Numerical Values for Single-Ion Properties

We now take a look at how numerical values are assigned to the thermodynamic properties of single ions. There is more than one method, of course. Most physical chemistry courses for example will mention the Macinnes convention, which postulates that because the K+ and Cr ions have similar properties, their activity coefficients should be identical. This means that 

However, this method runs into problems, such as not working well in mixed electrolytes, and not giving coefficients compatible with Debye-Hiickel coefficients, so it not widely used. 

In the following discussion of single ion properties, we do not at first make any assumptions about the properties of the elements or the hydrogen ion, but we do define properties in terms of differences. Then we introduce the conventions and see how this simplifies notation. The point is that thermodynamics is not dependent on any property being zero, only the notation is. In essence, the procedure followed is a slight variation of the formation from the elements procedure discussed in Chapter 3. 

It will be convenient to continue with HCl in water as our example, so that the question becomes how do we arrive at numerical values for all the thermodynamic properties of the ions H+ and Cl The answer begins with the equation for the formation of H+ and Cl from the elements. 

The standard Gibbs energy change for this reaction is found by combining data from three other reactions. First, the association of hydrogen and chlorine to give HCl gas has the properties 

At this point we can go no further without making some arbitrary decision, i.e., without formulating a convention for ionic properties. The decision is basically to define the free energy of formation of the chloride ion as 

Once this decision is made for one ion, such as Cl, the logjam is broken and values for all other ions can be derived. For example, we know that 

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