Physical Chemistry , 1st ed.

Solution

According to the half-reactions in Table 8.2, the only possible spontaneous

reaction is the oxidation of Fe to Fe^2 and the reduction of H^ to H 2 gas:

Fe (s) 2H^ (aq, ?? M) →Fe^2 (aq) H 2 (g)

Because we are reversing the Fe standard reduction reaction, the value for “E°

(other half-reaction)” that we use in equation 8.35 is the negative of

0.447 V, or 0.447 V. Using equation 8.35, we have

0.300 V ( 0.05916 V pH) 0.447 V

Solving for pH:

0.147

0.05916 pH

pH2.48

This is a fairly acidic pH, corresponding to an approximate concentration of

3.3 mM.

8.6 Ions in Solution

It is oversimplified to think that ions in solution behave “ideally” even for di-
lute solutions. For molecular solutes like ethanol or CO 2 , interactions between
solute and solvent are minimal or are dominated by hydrogen bonding or some
other polar interaction. However, we usually assume that individual solute
molecules do not strongly affect each other.
For ions in dilute solution, the presence of oppositely charged ions will af-
fect the expected properties of the solution.Diluteionic solutions have con-
centrations of 0.001 M or even less. (That’s one-thousandth of a molarity
unit. For comparison, seawater can be considered as about 0.5 M.) At such
low concentrations, the molarity is almost numerically equal to the molality,
which is the preferred unit for colligative properties (because then the solu-
tion properties do not depend on the identity of the solute). Therefore, we can
shift from molarity concentration units to molality concentration units, and
submit that dilute ionic solutions will have concentrations of 0.001 mor less.
In addition, the charge on the ion will also be a factor. Coulomb’s law, equa-
tion 8.2, says that the force between charges is directly related to the product
of the magnitudes of the charges. Therefore, the force of interaction between
charges of 2 and 2 will be four times as great as between charges of 1 and

1. Thus, the behavior of dilute NaCl should be different from the behavior
   of dilute ZnSO 4 , even if they are the same molal concentration.
   As with other nonideal chemical systems, in order to better understand
   ionic solutions we will go back to the concepts of chemical potentials and ac-
   tivities. In Chapter 4, we defined the chemical potential iof a material as the
   change in the Gibbs free energy versus the molar amount of that material:

i

n

G

i



T,p

(8.36)

We also defined the activity aiof a component in a multicomponent system as
some nonideal parameter that defines the actual chemical potential iin terms
of the standard chemical potential °:i

i°i RTln ai (8.37)

8.6 Ions in Solution 225