Question

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

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

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: \( \mathrm{Cd^{2+}(aq) + 2e^{-} \rightarrow Cd(s)} \qquad E^{\circ} = -0.403 \, \mathrm{V} \) \( \mathrm{Ag^{+}(aq) + e^{-} \rightarrow Ag(s)} \qquad E^{\circ} = +0.799 \, \mathrm{V} \) \( \mathrm{Au^{3+}(aq) + 3e^{-} \rightarrow Au(s)} \qquad E^{\circ} = +1.498 \, \mathrm{V} \) \( \mathrm{Ni^{2+}(aq) + 2e^{-} \rightarrow Ni(s)} \qquad E^{\circ} = -0.257 \, \mathrm{V} \)

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⁺ \( E^{\circ}_{Au^{3+}} > E^{\circ}_{Ag^{+}} > E^{\circ}_{Ni^{2+}} > E^{\circ}_{Cd^{2+}} \) \( +1.498 \, \mathrm{V} > +0.799 \, \mathrm{V} > -0.257 \, \mathrm{V} > -0.403 \, \mathrm{V} \)

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).

Key concepts

Standard Reduction Potential

Understanding standard reduction potential is crucial in predicting the behavior of ions in an electrolytic cell. The standard reduction potential, indicated as \(E^{\circ}\), measures how easily a species gains electrons and gets reduced under standard conditions. It represents the voltage associated with a reduction reaction when an electrode is combined with a standard hydrogen electrode.

• A positive \(E^{\circ}\) indicates a greater tendency to gain electrons, meaning the species is easily reduced.
• A negative \(E^{\circ}\) suggests a lesser tendency to gain electrons.

In the given exercise, the reduction potentials for ions like \(\mathrm{Cd}^{2+}\), \(\mathrm{Ag}^{+}\), \(\mathrm{Au}^{3+}\), and \(\mathrm{Ni}^{2+}\) are obtained from the electrochemical table. These potentials guide us in determining which ion will reduce and plate out first as voltage increases. Ions with a more positive \(E^{\circ}\) will reduce ahead of those with more negative values.

Electron Transfer

Electron transfer is the core mechanism in electrolysis and redox reactions, where electrons move from one species to another. In our electrolytic cell scenario, when voltage is applied, electrons are driven through the circuit to reduce metal ions into their solid form.

• The species receiving electrons undergoes reduction.
• The ions give up electrons during the oxidation process at the anode.

This transfer is what causes the metal ions to "plate" on the electrode corresponding to their standard reduction potential. In simpler terms, metals with higher reduction potentials attract electrons more strongly and hence are deposited first. The sequence in which this happens is vital for understanding the practical outcome of electroplating and similar processes.

Redox Reactions

Redox reactions encapsulate the processes of reduction and oxidation happening simultaneously. In an electrolytic cell, these reactions drive the transformation of ions into metals through electron exchange. A reduction reaction involves a gain of electrons, whereas oxidation involves a loss.

• Reduction takes place at the cathode.
• Oxidation occurs at the anode.

In our exercise, redox reactions allow metal ions to transition into a solid form on the electrode. The ion sequence is determined by each ion's readiness to participate in the redox process, primarily dictated by their standard reduction potentials. Understanding these principles enhances comprehension of how electroplating and electrolysis processes are controlled and predicted.