Question

A solution at \(25^{\circ} \mathrm{C}\) contains \(1.0 \mathrm{M} \mathrm{Cd}^{2+}, 1.0 \mathrm{MAg}^{+}, 1.0 \mathrm{M} \mathrm{Au}^{3+}\), 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 be plated out in the order of their reduction potentials: Ag from \(Ag^{+}\), Au from \(Au^{3+}\), Ni from \(Ni^{2+}\), and Cd from \(Cd^{2+}\). The order of plating will be Silver (Ag), Gold (Au), Nickel (Ni), and Cadmium (Cd) as the voltage is gradually increased.

Step-by-step solution

Determine the reduction potentials of the given metal ions

First, let's find the reduction potentials of the given metal ions. We can consult a table of standard reduction potentials or textbook, where the data can be found: For simplicity: \(E^{0}\) = Standard Reduction Potential \(E^{0}(Cd^{2+}/Cd) = -0.402 \, V\) \(E^{0}(Ag^{+}/Ag) = 0.799 \, V\) \(E^{0}(Au^{3+}/Au) = 1.498 \, V\) \(E^{0}(Ni^{2+}/Ni) = -0.257 \, V\)

Arrange the metal ions according to their reduction potentials

Now let's arrange the metal ions in ascending order according to their reduction potentials: 1. \(Cd^{2+}/Cd\) : \(-0.402 \, V\) 2. \(Ni^{2+}/Ni\) : \(-0.257 \, V\) 3. \(Ag^{+}/Ag\) : \(0.799 \, V\) 4. \(Au^{3+}/Au\) : \(1.498 \, V\)

Predict the order of plating based on the reduction potentials

In the cathode compartment of an electrolytic cell, the metal ion with the least negative (or most positive) reduction potential will plate out first as the voltage is gradually increased. So, based on our ranking from Step 2, the order in which the metals will plate out is as follows: 1. Silver (Ag) from \(Ag^{+}\) 2. Gold (Au) from \(Au^{3+}\) 3. Nickel (Ni) from \(Ni^{2+}\) 4. Cadmium (Cd) from \(Cd^{2+}\) Thus, as the voltage is gradually increased, the metals will be plated out in the order: Ag, Au, Ni, and Cd.

Key concepts

Standard Reduction Potential

A standard reduction potential is crucial when it comes to predicting reactions in electrolytic cells. It measures how easily a chemical species can acquire electrons, a process known as reduction. The standard reduction potential is given in volts (V), and every half-cell reaction has its own value. The higher the standard reduction potential of a half-cell reaction, the more likely it is to occur. For instance, in the problem, the reduction potentials were given for various reactions, including

• Cadmium: \(E^{0}(Cd^{2+}/Cd) = -0.402 \, V\)
• Silver: \(E^{0}(Ag^{+}/Ag) = 0.799 \, V\)
• Gold: \(E^{0}(Au^{3+}/Au) = 1.498 \, V\)
• Nickel: \(E^{0}(Ni^{2+}/Ni) = -0.257 \, V\)

This information allows us to predict which metal will reduce and deposit on the cathode first.

Metal Ion Plating Order

The order in which metal ions plate onto the cathode is determined by their standard reduction potentials. In an electrolytic cell, metal ions with higher (more positive) reduction potentials will plate out first upon increasing the voltage. Using our example:

• Silver (Ag) has the highest reduction potential of \(0.799 \, V\), so it will plate first.
• Gold (Au), with \(1.498 \, V\), follows due to its favorable potential.
• Nickel (Ni), at \(-0.257 \, V\), plates after gold.
• Cadmium (Cd), with \(-0.402 \, V\), comes last.

This sequence shows that metals are selectively deposited based on their potential, forming the basis for electroplating in industries.

Reduction Potentials in Electrolysis

In the process of electrolysis, understanding reduction potentials is key to predicting how substances will behave in an electrolytic cell. Reduction potentials decide the sequence and ease of reactions that occur at the electrodes. The standard reduction potential can predict whether a metal ion at the cathode will be reduced. This is because the potential indicates electron affinity—the higher the potential, the more a species wants to gain electrons. When gradually increasing voltage, ions with higher reduction potentials are reduced—and thus plate out—first. This systematic behavior helps us control and use electrolysis to our advantage, such as in purifying metals or coating objects with thin metal layers.

Cathode Reactions in Electrolysis

At the cathode of an electrolytic cell, reduction reactions occur. These involve the gain of electrons and lead to the deposition of metals. The overall aim in such a process is to convert metal ions from the solution into solid metal coatings. Key features of cathode reactions include:

• Metal ions from the solution accept electrons and form a solid metal.
• The electron supply is determined by the applied external voltage.
• The metal plating is influenced by the inherent reduction potentials as discussed above.

Remember, as an external power source supplies energy into the system, the electrolytic cell can drive reactions that would not occur spontaneously, which is a significant deviation from galvanic cells. This principle is harnessed in electroplating, refining metals, and other technological applications.