(a) Which ion is smaller, \(\mathrm{Co}^{3+}\) or \(\mathrm{Co}^{4+}
?(\mathbf{b})\) In a lithium-ion battery that is discharging to power a device,
for every \(\mathrm{Li}^{+}\) that inserts into the lithium cobalt oxide
electrode, a \(\mathrm{Co}^{4+}\) ion must be reduced to a \(\mathrm{Co}^{3+}\)
ion to balance charge. Using the CRC Handbook of Chemistry and Physics or
other standard reference, find the ionic radii of \(\mathrm{Li}^{+},
\mathrm{Co}^{3+},\) and \(\mathrm{Co}^{4+} .\) Order these ions from smallest to
largest. (c) Will the lithium cobalt oxide cathode expand or contract as
lithium ions are inserted? (d) Lithium is not nearly as abundant as sodium. If
sodium ion batteries were developed that function in the same manner as
lithium ion batteries, do you think "sodium cobalt oxide" would still work as
the electrode material? Explain. (e) If you don’t think cobalt would work as
the redox-active partner ion in the sodium version of the electrode, suggest
an alternative metal ion and explain your reasoning.