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Chapter 18: Problem 7

Consider a salt bridge cell in which the anode is a manganese rod immersed in an aqueous solution of manganese(II) sulfate. The cathode is a chromium strip immersed in an aqueous solution of chromium(III) sulfate. Sketch a diagram of the cell, indicating the flow of the current throughout. Write the half- equations for the electrode reactions, the overall equation, and the abbreviated notation for the cell.

Short Answer

Expert verified
Answer: The half-reactions are: Anode: Mn(s) -> Mn^{2+}(aq) + 2e^- Cathode: Cr^{3+}(aq) + 3e^- -> Cr(s) The overall equation is: 3Mn(s) + 2Cr^{3+}(aq) -> 3Mn^{2+}(aq) + 2Cr(s) The abbreviated notation for the cell is: Mn(s)|Mn^{2+}(aq)||Cr^{3+}(aq)|Cr(s)

Step by step solution

01

Sketch a Diagram of the Cell

Draw a diagram with a manganese (Mn) rod as the anode and a chromium (Cr) strip as the cathode. The anode should be immersed in an aqueous solution of manganese(II) sulfate (MnSO4), and the cathode should be immersed in an aqueous solution of chromium(III) sulfate (Cr2(SO4)3). Connect the anode and the cathode with a wire, and also connect them with a salt bridge, which allows the flow of ions but not electrons.
02

Identify the Redox Reactions

In this cell, the anode (Mn rod) undergoes oxidation, while the cathode (Cr strip) undergoes reduction. The oxidation half-reaction occurring at the anode is: Mn(s) -> Mn^{2+}(aq) + 2e^- The reduction half-reaction occurring at the cathode is: Cr^{3+}(aq) + 3e^- -> Cr(s)
03

Write the Overall Equation

To combine the two half-equations and get the overall equation, we must ensure that the number of electrons in both half-reactions is the same. To achieve this, multiply the first half-reaction by 3 and the second half-reaction by 2: 3Mn(s) -> 3Mn^{2+}(aq) + 6e^- 2Cr^{3+}(aq) + 6e^- -> 2Cr(s) Now we can add both half-reactions: 3Mn(s) + 2Cr^{3+}(aq) -> 3Mn^{2+}(aq) + 2Cr(s)
04

Write the Abbreviated Notation for the Cell

In the abbreviated notation, the anode is written first, followed by its solution, then the cathode and its solution. For the anode, the half-reaction is: Mn(s) -> Mn^{2+}(aq) For the cathode, the half-reaction is: Cr^{3+}(aq) -> Cr(s) So, the abbreviated notation is: Mn(s)|Mn^{2+}(aq)||Cr^{3+}(aq)|Cr(s) In summary, the cell consists of a manganese anode and a chromium cathode connected by a salt bridge, with the following half-reactions: Anode: Mn(s) -> Mn^{2+}(aq) + 2e^- Cathode: Cr^{3+}(aq) + 3e^- -> Cr(s) The overall equation is: 3Mn(s) + 2Cr^{3+}(aq) -> 3Mn^{2+}(aq) + 2Cr(s) And the abbreviated notation for the cell is: Mn(s)|Mn^{2+}(aq)||Cr^{3+}(aq)|Cr(s)

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Most popular questions from this chapter

Calculate voltages of the following cells at \(25^{\circ} \mathrm{C}\) and under the following conditions. (a) \(\mathrm{Fe}\left|\mathrm{Fe}^{2+}(0.010 \mathrm{M}) \| \mathrm{Cu}^{2+}(0.10 \mathrm{M})\right| \mathrm{Cu}\) (b) \(\mathrm{Pt}\left|\mathrm{Sn}^{2+}(0.10 \mathrm{M}), \mathrm{Sn}^{4+}(0.010 \mathrm{M}) \| \mathrm{Co}^{2+}(0.10 \mathrm{M})\right| \mathrm{Co}\)

Calculate \(E^{\circ}\) for the following cells: (a) \(\mathrm{Pb}\left|\mathrm{PbSO}_{4} \| \mathrm{Pb}^{2+}\right| \mathrm{Pb}\) (b) \(\mathrm{Pt}\left|\mathrm{Cl}_{2}\right| \mathrm{ClO}_{3}^{-} \| \mathrm{O}_{2}\left|\mathrm{H}_{2} \mathrm{O}\right| \mathrm{Pt}\) (c) \(\mathrm{Pt}\left|\mathrm{OH}^{-}\right| \mathrm{O}_{2} \| \mathrm{ClO}_{3}^{-}, \mathrm{Cl}^{-} \mid \mathrm{Pt} \quad\) (basic medium)

Which species in each pair is the stronger oxidizing agent? (a) \(\mathrm{NO}_{3}^{-}\) or \(\mathrm{I}_{2}\) (b) \(\mathrm{Fe}(\mathrm{OH})_{3}\) or \(\mathrm{S}\) (c) \(\mathrm{Mn}^{2+}\) or \(\mathrm{MnO}_{2}\) (d) \(\mathrm{ClO}_{3}^{-}\) in acidic solution or \(\mathrm{ClO}_{3}^{-}\) in basic solution

Consider the reaction below at \(25^{\circ} \mathrm{C}\) : $$ 3 \mathrm{SO}_{4}{ }^{2-}(a q)+12 \mathrm{H}^{+}(a q)+2 \mathrm{Cr}(s) \longrightarrow 3 \mathrm{SO}_{2}(g)+2 \mathrm{Cr}^{3+}(a q)+6 \mathrm{H}_{2} \mathrm{O} $$ Use Table \(18.1\) to answer the following questions. Support your answers with calculations. (a) Is the reaction spontaneous at standard conditions? (b) Is the reaction spontaneous at a \(\mathrm{pH}\) of \(3.00\) with all other ionic species at \(0.100 \mathrm{M}\) and gases at \(1.00\) atm? (c) Is the reaction spontaneous at a pH of \(8.00\) with all other ionic species at \(0.100 \mathrm{M}\) and gases at \(1.00 \mathrm{~atm}\) ? (d) At what \(\mathrm{pH}\) is the reaction at equilibrium with all other ionic species at \(0.100 \mathrm{M}\) and gases at \(1.00 \mathrm{~atm}\) ?

Which of the following reactions is (are) spontaneous at standard conditions? (a) \(\mathrm{Zn}(s)+2 \mathrm{Fe}^{3+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+2 \mathrm{Fe}^{2+}(a q)\) (b) \(\mathrm{Cu}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+\mathrm{H}_{2}(g)\) (c) \(2 \mathrm{Br}^{-}(a q)+\mathrm{I}_{2}(s) \longrightarrow \mathrm{Br}_{2}(l)+2 \mathrm{I}^{-}(a q)\)
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