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Chapter 18: Problem 103

A solution at \(25^{\circ} \mathrm{C}\) contains $1.0 M \mathrm{Cd}^{2+}, 1.0 M \mathrm{Ag}^{+}, 1.0 \mathrm{M}\( \)\mathrm{Au}^{3+},\( and 1.0 \)\mathrm{M} \mathrm{Ni}^{2+}$ in the cathode compartment of an electrolytic cell. Predict the order in which the metals will plate out as the voltage is gradually increased.

Short Answer

Expert verified
The metals will plate out in the following order as the voltage is gradually increased: Gold (Au), Silver (Ag), Nickel (Ni), and Cadmium (Cd), due to their decreasing standard reduction potentials: \( +1.498 \, \mathrm{V} > +0.799 \, \mathrm{V} > -0.257 \, \mathrm{V} > -0.403 \, \mathrm{V} \).

Step by step solution

01

List the standard reduction potentials of the ions

To determine the order in which the ions will start depositing, we need to look at their standard reduction potentials. The reduction potential values can be found in an electrochemical table. Here are the standard reduction potentials of the ions: \( \mathrm{Cd^{2+}(aq) + 2e^{-} \rightarrow Cd(s)} \qquad E^{\circ} = -0.403 \, \mathrm{V} \) \( \mathrm{Ag^{+}(aq) + e^{-} \rightarrow Ag(s)} \qquad E^{\circ} = +0.799 \, \mathrm{V} \) \( \mathrm{Au^{3+}(aq) + 3e^{-} \rightarrow Au(s)} \qquad E^{\circ} = +1.498 \, \mathrm{V} \) \( \mathrm{Ni^{2+}(aq) + 2e^{-} \rightarrow Ni(s)} \qquad E^{\circ} = -0.257 \, \mathrm{V} \)
02

Arrange the ions in decreasing order of reduction potential

Now that we have the standard reduction potential values, arrange the given ions in decreasing order of their reduction potential. Au³⁺ > Ag⁺ > Ni²⁺ > Cd²⁺ \( E^{\circ}_{Au^{3+}} > E^{\circ}_{Ag^{+}} > E^{\circ}_{Ni^{2+}} > E^{\circ}_{Cd^{2+}} \) \( +1.498 \, \mathrm{V} > +0.799 \, \mathrm{V} > -0.257 \, \mathrm{V} > -0.403 \, \mathrm{V} \)
03

Determine the plating order based on reduction potentials

As the voltage is increased, the metal ion with the highest reduction potential will be reduced to its metal form and plate out first, followed by the ions with lower reduction potentials in order. Therefore, the plating order is: Au³⁺ > Ag⁺ > Ni²⁺ > Cd²⁺ The metals will plate out in the order of: Gold (Au), Silver (Ag), Nickel (Ni), and Cadmium (Cd).

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Most popular questions from this chapter

What is electrochemistry? What are redox reactions? Explain the difference between a galvanic and an electrolytic cell.

What reaction will take place at the cathode and the anode when each of the following is electrolyzed? (Assume standard conditions.) a. 1.0 \(M \mathrm{KF}\) solution b. 1.0\(M \mathrm{CuCl}_{2}\) solution c. 1.0 \( M \mathrm{MgI}_{2}\) solution

A galvanic cell is based on the following half-reactions: $$\begin{aligned} \mathrm{Ag}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}(s) & \mathscr{E}^{\circ}=0.80 \mathrm{V} \\ \mathrm{Cu}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Cu}(s) & \mathscr{E}^{\circ}=0.34 \mathrm{V} \end{aligned}$$ In this cell, the silver compartment contains a silver electrode and excess AgCl(s) \(\left(K_{\mathrm{sp}}=1.6 \times 10^{-10}\right),\) and the copper compartment contains a copper electrode and $\left[\mathrm{Cu}^{2+}\right]=2.0 \mathrm{M}$ . a. Calculate the potential for this cell at \(25^{\circ} \mathrm{C}\) . b. Assuming 1.0 \(\mathrm{L}\) of 2.0\(M \mathrm{Cu}^{2+}\) in the copper compartment, calculate the moles of \(\mathrm{NH}_{3}\) that would have to be added to give a cell potential of 0.52 \(\mathrm{V}\) at \(25^{\circ} \mathrm{C}\) (assume no volume change on addition of \(\mathrm{NH}_{3} )\) . $$\mathrm{Cu}^{2+}(a q)+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(a q) \qquad K=1.0 \times 10^{13}$$

What reactions take place at the cathode and the anode when each of the following is electrolyzed? a. molten \(\mathrm{NiBr}_{2} \quad\) b. molten \(\mathrm{AlF}_{3} \quad\) c. molten \(\mathrm{MgI}_{2}\)

When jump-starting a car with a dead battery, the ground jumper should be attached to a remote part of the engine block. Why?
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