Problem 98 - Chemistry The Molecular Science

Question

Consider two different electrolytic cells; one cell contains aqueous \(\mathrm{Zn}^{2+}\) and the other contains \(\mathrm{Cr}^{3+}\). The initial metal ion concentration is the same in each cell and the metal ions are reduced to the metal during the electrolysis. Each cell operates at the same current. Without doing calculations, predict which cell has the greater mass of metal deposited after 5 min. Explain your prediction.

Step-by-Step Solution

Answer

The Zn cell will deposit more metal because it requires fewer electrons per mole of metal.

Step 1: Understand the Electrolysis Process

In electrolytic cells, metal ions in solution gain electrons (are reduced) to form solid metal during electrolysis. The amount of metal deposited depends on the charge passed through the cell and the reduction equivalent of the metal ion.

Step 2: Identify Key Factor - Reduction Equivalent

The reduction equivalent is determined by the number of moles of electrons required to reduce one mole of metal ions to its pure metal form. The general consideration for reduction equivalent is based on the ion's valence.

Step 3: Determine Reduction Equivalents

For one mole of \(\text{Zn}^{2+}\), 2 moles of electrons are required, while for \(\text{Cr}^{3+}\), 3 moles of electrons are required. Therefore, \(\text{Cr}^{3+}\) has a higher reduction equivalent than \(\text{Zn}^{2+}\).

Step 4: Relate Reduction Equivalent to Mass Deposition

The metal with the lower reduction equivalent (\(\text{Zn}^{2+}\)) will deposit a greater mass when the same total charge is passed through the cell, as it requires fewer electrons per mole of metal deposited.

Step 5: Make the Prediction

Since \(\text{Zn}^{2+}\) requires fewer electrons to deposit a mole of metal compared to \(\text{Cr}^{3+}\), the \(\text{Zn}^{2+}\) cell will have a greater mass of metal deposited after 5 minutes under the same current.

Key Concepts

Electrolytic Cells

Electrolytic cells are essential components of the electrolysis process. They are special types of devices that use electrical energy to drive non-spontaneous chemical reactions. In the context of our exercise, electrolysis converts metal ions in solution into solid metal. This process takes place when the metal ions gain electrons, which is known as a reduction reaction. Understanding electrolytic cells helps comprehend how ions like \(\mathrm{Zn}^{2+}\) and \(\mathrm{Cr}^{3+}\) are transformed back into their respective metals when an electric current is applied.

Key features of electrolytic cells include:

• Two electrodes: the anode (positive) and the cathode (negative).
• An electrolyte solution that contains ions.
• A power source that supplies the electrical energy needed for the reaction.

In summary, electrolytic cells make electrolysis possible by using electricity to reduce metal ions to metal atoms. The process depends heavily on the type of ions involved and the amount of current passing through the cell.

Reduction Equivalent

The reduction equivalent is an important concept when evaluating which metal is deposited during electrolysis. It represents the number of moles of electrons needed to reduce one mole of metal ions to its pure metallic state. This is crucial for predicting which metal will be deposited more under controlled current conditions.

To determine the reduction equivalent:

• Examine the charge on each ion. \(\mathrm{Zn}^{2+}\) requires two electrons for each ion to be reduced (\(\mathrm{Zn}^{2+} + 2e^- \rightarrow \mathrm{Zn}\)), while \(\mathrm{Cr}^{3+}\) needs three electrons per ion (\(\mathrm{Cr}^{3+} + 3e^- \rightarrow \mathrm{Cr}\)).

The significance of knowing the reduction equivalent lies in its direct influence on the amount of metal deposited. A lower reduction equivalent means fewer electrons are needed, thus allowing more of that metal to be deposited given the same charge is applied.

Metal Deposition Chemistry

The chemistry of metal deposition during electrolysis revolves around how easily electrons can convert metal ions in solution to solid metal atoms. The mass of the metal deposited is directly related to the total charge passed through the electrolytic cell and the reduction equivalent of the ions present.

Two factors influencing metal deposition include:

• The magnitude of current: A higher current means more electrons are available to facilitate the reaction.
• The reduction equivalent: As explained, it determines how efficiently ions can be reduced to their metallic form.

Considering the exercise, \(\mathrm{Zn}^{2+}\) ions, requiring a reduction equivalent of 2, will deposit more mass compared to \(\mathrm{Cr}^{3+}\) ions, which have a reduction equivalent of 3, under the same conditions. Understanding these chemical principles clarifies why certain metals are deposited more prominently than others during electrolysis.