Question

Which product, Ca or \(\mathrm{H}_{2}\), is more likely to form at the cathode in the electrolysis of \(\mathrm{CaCl}_{2}\) ? Explain your reasoning.

Short answer

Hydrogen ( \(\text{H}_2\)) is more likely to form at the cathode.

Step-by-step solution

Understand Electrolysis of CaCl2

Electrolysis involves passing an electric current through a compound to cause a chemical change. At the cathode, reduction occurs. For the electrolysis of calcium chloride (\(\text{CaCl}_2\), we need to determine which species is more likely to be reduced: calcium ions (\(\text{Ca}^{2+}\)) or hydrogen ions (\(\text{H}^{+}\) from water).

Identify Possible Reactions

At the cathode, two possible reduction reactions can occur:1. Reduction of calcium ions: \(\text{Ca}^{2+} + 2e^- \rightarrow \text{Ca}\)2. Reduction of water: \(2\text{H}_2\text{O} + 2e^- \rightarrow \text{H}_2 + 2\text{OH}^-\).

Compare Standard Electrode Potentials

To determine which reaction is more favorable, compare the standard electrode potentials:- \(\text{E}^0(\text{Ca}^{2+}/\text{Ca}) = -2.87\,\text{V}\)- \(\text{E}^0(\text{H}^{+}/\text{H}_2) = 0.00\,\text{V}\)Since \(0.00\,\text{V}\) is less negative than \(-2.87\,\text{V}\), the reduction of hydrogen is thermodynamically more favorable than the reduction of calcium.

Conclusion

Given the electrode potentials, hydrogen (\(\text{H}_2\)) will preferentially be produced over calcium (\(\text{Ca}\)) at the cathode during electrolysis of \(\text{CaCl}_2\). This is because the reduction potential of hydrogen ions is higher than that of calcium ions.

Key concepts

Standard Electrode Potentials

Standard electrode potentials are crucial in determining the likelihood of a reaction occurring at an electrode during electrolysis. They are a measure of the tendency of a chemical species to acquire electrons and be reduced. For each species, a standard electrode potential, denoted as \(E^0\), is gathered under standard conditions. These conditions typically include a temperature of 298 Kelvin, a 1 M concentration for the ions, and a pressure of 1 atmosphere for gases.

In the context of which product forms at the cathode during electrolysis, comparing their \(E^0\) values helps us predict which reduction reaction is more favorable. A less negative or more positive standard electrode potential indicates a higher likelihood of reduction occurring for that species. For instance, in the electrolysis of \(\text{CaCl}_2\), we compare the \(E^0\) values for \(\text{Ca}^{2+}/\text{Ca}\) and \(\text{H}^{+}/\text{H}_2\).

- \(E^0(\text{Ca}^{2+}/\text{Ca}) = -2.87 \, \text{V}\)- \(E^0(\text{H}^{+}/\text{H}_2) = 0.00 \, \text{V}\)

Hydrogen's electrode potential is higher, indicating that hydrogen ions are more easily reduced than calcium ions under these conditions. Therefore, hydrogen production is favored at the cathode.

Reduction Reactions

Reduction reactions are processes where a species gains electrons, decreasing its oxidation state. In electrolysis, these reactions occur at the cathode, where positive ions move to acquire electrons.

During the electrolysis of \(\text{CaCl}_2\), two main reduction reactions can occur, each involving a different species:

• Reduction of calcium ions: \(\text{Ca}^{2+} + 2e^- \rightarrow \text{Ca}\)
• Reduction of water or hydrogen ions from water: \(2\text{H}_2\text{O} + 2e^- \rightarrow \text{H}_2 + 2\text{OH}^-\)

The reaction that occurs more readily will be the one with the higher standard electrode potential. As evidenced by the potential values provided, the reduction of hydrogen ions is preferred, leading to the formation of \(\text{H}_2\) gas at the cathode. This preference is due to the less negative or more positive potential for the hydrogen reduction reaction. Thus, despite both reactions being possible, the thermodynamically favorable one will dominate.

Reducing the more electropositive ion first ensures a consistent and predictable result during electrolysis experiments.

Cathode Processes

Cathode processes in electrolysis are fundamental to understanding which substances are produced during the process. The cathode serves as the site for reduction reactions; thus, it attracts cations or positively charged ions that gain electrons.

In the electrolysis setup, electrons move from the external circuit into the cathode. This electron flow allows the positive ions present in the electrolytic solution to be reduced. Let's consider the example of \(\text{CaCl}_2\) electrolysis. Here, calcium ions \((\text{Ca}^{2+})\) and hydrogen ions \((\text{H}^+)\) are in competition at the cathode.

- At the cathode, the species with the higher reduction potential are more likely to gain electrons.- In this particular example, the reduction of \(\text{H}^+\) to \(\text{H}_2\) is more thermodynamically favorable than reducing \(\text{Ca}^{2+}\) to calcium metal.

Therefore, hydrogen gas is the preferred product at the cathode during the electrolysis of \(\text{CaCl}_2\). This understanding of cathode processes and the role they play in electrolysis helps predict and control the outcomes of electrochemical reactions.