each one of the C components in the system in transfer equUibrium between any two phases. Thus, C(p — 1) independent relationships among the chemical potentials can be written. As chemical potentials are functions of the mole fractions at constant temperamre and pressure, C(p — 1) relationships exist among the mole fractions. If we sum the independent relationships for temperature. 

The nonpolar portion of surfactant ions has an important role in promoting the adsorption process because it increases the affinity of these organic ions to the interfacial region. The effect derives from mutual attraction between the hydrophobic tails as well as their tendency to escape from an aqueous environment. That mechanism is precisely the same one which causes the spontaneous formation of micelles in aqueous solution and is known as the hydrophobic effect [78]. In the case of surfactant adsorption, it is responsible for the formation of surface aggregates. However, it is not easy to accurately predict the shape and the size of such molecular associations in the same way that the structure of bulk aggregates can be determined from the geometry of the molecule. This is because the surface imposes different restrictions on the organization of the adsorbed layer. 

A solution consisting of a volatile liquid solvent and a nonvolatile solute forms spontaneously because of the increase in entropy that accompanies their mixing. In effect, the solvent molecules are stabilized in their liquid state by this process and thus have a lower tendency to escape into the vapor state. Therefore, when a nonvolatile solute is present, the vapor pressure of the solvent is lower than the vapor pressure of the pure solvent, as illustrated in FIGURE 13.21. 

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