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Chapter 20: Problem 1

From the observations listed, estimate the value of \(E^{\circ}\) for the half- reaction \(\mathrm{M}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{M}(\mathrm{s})\) (a) The metal M reacts with HNO \(_{3}(\text { aq })\), but not with \(\mathrm{HCl}(\mathrm{aq}) ; \mathrm{M}\) displaces \(\mathrm{Ag}^{+}(\mathrm{aq}),\) but not \(\mathrm{Cu}^{2+}(\mathrm{aq})\) (b) The metal \(M\) reacts with \(\mathrm{HCl}(\mathrm{aq}),\) producing \(\mathrm{H}_{2}(\mathrm{g}),\) but displaces neither \(\mathrm{Zn}^{2+}(\text { aq })\) nor \(\mathrm{Fe}^{2+}(\mathrm{aq})\).

Short Answer

Expert verified
The standard electrode potential for the half-reaction of M lies between that of \(H_2/H^+\) and \(Ag^+/Ag\), or \(H_2/H^+\) and \(Zn^{2+}/Zn\) or \(Fe^{2+}/Fe\). Precise ranking needs additional information.

Step by step solution

01

Analyzing Part (a)

The metal M reacts with nitric acid (HNO3), but not with hydrochloric acid (HCl). This suggests that the metal M can reduce H+ ions to hydrogen gas. However, not reacting with HCl means it does not have a higher reactivity than hydrogen. Therefore, it must lie below hydrogen in electrochemical series. Additionally, M can displace silver ions (Ag+), but not copper ions (Cu2+). This suggests that it lies between silver and copper. So, it can be deducted that M's \(E^{\circ}\) value lies between that of \(H_2/H^+\) and \(Ag^+/Ag\).
02

Analyzing Part (b)

In this case, M reacts with hydrochloric acid (HCl) to produce hydrogen gas. This suggests a higher reactivity than hydrogen, implying it is above hydrogen in the electrochemical series. However, it can't displace \(Zn^{2+}\) or \(Fe^{2+}\), suggesting its position below zinc and iron in the series. So, M's \(E^{\circ}\) value lies between that of \(H_2/H^+\) and \(Zn^{2+}/Zn\) or \(Fe^{2+}/Fe\).
03

Concluding from Part (a) and (b)

Combining the conclusions from part (a) and part (b), the \(E°\) for the half-reaction of M must lie between that of \(H_2/H^+\) and \(Ag^+/Ag\), or \(H_2/H^+\) and \(Zn^{2+}/Zn\) or \(Fe^{2+}/Fe\). Deciding the exact value or narrower range requires additional data or observations.

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Most popular questions from this chapter

A lithium battery, which is different from a lithiumion battery, uses lithium metal as one electrode and carbon in contact with \(\mathrm{MnO}_{2}\) in a paste of \(\mathrm{KOH}\) as the other electrode. The electrolyte is lithium perchlorate in a nonaqueous solvent, and the construction is similar to the silver battery. The half-cell reactions involve the oxidation of lithium and the reaction $$\begin{aligned}\mathrm{MnO}_{2}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(1)+\mathrm{e}^{-} \longrightarrow \mathrm{Mn}(\mathrm{OH})_{3}(\mathrm{s})+& \\\\\mathrm{OH}^{-}(\mathrm{aq}) &E^{\circ}=-0.20 \mathrm{V}\end{aligned}$$ Draw a cell diagram for the lithium battery, identify the negative and positive electrodes, and estimate the cell potential under standard conditions.

Calculate the quantity indicated for each of the following electrolyses. (a) \(\left[\mathrm{Cu}^{2+}\right]\) remaining in \(425 \mathrm{mL}\) of a solution that was originally \(0.366 \mathrm{M} \mathrm{CuSO}_{4},\) after passage of \(2.68 \mathrm{A}\) for 282 s and the deposition of Cu at the cathode (b) the time required to reduce \(\left[\mathrm{Ag}^{+}\right]\) in \(255 \mathrm{mL}\) of \(\mathrm{AgNO}_{3}(\mathrm{aq})\) from 0.196 to \(0.175 \mathrm{M}\) by electrolyzing the solution between \(\mathrm{Pt}\) electrodes with a current of \(1.84 \mathrm{A}\)

For the voltaic cell, $$\begin{array}{l} \mathrm{Ag}(\mathrm{s}) | \mathrm{Ag}^{+}(0.015 \mathrm{M}) \| \mathrm{Fe}^{3+}(0.055 \mathrm{M}) \\ \quad \mathrm{Fe}^{2+}(0.045 \mathrm{M}) | \mathrm{Pt}(\mathrm{s}) \end{array}$$ (a) what is \(E_{\text {cell initially? }}\) (b) As the cell operates, will \(E_{\text {cell increase }}\) decrease, or remain constant with time? Explain. (c) What will be \(E_{\text {cell }}\) when \(\left[\mathrm{Ag}^{+}\right]\) has increased to \(0.020 \mathrm{M} ?\) (d) What will be \(\left[\mathrm{Ag}^{+}\right]\) when \(E_{\text {cell }}=0.010 \mathrm{V} ?\) (e) What are the ion concentrations when \(E_{\text {cell }}=0 ?\)

Silver tarnish is mainly \(\mathrm{Ag}_{2} \mathrm{S}\) : $$\begin{array}{r}\mathrm{Ag}_{2} \mathrm{S}(\mathrm{s})+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Ag}(\mathrm{s})+\mathrm{S}^{2-}(\mathrm{aq}) \\\E^{\circ}=-0.691 \mathrm{V}\end{array}$$ A tarnished silver spoon is placed in contact with a commercially available metallic product in a glass baking dish. Boiling water, to which some \(\mathrm{NaHCO}_{3}\) has been added, is poured into the dish, and the product and spoon are completely covered. Within a short time, the removal of tarnish from the spoon begins. (a) What metal or metals are in the product? (b) What is the probable reaction that occurs? (c) What do you suppose is the function of the \(\mathrm{NaHCO}_{3} ?\) (d) An advertisement for the product appears to make two claims: (1) No chemicals are involved, and (2) the product will never need to be replaced. How valid are these claims? Explain.

Describe in words how you would calculate the standard potential of the \(\mathrm{Fe}^{2+} / \mathrm{Fe}(\mathrm{s})\) couple from those of \(\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+} / \mathrm{Fe}(\mathrm{s})\).
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