Answer :
To calculate the minimum voltage needed to electrolyze potassium chloride (KCl) into its elements (potassium metal, K(s), and chlorine gas, Cl₂(g)), we will look at the standard reduction potentials of the reactions involved.
1. Identify the reactions:
- Potassium Ion to Potassium: The reduction of potassium ions ([tex]\(K^+\)[/tex]) to potassium metal ([tex]\(K\)[/tex]) is represented as:
[tex]\[
K^+ + e^- \rightarrow K (s)
\][/tex]
The standard reduction potential for this reaction is about [tex]\(-2.93 \, \text{V}\)[/tex].
- Chloride to Chlorine Gas: The oxidation of chloride ions ([tex]\(Cl^-\)[/tex]) to chlorine gas ([tex]\(Cl_2\)[/tex]) can be understood as the reverse of the reduction:
[tex]\[
2Cl^- \rightarrow Cl_2 (g) + 2e^-
\][/tex]
The reduction potential for the [tex]\(Cl_2\)[/tex] to [tex]\(Cl^-\)[/tex] reaction is approximately [tex]\(+1.36 \, \text{V}\)[/tex], so for the oxidation, it would be the negative of this, [tex]\(-1.36 \, \text{V}\)[/tex].
2. Calculate the minimum voltage required:
To find the minimum voltage needed to drive the electrolytic process, we need to consider the reverse of the reduction potentials. Electrolysis requires input energy, so the minimum voltage needed will be equal to or greater than the difference in potentials (since we are forcing the reaction to go in the non-spontaneous direction).
[tex]\[
\text{Minimum voltage} = \text{Oxidation potential of } Cl_2 + \text{Reduction potential of } K^+
\][/tex]
[tex]\[
\text{Minimum voltage} = -(-2.93) + (-1.36) = 2.93 + 1.36 = 4.29 \, \text{V}
\][/tex]
So, the minimum voltage needed to electrolyze potassium chloride into its elements is [tex]\(4.29 \, \text{V}\)[/tex].
Therefore, the correct answer is C) 4.29 V.
1. Identify the reactions:
- Potassium Ion to Potassium: The reduction of potassium ions ([tex]\(K^+\)[/tex]) to potassium metal ([tex]\(K\)[/tex]) is represented as:
[tex]\[
K^+ + e^- \rightarrow K (s)
\][/tex]
The standard reduction potential for this reaction is about [tex]\(-2.93 \, \text{V}\)[/tex].
- Chloride to Chlorine Gas: The oxidation of chloride ions ([tex]\(Cl^-\)[/tex]) to chlorine gas ([tex]\(Cl_2\)[/tex]) can be understood as the reverse of the reduction:
[tex]\[
2Cl^- \rightarrow Cl_2 (g) + 2e^-
\][/tex]
The reduction potential for the [tex]\(Cl_2\)[/tex] to [tex]\(Cl^-\)[/tex] reaction is approximately [tex]\(+1.36 \, \text{V}\)[/tex], so for the oxidation, it would be the negative of this, [tex]\(-1.36 \, \text{V}\)[/tex].
2. Calculate the minimum voltage required:
To find the minimum voltage needed to drive the electrolytic process, we need to consider the reverse of the reduction potentials. Electrolysis requires input energy, so the minimum voltage needed will be equal to or greater than the difference in potentials (since we are forcing the reaction to go in the non-spontaneous direction).
[tex]\[
\text{Minimum voltage} = \text{Oxidation potential of } Cl_2 + \text{Reduction potential of } K^+
\][/tex]
[tex]\[
\text{Minimum voltage} = -(-2.93) + (-1.36) = 2.93 + 1.36 = 4.29 \, \text{V}
\][/tex]
So, the minimum voltage needed to electrolyze potassium chloride into its elements is [tex]\(4.29 \, \text{V}\)[/tex].
Therefore, the correct answer is C) 4.29 V.
