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 \(1.0 M\) and that all partial pressures are 1.0 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. \(\mathrm{Cu}^{2+}(a q)+\mathrm{Mg}(s) \rightleftharpoons \mathrm{Mg}^{2+}(a q)+\mathrm{Cu}(s)\)

1. Identify the half-reactions: We need to break the overall reaction into reduction and oxidation half-reactions: - Oxidation half-reaction: \(\mathrm{Cl}_{2}(g) \rightarrow 2\mathrm{Cl}^{-}(a q)\) - Reduction half-reaction: \(\mathrm{Cr}^{3+}(a q) \rightarrow \frac{1}{2}\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)\), multiply by 2 to balance the Cr atoms: \(2\mathrm{Cr}^{3+}(a q) \rightarrow \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)\) 2. Identify the anode and cathode: - Anode (oxidation): \(\mathrm{Cl}_{2}(g) \rightarrow 2\mathrm{Cl}^{-}(a q)\) - Cathode (reduction): \(2\mathrm{Cr}^{3+}(a q) \rightarrow \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)\) 3. Sketch the galvanic cell: - Anode: Chlorine gas is bubbled through an aqueous solution containing Cl⁻ ions. Electrons flow from the anode to the cathode through an external wire. - Cathode: Chromium(III) ions are present in the aqueous solution to form dichromate ions, Cr2O72-. - Salt bridge: A salt bridge or porous disk connects the two half-cells to maintain charge neutrality. 4. Write the overall balanced equation: The overall balanced equation is given in the problem statement itself: \(\mathrm{Cr}^{3+}(a q)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{Cl}^{-}(a q)\)

1. Identify the half-reactions: We need to break the overall reaction into reduction and oxidation half-reactions: - Oxidation half-reaction: \(\mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+}(a q) + 2e^-\) - Reduction half-reaction: \(\mathrm{Cu}^{2+}(a q) + 2e^- \rightarrow \mathrm{Cu}(s)\) 2. Identify the anode and cathode: - Anode (oxidation): \(\mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+}(a q) + 2e^-\) - Cathode (reduction): \(\mathrm{Cu}^{2+}(a q) + 2e^- \rightarrow \mathrm{Cu}(s)\) 3. Sketch the galvanic cell: - Anode: Mg(s) metal electrode is oxidized to Mg²⁺(aq) ions and loses 2 electrons. - Cathode: Cu²⁺(aq) ions are reduced to Cu(s) metal by gaining 2 electrons. - Salt bridge: A salt bridge or porous disk connects the two half-cells to maintain charge neutrality. 4. Write the overall balanced equation: The overall balanced equation is given in the problem statement itself: \(\mathrm{Cu}^{2+}(a q)+\mathrm{Mg}(s) \rightleftharpoons \mathrm{Mg}^{2+}(a q)+\mathrm{Cu}(s)\)