Ultrapure germanium, like silicon, is used in semiconductors. Germanium of
"ordinary" purity is prepared by the high-temperature reduction of
\(\mathrm{GeO}_{2}\) with carbon. The Ge is converted to \(\mathrm{GeCl}_{4}\) by
treatment with \(\mathrm{Cl}_{2}\) and then purified by distillation;
\(\mathrm{GeCl}_{4}\) is then hydrolyzed in water to \(\mathrm{GeO}_{2}\) and
reduced to the elemental form with \(\mathrm{H}_{2}\). The element is then zone
refined. Write a balanced chemical equation for each of the chemical
transformations in the course of forming ultrapure Ge from \(\mathrm{GeO}_{2}\).