Physical Chemistry , 1st ed.

formation reaction of H^. Second, in reality the formation of cations like H^
is always accompanied by the formation of anions.
Just as we have defined the fHvalues of elements to be zero and used
them as benchmarks to determine the heats of formations of compounds,
we make a similar definition for ions. We definethe standard enthalpy of
formation and the standard free energy of formation of the hydrogen ion
as zero:

fG°[H^ (aq)] fH°[H^ (aq)]  0 (8.48)

Thus, the enthalpies and free energies of formation of other ions can be mea-
sured relative to the aqueous hydrogen ion.
The same issue exists for entropies of ions: again, the entropy of any one
ion cannot be experimentally separated from the entropy of an oppositely
charged ion that must be present. Again, we get around this problem by defin-
ing the entropy of the hydrogen ion as zero:

S[H^ (aq)]  0 (8.49)

Entropies of other ions are determined with respect to this benchmark.
The concept of free energies, enthalpies, and entropies of ions are com-
plicated by the fact that these ions are forming in some solvent (most com-
monly, water). The values offH,fG, and Shave contributions from the
solvent molecules rearranging due to the presence of the ion. Enthalpies and
free energies of formation, and even entropies, may be higher or lower than
those for H^ (aq) (that is, they may be positive or negative) depending in
part on the solvation effects. Trends in thermodynamic values for ions may
be difficult to explain unless these effects are taken into account. Note, too,
that this implies that entropies of ions may be negative, in apparent contra-
diction with the very concept of absolute entropy and the third law of ther-
modynamics. You must keep in mind that the entropies of ions are deter-
mined with respect to those of H^ and, as such, ions may have higher or
lower entropies.

Example 8.11

a.Determine fH°[Cl^ (aq)] if the enthalpy of reaction for

^12 H 2 (g) ^12 Cl 2 (g) →H^ (aq) Cl^ (aq)

is 167.2 kJ.

b.Determine fH°[Na^ (aq)] if the enthalpy of reaction for

NaCl (s) →Na^ (aq) Cl^ (aq)

is 3.9 kJ. Use fH°[NaCl] 

411.2 kJ. Assume standard conditions for all

species in both reactions.

Solution

a.If standard conditions are assumed, we know that fH°[H 2 (g)] 

fH°[Cl 2 (g)] 0. By definition,fH°[H^ (aq)] 0, so if we know that

rxnHis 167.2 kJ, we have

167.2 kJ fH[prods] (^) fH[reacts]
167.2 kJ (fH[Cl^ (aq)] 0) (0 0)
167.2 kJ fH[Cl^ (aq)]
8.6 Ions in Solution 229