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Chapter 18: Problem 1

Write a balanced chemical equation for the overall cell reaction represented as (a) \(\mathrm{Mg}\left|\mathrm{Mg}^{2+} \| \mathrm{Sc}^{3+}\right| \mathrm{Sc}\) (b) Sn \(\left|\mathrm{Sn}^{2+} \| \mathrm{Pb}^{2+}\right| \mathrm{Pb}\) (c) \(\mathrm{Pt}\left|\mathrm{Cl}^{-}\right| \mathrm{Cl}_{2} \| \mathrm{NO}_{3}^{-}|\mathrm{NO}| \mathrm{Pt}\)

Short Answer

Expert verified
Question: Write the balanced chemical equations for the overall cell reactions represented by the given cell notations: (a) Mg|Mg²⁺||Sc³⁺|Sc (b) Sn|Sn²⁺||Pb²⁺|Pb (c) Pt|Cl⁻|Cl₂||NO₃⁻|NO|Pt Answer: (a) 3Mg + 2Sc³⁺ → 3Mg²⁺ + 2Sc (b) Sn + Pb²⁺ → Sn²⁺ + Pb (c) 2Cl⁻ + NO₃⁻ + 2H⁺ → Cl₂ + NO + H₂O

Step by step solution

01

Identify the oxidation and reduction reactions

In this cell notation, Magnesium (\(\mathrm{Mg}\)) is getting oxidized to \(\mathrm{Mg}^{2+}\) while Scandium (\(\mathrm{Sc}\)) ions are getting reduced to form the \(\mathrm{Sc}\) atom.
02

Balance the oxidation and reduction reactions

For oxidation: \(\mathrm{Mg} \rightarrow \mathrm{Mg}^{2+} + 2\mathrm{e}^{-}\) For reduction: \( \mathrm{Sc}^{3+} + 3\mathrm{e}^{-} \rightarrow \mathrm{Sc}\)
03

Combine and balance the overall cell reaction

Multiply the oxidation reaction by 3 and the reduction reaction by 2 to equalize the electrons exchanged. (3)\(\mathrm{Mg} \rightarrow 3\mathrm{Mg}^{2+} + 6\mathrm{e}^{-}\) (2)\(\mathrm{Sc}^{3+} + 6\mathrm{e}^{-} \rightarrow 2\mathrm{Sc}\) Now, combine the reactions: \(3\mathrm{Mg} + 2\mathrm{Sc}^{3+} \rightarrow 3\mathrm{Mg}^{2+} + 2\mathrm{Sc}\) (b) Sn \(\left|\mathrm{Sn}^{2+} \| \mathrm{Pb}^{2+}\right| \mathrm{Pb}\)
04

Identify the oxidation and reduction reactions

In this cell notation, Tin (\(\mathrm{Sn}\)) is getting oxidized to \(\mathrm{Sn}^{2+}\), while Lead (\(\mathrm{Pb}\)) ions are getting reduced to form the \(\mathrm{Pb}\) atom.
05

Balance the oxidation and reduction reactions

For oxidation: \( \mathrm{Sn} \rightarrow \mathrm{Sn}^{2+} + 2\mathrm{e}^{-}\) For reduction: \( \mathrm{Pb}^{2+} + 2\mathrm{e}^{-} \rightarrow \mathrm{Pb}\)
06

Combine and balance the overall cell reaction

The number of electrons exchanged in both reactions is already equal, so we can combine the reactions directly: \(\mathrm{Sn} + \mathrm{Pb}^{2+} \rightarrow \mathrm{Sn}^{2+} + \mathrm{Pb}\) (c) \(\mathrm{Pt}\left|\mathrm{Cl}^{-}\right| \mathrm{Cl}_{2} \| \mathrm{NO}_{3}^{-}|\mathrm{NO}| \mathrm{Pt}\)
07

Identify the oxidation and reduction reactions

In this cell notation, Chloride ions (\(\mathrm{Cl}^{-}\)) are getting oxidized to form \(\mathrm{Cl}_{2}\), while Nitrate ions (\(\mathrm{NO}_{3}^{-}\)) are getting reduced to form \(\mathrm{NO}\).
08

Balance the oxidation and reduction reactions

For oxidation: \( 2\mathrm{Cl}^{-} \rightarrow \mathrm{Cl}_{2} + 2\mathrm{e}^{-}\) For reduction: \( \mathrm{NO}_{3}^{-} + 2\mathrm{e}^{-} + 2\mathrm{H}^+ \rightarrow \mathrm{NO} + \mathrm{H_2 O}\) (Adding \(\mathrm{H}^+\) for balancing the oxygen in the reaction)
09

Combine and balance the overall cell reaction

The number of electrons exchanged in both reactions is already equal, so we can combine the reactions directly: \(2\mathrm{Cl}^{-} + \mathrm{NO}_{3}^{-} + 2\mathrm{H}^+ \rightarrow \mathrm{Cl}_{2} + \mathrm{NO} + \mathrm{H_2 O}\)

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Most popular questions from this chapter

Which of the changes below will increase the voltage of the following cell? $$ \text { Co }\left|\mathrm{Co}^{2+}(0.010 M) \| \mathrm{H}^{+}(0.010 \mathrm{M})\right| \mathrm{H}_{2}(0.500 \mathrm{~atm}) \mid \mathrm{Pt} $$ (a) Increase the volume of \(\mathrm{CoCl}_{2}\) solution from \(100 \mathrm{~mL}\) to \(300 \mathrm{~mL}\). (b) Increase \(\left[\mathrm{H}^{+}\right]\) from \(0.010 \mathrm{M}\) to \(0.500 \mathrm{M}\) (c) Increase the pressure of \(\mathrm{H}_{2}\) from \(0.500 \mathrm{~atm}\) to \(1 \mathrm{~atm}\). (d) Increase the mass of the Co electrode from \(15 \mathrm{~g}\) to \(25 \mathrm{~g}\). (e) Increase \(\left[\mathrm{Co}^{2+}\right]\) from \(0.010 \mathrm{M}\) to \(0.500 \mathrm{M}\).

Write the equation for the reaction, if any, that occurs when each of the following experiments is performed under standard conditions. (a) Sulfur is added to mercury. (b) Manganese dioxide in acidic solution is added to liquid mercury. (c) Aluminum metal is added to a solution of potassium ions.

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 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

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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