Solubility, Chemical Potential, and Ion Activities

The chemical potential of species i, is expressed in terms of the Gibbs free energy added to a system at constant T and P, as well as relative to the mole fraction of each added increment of i. When adding an incremental number of molecules of i, free energy is introduced in the form of internal energies of i as well as by the 

Because i. = G. = H. TS., the chemical potential can be nsed to assess the tendency of components i to be transferred to another system or transformed within a system in other words, matter flows spontaneously from a region of high chemical potential to a region of low chemical potential, jnst as mass flows from a position of high gravitational potential to a position of low gravitational potential. The chemical potential, therefore, can be nsed to determine whether or not a system is in equilib-rinm at eqnilibrium, the chemical potential of each snbstance is the same in all phases appearing in the system. 

An ideal solution can be defined as a solntion in which the chemical potential of each species is given by the expression 

Usnally, only very dilute solutions can be considered ideal. In most aqueous solutions, ions are stabilized because they are solvated by water molecules. As the ionic strength is increased, ions interact with each other. Thus, when calculating the chemical potential of species i, a term that takes into account the deviation from ideal conditions is added. This term is called an excess term and can be either positive or negative. The term usually is written as 7 riny., where y. is the activity coefficient of component i. The complete expression for the chemical potential of species i then becomes 

As mentioned previously, in this expression, ix/ CP, 7) is the chemical potential of a pure species i. For a pure species i, x.= l, and consequently, from Eq. 2.10, y=l, too. 

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