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Chapter 19: Problem 92

What are the half-reactions in the electrolysis of a. \(\operatorname{MgBr}_{2}(l)\) b. \(\mathrm{Ca}(\mathrm{OH})_{2}(l) ?\)

Short Answer

Expert verified
a. Mg: \( ext{Mg}^{2+} + 2e^- \rightarrow ext{Mg} \); Br: \( 2 ext{Br}^- \rightarrow ext{Br}_2 + 2e^- \) b. Ca: \( ext{Ca}^{2+} + 2e^- \rightarrow ext{Ca} \); OH: \( 4 ext{OH}^- \rightarrow ext{O}_2 + 2 ext{H}_2 ext{O} + 4e^- \)

Step by step solution

01

Identify Components of Electrolysis

In electrolysis, the chemical compound is decomposed into its elements. For the given compounds: - In \( ext{MgBr}_2\), we have magnesium \( ext{Mg}^{2+}\) ions and bromide \( ext{Br}^{-}\) ions.- In \( ext{Ca(OH)}_2\), we have calcium \( ext{Ca}^{2+}\) ions, hydroxide \( ext{OH}^{-}\) ions, and \( ext{H}_2 ext{O}\).
02

Write Reduction Half-Reaction

During electrolysis, one electrode (cathode) will undergo reduction. - For \( ext{MgBr}_2\): \( ext{Mg}^{2+} + 2e^- \rightarrow ext{Mg} \) - For \( ext{Ca(OH)}_2\): \( ext{Ca}^{2+} + 2e^- \rightarrow ext{Ca} \)
03

Write Oxidation Half-Reaction

The other electrode (anode) will undergo oxidation. - For \( ext{MgBr}_2\): \( 2 ext{Br}^- \rightarrow ext{Br}_2 + 2e^- \)- For \( ext{Ca(OH)}_2\): The oxidation of hydroxide ions takes place. \( 4 ext{OH}^- \rightarrow ext{O}_2 + 2 ext{H}_2 ext{O} + 4e^- \)
04

Put it Together

Combine the half-reactions for each compound to represent the full reaction:- For \( ext{MgBr}_2\): - Reduction: \( ext{Mg}^{2+} + 2e^- \rightarrow ext{Mg} \) - Oxidation: \( 2 ext{Br}^- \rightarrow ext{Br}_2 + 2e^- \)- For \( ext{Ca(OH)}_2\): - Reduction: \( ext{Ca}^{2+} + 2e^- \rightarrow ext{Ca} \) - Oxidation: \( 4 ext{OH}^- \rightarrow ext{O}_2 + 2 ext{H}_2 ext{O} + 4e^- \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Half-reactions
In electrochemistry, a half-reaction is a part of the overall reaction in electrolysis that occurs at either the anode or cathode. It is crucial to understand that electrolysis involves splitting a compound into its constituent elements. Typically, one part of the compound is oxidized while another is reduced.
  • Reduction Half-Reaction: Occurs at the cathode. Involves a gain of electrons. For example, in the electrolysis of \(\mathrm{MgBr}_2\), \(\mathrm{Mg}^{2+} + 2e^- \rightarrow \mathrm{Mg}\).
  • Oxidation Half-Reaction: Takes place at the anode. Here, there is a loss of electrons. For instance, in the electrolysis of \(\mathrm{MgBr}_2\), \(2\mathrm{Br}^- \rightarrow \mathrm{Br}_2 + 2e^-\).
Each compound in electrolysis will have its unique set of half-reactions, reflecting how different ions gain or lose electrons.
Oxidation-reduction
Oxidation-reduction reactions - or redox reactions - are processes where the oxidation state of molecules, atoms, or ions is changed. These reactions are fundamental in electrolysis as they represent the chemical changes needed to separate a compound into its elements.
  • Oxidation involves losing electrons and an increase in the oxidation state.
  • Reduction, on the other hand, means gaining electrons and a reduction in oxidation state.
In electrolysis, redox reactions are split into oxidation and reduction half-reactions. These are crucial for balancing the charges and ensuring that electrons lost are equal to those gained. This maintains the principle of conservation of charge.
Electrochemistry
Electrochemistry is the branch of chemistry that deals with the relationship between electricity and chemical reactions. It plays a pivotal role in processes like electrolysis, where electrical energy is used to drive a non-spontaneous chemical reaction.
Electrolysis is a classic example where electrochemistry is applied to break down compounds. It uses an external electric current to prompt the chemical changes needed to decompose a substance. The process involves electrochemical cells, which contain:
  • Anode: The electrode where oxidation occurs.
  • Cathode: The electrode where reduction occurs.
  • Electrolyte: The substance being decomposed.
Understanding electrochemistry is key to exploring how energy can be converted from electrical to chemical form and how chemical energy can be stored or released.
Chemical decomposition
Chemical decomposition is the process of breaking down a chemical compound into simpler substances, often its elemental parts. In the context of electrolysis, it refers to the transformation of compounds, such as \(\mathrm{MgBr}_2\) and \(\mathrm{Ca(OH)}_2\), into their elemental forms.
During electrolysis:
  • Energy from an external electric source causes ions in a compound to move, resulting in decomposition.
  • Cations move to the cathode to get reduced, whereas anions move to the anode to get oxidized.
This breakdown is governed by the principles of redox reactions, ensuring that each side of the reaction gains and loses the same number of electrons. It is a controlled way to recover elements from compounds, which can be useful in various applications in industry and research.

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Most popular questions from this chapter

Order the following oxidizing agents by increasing strength under standard- state conditions: \(\mathrm{Ag}^{+}(a q)\); \(\mathrm{Cd}^{2+}(a q) ; \mathrm{MnO}_{4}^{-}(a q)\) (in acidic solution).

A voltaic cell is constructed from a half-cell in which a chromium rod dips into a solution of chromium(III) nitrate, \(\operatorname{Cr}\left(\mathrm{NO}_{3}\right)_{3},\) and another halfcell in which a lead rod dips into a solution of lead(II) nitrate, \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\). The two half-cells are connected by a salt bridge. Chromium metal is oxidized during operation of the voltaic cell. What is the half-reaction that occurs at the cathode?

Dichromate ion, \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\), is added to an acidic solution containing \(\mathrm{Br}^{-}\) and \(\mathrm{Mn}^{2+}\). Write a balanced equation for any reaction that occurs. Assume standard conditions at \(25^{\circ} \mathrm{C}\).

An electrode is prepared by dipping a silver strip into a solution saturated with silver thiocyanate, \(\mathrm{AgSCN}\), and containing \(0.10 \mathrm{M} \mathrm{SCN}^{-} .\) The cell potential of the voltaic cell constructed by connecting this electrode as the cathode to the standard hydrogen half-cell as the anode is \(0.45 \mathrm{~V}\). What is the solubility product of silver thiocyanate?

What are the half-reactions in the electrolysis of a. \(\operatorname{CaS}(l)\) b. \(\mathrm{CsOH}(l) ?\)
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