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Chapter 20: Problem 83

(a) Write the anode and cathode reactions that cause the corrosion of iron metal to aqueous iron(II). (b) Write the balanced half-reactions involved in the air oxidation of \(\mathrm{Fe}^{2+}(a q)\) to \(\mathrm{Fe}_{2} \mathrm{O}_{3} \cdot 3 \mathrm{H}_{2} \mathrm{O}\).

Short Answer

Expert verified
(a) Anode reaction: \(\mathrm{Fe}(s) \rightarrow \mathrm{Fe}^{2+}(aq) + 2e^{-}\) and cathode reaction: \( \frac{1}{2} \mathrm{O}_{2}(g) + \mathrm{H}_{2}\mathrm{O}(l) + 2e^{-} \rightarrow 2\mathrm{OH}^{-}(aq)\) (b) Balanced overall air oxidation reaction: \(4 \mathrm{Fe}^{2+}(aq) + \mathrm{O}_{2}(g) + 4\mathrm{H}^{+}(aq) \rightarrow 4 \mathrm{Fe}^{3+}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l)\) and subsequent reaction: \( 4 \mathrm{Fe}^{3+}(aq) + 12\mathrm{OH}^{-}(aq) \rightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \cdot 3 \mathrm{H}_{2} \mathrm{O}(l)\)

Step by step solution

01

Anode Reaction

In the anode reaction, oxidation occurs. Iron loses two electrons to form iron(II) ions: \[\mathrm{Fe}(s) \rightarrow \mathrm{Fe}^{2+}(aq) + 2e^{-}\]
02

Cathode Reaction

In the cathode reaction, reduction occurs. Some other species, typically present in the aqueous environment, will gain electrons. In case of corrosion of iron, oxygen dissolved in water is usually the electron acceptor; forming hydroxide ions: \( \frac{1}{2} \mathrm{O}_{2}(g) + \mathrm{H}_{2}\mathrm{O}(l) + 2e^{-} \rightarrow 2\mathrm{OH}^{-}(aq)\) (b)
03

Reaction of Iron(II) with Oxygen

In air oxidation, the reaction of \(\mathrm{Fe}^{2+}(aq)\) with oxygen in the presence of water forms iron(III) hydroxide, which further dehydrates to form iron(III) oxide: \[ 4 \mathrm{Fe}^{2+}(aq) + \mathrm{O}_{2}(g) + 6\mathrm{H}_{2}\mathrm{O}(l) \rightarrow 4 \mathrm{Fe(OH)}_{3}(s) \]
04

Dehydration of Iron(III) Hydroxide to Iron(III) Oxide

Iron(III) hydroxide dehydrates to form iron(III) oxide and water: \[ 2 \mathrm{Fe(OH)}_{3}(s) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s) + 3\mathrm{H}_{2}\mathrm{O}(l)\] To write the balanced half-reactions, we can split the air oxidation reaction into two parts - the oxidation of \(\mathrm{Fe}^{2+}\) ions and the reduction of oxygen.
05

Oxidation Half-Reaction

In the oxidation half-reaction, the iron(II) ions lose their electrons to form iron(III) ions: \[2 \mathrm{Fe}^{2+}(aq) \rightarrow 2 \mathrm{Fe}^{3+}(aq) + 2e^{-}\]
06

Reduction Half-Reaction

In the reduction half-reaction, oxygen gains electrons to form water: \[\mathrm{O}_{2}(g) + 4e^{-} + 4\mathrm{H}^{+}(aq) \rightarrow 2\mathrm{H}_{2}\mathrm{O}(l)\] Combine these half-reactions, ensuring that the total number of electrons lost and gained is the same. Solution for part (b):
07

Balanced Overall Air Oxidation Reaction

By combining the oxidation and reduction half-reactions (multiplied as necessary to have equal numbers of electrons), we obtain the balanced overall air oxidation reaction: \[4 \mathrm{Fe}^{2+}(aq) + \mathrm{O}_{2}(g) + 4\mathrm{H}^{+}(aq) \rightarrow 4 \mathrm{Fe}^{3+}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l)\] The subsequent step, where iron(III) ions react with water to form iron(III) hydroxide and finally dehydrate to \(\mathrm{Fe}_{2} \mathrm{O}_{3} \cdot 3 \mathrm{H}_{2} \mathrm{O}\), can be represented as: \[ 4 \mathrm{Fe}^{3+}(aq) + 12\mathrm{OH}^{-}(aq) \rightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \cdot 3 \mathrm{H}_{2} \mathrm{O}(l)\]

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Most popular questions from this chapter

Using the standard reduction potentials listed in Appendix \(\mathrm{E}\), calculate the equilibrium constant for each of the following reactions at \(298 \mathrm{~K}\) : $$ \text { (a) } \mathrm{Cu}(s)+2 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+2 \mathrm{Ag}(s) $$ (b) \(3 \mathrm{Ce}^{4+}(a q)+\mathrm{Bi}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow\) $$ 3 \mathrm{Ce}^{3+}(a q)+\mathrm{BiO}^{+}(a q)+2 \mathrm{H}^{+}(a q) $$ (c) \(\mathrm{N}_{2} \mathrm{H}_{5}^{+}(a q)+4 \mathrm{Fe}(\mathrm{CN})_{6}{ }^{3-}(a q) \longrightarrow\) $$ \mathrm{N}_{2}(g)+5 \mathrm{H}^{+}(a q)+4 \mathrm{Fe}(\mathrm{CN})_{6}^{4-}(a q) $$

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For each of the following reactions, write a balanced equation, calculate the standard emf, calculate \(\Delta G^{\circ}\) at \(298 \mathrm{~K},\) and calculate the equilibrium constant \(K\) at \(298 \mathrm{~K}\). (a) Aqueous iodide ion is oxidized to \(\mathrm{I}_{2}(s)\) by \(\mathrm{Hg}_{2}^{2+}(a q) .\) (b) In acidic solution, copper(I) ion is oxidized to copper(II) ion by nitrate ion. (c) In basic solution, \(\mathrm{Cr}(\mathrm{OH})_{3}(s)\) is oxidized to \(\mathrm{CrO}_{4}^{2-}(a q)\) by \(\mathrm{ClO}^{-}(a q)\).

Consider the half-reaction \(\mathrm{Ag}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s)\). Which of the lines in the following diagram indicates how the reduction potential varies with the concentration of \(\mathrm{Ag}^{+} ?(\mathrm{~b})\) What is the value of \(E_{\mathrm{red}}\) when \(\log \left[\mathrm{Ag}^{+}\right]=0 ?\) [Section \(\left.20.6\right]\)
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