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 \(\mathrm{GeO}_{2}\).

In this step, germanium dioxide (GeO₂) reacts with carbon (C) to produce germanium (Ge) and carbon monoxide (CO). The balanced chemical equation for this reaction is: \[ GeO_{2}(s) + C(s) \rightarrow Ge(s) + CO(g) \]

In this step, germanium (Ge) reacts with chlorine gas (Cl₂) to produce germanium tetrachloride (GeCl₄). The balanced chemical equation for this reaction is: \[ Ge(s) + 2Cl_{2}(g) \rightarrow GeCl_{4}(g) \]

This step can be broken down into two substeps: Substep 4.1: Hydrolysis of GeCl₄ in water In this substep, germanium tetrachloride (GeCl₄) reacts with water (H₂O) to produce germanium dioxide (GeO₂) and hydrochloric acid (HCl). The balanced chemical equation for this reaction is: \[ GeCl_{4}(g) + 2H_{2}O(l) \rightarrow GeO_{2}(s) + 4HCl(aq) \] Substep 4.2: Reduction of GeO₂ with Hydrogen In this substep, germanium dioxide (GeO₂) reacts with hydrogen gas (H₂) to produce germanium (Ge) and water (H₂O). The balanced chemical equation for this reaction is: \[ GeO_{2}(s) + H_{2}(g) \rightarrow Ge(s) + H_{2}O(g) \] So, the balanced chemical equations for the chemical transformations in the course of forming ultrapure Ge from GeO₂ are as follows: 1. \( GeO_{2}(s) + C(s) \rightarrow Ge(s) + CO(g) \) 2. \( Ge(s) + 2Cl_{2}(g) \rightarrow GeCl_{4}(g) \) 3. \( GeCl_{4}(g) + 2H_{2}O(l) \rightarrow GeO_{2}(s) + 4HCl(aq) \) 4. \( GeO_{2}(s) + H_{2}(g) \rightarrow Ge(s) + H_{2}O(g) \)