Sketch the galvanic cells based on the following overall reactions. Show the direction of electron flow, and identify the cathode and anode. Give the overall balanced equation. Assume that all concentrations are \(1.0 \mathrm{M}\) and that all partial pressures are \(1.0 \mathrm{~atm}\). a. \(\mathrm{Cr}^{3+}(a q)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{Cl}^{-}(a q)\) b. \(\mathrm{Cu}^{2+}(a q)+\mathrm{Mg}(s) \rightleftharpoons \mathrm{Mg}^{2+}(a q)+\mathrm{Cu}(s)\)

a. In the galvanic cell for the chromium and chlorine reaction, the cathode is the reduction half-reaction: \(2Cr^{3+}(aq) + 7H_2O(l) \rightarrow Cr_2O_7^{2-}(aq) + 14H^+(aq) + 6e^-\), and the anode is the oxidation half-reaction: \(2Cl^-(aq) \rightarrow Cl_2(g) + 2e^-\). The overall balanced equation is: \(2Cr^{3+}(aq) + 2Cl^-(aq) + 7H_2O(l) \rightleftharpoons Cr_2O_7^{2-}(aq) + Cl_2(g) + 14H^+(aq)\). b. For the copper and magnesium reaction, the cathode is the reduction half-reaction: \(Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)\), and the anode is the oxidation half-reaction: \(Mg(s) \rightarrow Mg^{2+}(aq) + 2e^-\). The overall balanced equation is: \(Cu^{2+}(aq) + Mg(s) \rightleftharpoons Mg^{2+}(aq) + Cu(s)\).