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Chapter 24: Problem 36

Show that the oxidation of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) to \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) referred to on page 1098 should occur spontaneously in alkaline solution with \(\mathrm{H}_{2} \mathrm{O}_{2}\) as an oxidizing agent.

Short Answer

Expert verified
The spontaneity of the oxidation of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\) to \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) in an alkaline solution with \(\mathrm{H}_{2} \mathrm{O}_{2}\) as an oxidizing agent can be shown by writing the half-reactions, combining them into the redox reaction, and using the Nernst equation to calculate the redox potential. If the potential is positive, the reaction is spontaneous.

Step by step solution

01

Write the Half-reactions

Begin by writing the half-reactions. For the oxidation of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+}\), the half-reaction is: \[ \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+} → \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} + e^- \]. For the reduction of \(\mathrm{H}_{2} \mathrm{O}_{2}\), in alkaline conditions, the half-reaction is: \[ \mathrm{H}_{2} \mathrm{O}_{2} + 2 e^- → 2 OH^- \]
02

Combine the Half-reactions

Combine the two half-reactions to form the overall redox reaction. Ensure that the electrons are balanced. This yields: \[ \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{2+} + \mathrm{H}_{2} \mathrm{O}_{2} → \left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} + 2 OH^- \]
03

Use the Nernst Equation

The Nernst equation is used to calculate the redox potential of a half-cell in an electrochemical cell. It is given by: \[ E = E^\circ - \frac{RT}{nF} \ln Q \] where \(E\) is the cell potential, \(E^\circ\) is the standard cell potential, \(R\) is the universal gas constant, \(T\) is the temperature in Kelvin, \(n\) is the number of moles of electrons transferred in the redox reaction, \(F\) is the Faraday's constant and \(Q\) is the reaction quotient. The values of \(E^\circ\) for the half-reactions can be obtained from standard redox potential tables. Calculate \(E\) for the reaction and if \(E>0\), the reaction is spontaneous.
04

Determine Spontaneity

If the calculated cell potential (\(E\)) is positive, the reaction is spontaneous. If \(E=0\), the reaction is in equilibrium. If \(E<0\), the reaction is non-spontaneous and will not occur under standard conditions.

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Most popular questions from this chapter

Acetyl acetone undergoes an isomerization to form a type of alcohol called an enol. The enol, abbreviated acacH, can act as a bidentate ligand as the anion acac^-. Which of the following compounds are optically active: \(\operatorname{Co}(\mathrm{acac})_{3} ;\) trans\(\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2} ; \operatorname{cis}-\left[\mathrm{Co}(\mathrm{acac})_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right] \mathrm{Cl}_{2} ?\)

Predict: (a) whether the square-planar complex ion \(\left[\mathrm{Cu}(\mathrm{py})_{4}\right]^{2+}\) is diamagnetic or paramagnetic (b) whether octahedral \(\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{3-}\) or tetrahedral \(\left[\mathrm{FeCl}_{4}\right]^{-}\) has the greater number of unpaired electrons.

How many different structures are possible for each of the following complex ions? (a) \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)\left(\mathrm{NH}_{3}\right)_{5}\right]^{3+}\) (b) \(\left[\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\left(\mathrm{NH}_{3}\right)_{4}\right]^{3+}\) (c) \(\left[\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\left(\mathrm{NH}_{3}\right)_{3}\right]^{3+}\) (d) \(\left[\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)_{2}\right]^{3+}\)

We have seen that complex formation can stabilize oxidation states. An important illustration of this fact is the oxidation of water in acidic solutions by \(\mathrm{Co}^{3+}(\) aq) but not by \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+} .\) Use the following data. \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}+\mathrm{e}^{-} \longrightarrow\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) $$ E^{\circ}=1.82 \mathrm{V} $$ \(\left[\operatorname{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}+3 \mathrm{en} \longrightarrow\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{2+}+6 \mathrm{H}_{2} \mathrm{O}(1)\) $$ \log \beta_{3}=12.18 $$ \(\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}+3 \mathrm{en} \longrightarrow\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}+6 \mathrm{H}_{2} \mathrm{O}(1)\) $$ \log \beta_{3}=47.30 $$ Calculate \(E^{\circ}\) for the reaction $$ \left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}+\mathrm{e}^{-} \longrightarrow\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{2+} $$ Show that \(\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}\) is stable in water but \(\mathrm{Co}^{3+}(\mathrm{aq})\) is not.

The most soluble of the following solids in \(\mathrm{NH}_{3}(\mathrm{aq})\) is (a) \(\mathrm{Ca}(\mathrm{OH})_{2} ;\) (b) \(\mathrm{Cu}(\mathrm{OH})_{2} ;\) (c) \(\mathrm{BaSO}_{4} ;\) (d) \(\mathrm{MgCO}_{3}\) (e) \(\overline{\mathrm{Fe}_{2} \mathrm{O}_{3}}\).
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