A Consider the standard reduction potentials of cesium and lithium. $$
\begin{array}{ll} \mathrm{Cs}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow
\mathrm{Cs}(\mathrm{s}) & E^{\circ}=-3.026 \mathrm{~V} \\\
\mathrm{Li}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow
\mathrm{Li}(\mathrm{s}) & E^{\circ}=-3.095 \mathrm{~V} \end{array} $$ The
periodic trends in the properties of the element indicate that fluorine is the
most chemically reactive nonmetal, so perhaps it is not surprising that the
standard reduction potential of fluorine has the highest positive value for a
nonmetallic element. However, periodic properties of the elements also
indicate that cesium should be the most reactive metal. Comparison of the
voltage of the cesium half-reaction with that of lithium shows that the
standard reduction potential of lithium is less negative than that of cesium,
indicating that lithium is a better oxidizer than is cesium.
(a) Calculate the standard cell voltages of the voltaic cells based on the
reaction $$ 2 \mathrm{M}(\mathrm{s})+\mathrm{F}_{2}(\mathrm{~g}) \rightarrow 2
\mathrm{M}^{+}(\mathrm{aq})+2 \mathrm{~F}^{-}(\mathrm{aq}) $$ where
\(\mathrm{M}\) is \(\mathrm{Cs}\) and \(\mathrm{Li}\). (b) Assuming that the
pressure of \(\mathrm{F}_{2}(\mathrm{~g})\) stays at \(1.00 \mathrm{~atm}\), what
concentration does \(\mathrm{Li}^{+}(\mathrm{aq})\) have to be for the voltage
of the \(\mathrm{Li} / \mathrm{F}_{2}\) voltaic cell to equal the standard
voltage of the \(\mathrm{Cs} / \mathrm{F}_{2}\) voltaic cell?
(c) Can you suggest a reason why the standard reduction potential of lithium
is lower than that of cesium, even though periodic trends indicate that cesium
is the more reactive metal?
(d) Calculate \(\Delta G^{o}\) for both the \(\mathrm{Li} / \mathrm{F}_{2}\) and
the \(\mathrm{Cs} / \mathrm{F}_{2}\) voltaic cells from their \(E^{\circ}
\mathrm{s}\). Compare this with the Gibbs' free energies of formation of \(2
\mathrm{~mol} \mathrm{LiF}\) and CsF. Can you explain the difference?
(e) Given the fact that alkali metals react rather violently with water, it
would be unlikely that any voltaic cell can be constructed using Li(s) or
\(\mathrm{Cs}(\mathrm{s})\) in the presence of water. A more likely scenario is
that the voltaic cell would have no solvent, so that the voltaic cell reaction
would be $$ 2 \mathrm{M}(\mathrm{s})+\mathrm{F}_{2}(\mathrm{~g}) \rightarrow 2
\mathrm{MF}(\mathrm{xtal}) $$ where \(\mathrm{M}\) is \(\mathrm{Cs}\) or
\(\mathrm{Li}\). What would be the \(E^{\circ}\) s of the two different voltaic
cells if this were the reaction? (Hint: See your answer to part d.)