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Chapter 10: Problem 82

Recharging a battery means forcing a spontaneous redox reaction to run backwards - in the nonspontaneous direction - once all the reactants have been used up. In Practice Problem \(10.24\), you considered a battery made from lead and copper. (a) Write the spontaneous redox reaction for this battery. (b) Write the recharging reaction for this battery.

Short Answer

Expert verified
(a) The spontaneous redox reaction for the battery is: \(Pb^{2+}(aq) + 2Cu(s) \rightarrow Pb(s) + 2Cu^{2+}(aq)\) (b) The recharging reaction for the battery is: \(Pb(s) + 2Cu^{2+}(aq) \rightarrow Pb^{2+}(aq) + 2Cu(s)\)

Step by step solution

01

Identify half-reactions for lead and copper

For a battery made from lead and copper, we need to identify the half-reactions for both the metals involved. Lead reacts as follows: \(Pb^{2+}(aq) + 2e^- \rightarrow Pb(s)\) And copper reacts as: \(Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)\)
02

Combine half-reactions to find the spontaneous redox reaction

Now, we need to combine both half-reactions to find the overall redox reaction for the battery. Balance the number of electrons in both half-reactions by multiplying the entire copper reaction by 2, so the electrons balance out. Then, add both half-reactions: \(Pb^{2+}(aq) + 2e^- \rightarrow Pb(s)\) \(2(Cu^{2+}(aq) + 2e^- \rightarrow Cu(s))\) The balanced redox reaction is: \(Pb^{2+}(aq) + 2Cu(s) \rightarrow Pb(s) + 2Cu^{2+}(aq)\)
03

Write the recharging reaction for the battery

Finally, the recharging reaction for the battery can be found by reversing the spontaneous redox reaction we've found in Step 2: \(Pb(s) + 2Cu^{2+}(aq) \rightarrow Pb^{2+}(aq) + 2Cu(s)\) So, the answers are: (a) The spontaneous redox reaction for the battery is: \(Pb^{2+}(aq) + 2Cu(s) \rightarrow Pb(s) + 2Cu^{2+}(aq)\) (b) The recharging reaction for the battery is: \(Pb(s) + 2Cu^{2+}(aq) \rightarrow Pb^{2+}(aq) + 2Cu(s)\)

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