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Chapter 18: Problem 109

What reactions take place at the cathode and the anode when each of the following is electrolyzed? (Assume standard conditions.) a. 1.0 \(M \mathrm{NiBr}_{2}\) solution b. 1.0 \(M \mathrm{AlF}_{3}\) solution c. 1.0 \(M \mathrm{MnI}_{2}\) solution

Short Answer

Expert verified
For the electrolysis of the given solutions under standard conditions, the following half-reactions take place: a. 1.0 M NiBr鈧 solution: Cathode: Ni虏鈦 + 2e鈦 鈫 Ni Anode: 2Br鈦 鈫 Br鈧 + 2e鈦 b. 1.0 M AlF鈧 solution: Cathode: Al鲁鈦 + 3e鈦 鈫 Al Anode: 2F鈦 鈫 F鈧 + 2e鈦 c. 1.0 M MnI鈧 solution: Cathode: Mn虏鈦 + 2e鈦 鈫 Mn Anode: 2I鈦 鈫 I鈧 + 2e鈦

Step by step solution

01

Identify the ions in the solution

In a 1.0 M NiBr鈧 solution, the ions present are Ni虏鈦 and Br鈦.
02

Determine the reactions at the cathode and anode using reduction potentials

The standard reduction potentials for the relevant half-reactions are: Ni虏鈦 + 2e鈦 鈫 Ni (E掳 = -0.25 V) 2Br鈦 鈫 Br鈧 + 2e鈦 (E掳 = +1.09 V) Since the reaction with the more positive reduction potential occurs at the cathode, Ni虏鈦 will be reduced to Ni, and Br鈦 will be oxidized to Br鈧 at the anode.
03

Write balanced half-reactions

The balanced half-reactions for the electrolysis of 1.0 M NiBr鈧 are: Cathode: Ni虏鈦 + 2e鈦 鈫 Ni Anode: 2Br鈦 鈫 Br鈧 + 2e鈦 #1.0 M AlF鈧 solution#
04

Identify the ions in the solution

In a 1.0 M AlF鈧 solution, the ions present are Al鲁鈦 and F鈦.
05

Determine the reactions at the cathode and anode using reduction potentials

The standard reduction potentials for the relevant half-reactions are: Al鲁鈦 + 3e鈦 鈫 Al (E掳 = -1.66 V) 2F鈦 鈫 F鈧 + 2e鈦 (E掳 = +2.87 V) Since the reaction with the more positive reduction potential occurs at the cathode, Al鲁鈦 will be reduced to Al, and F鈦 will be oxidized to F鈧 at the anode.
06

Write balanced half-reactions

The balanced half-reactions for the electrolysis of 1.0 M AlF鈧 are: Cathode: Al鲁鈦 + 3e鈦 鈫 Al Anode: 2F鈦 鈫 F鈧 + 2e鈦 #1.0 M MnI鈧 solution#
07

Identify the ions in the solution

In a 1.0 M MnI鈧 solution, the ions present are Mn虏鈦 and I鈦.
08

Determine the reactions at the cathode and anode using reduction potentials

The standard reduction potentials for the relevant half-reactions are: Mn虏鈦 + 2e鈦 鈫 Mn (E掳 = -1.18 V) 2I鈦 鈫 I鈧 + 2e鈦 (E掳 = +0.54 V) Since the reaction with the more positive reduction potential occurs at the cathode, Mn虏鈦 will be reduced to Mn, and I鈦 will be oxidized to I鈧 at the anode.
09

Write balanced half-reactions

The balanced half-reactions for the electrolysis of 1.0 M MnI鈧 are: Cathode: Mn虏鈦 + 2e鈦 鈫 Mn Anode: 2I鈦 鈫 I鈧 + 2e鈦

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Key Concepts

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

Reduction Potential
Reduction potential is a critical concept in understanding electrolysis. It tells us how likely a substance is to gain electrons, or reduce, in a chemical reaction. Each element or compound has a specific reduction potential, usually given in volts under standard conditions. A higher reduction potential means a higher likelihood of getting reduced.

To predict which ion gets reduced at the cathode during electrolysis, we look at the standard reduction potentials of the ions in solution.
  • The ion with the higher reduction potential will be reduced at the cathode.
  • For example, in a solution of NiBr鈧, Ni虏鈦 has a reduction potential of -0.25 V.
  • The reaction at the cathode is Ni虏鈦 gaining electrons to become Ni metal.
Understanding these potentials is crucial in predicting the outcomes of electrolysis reactions.
Cathode Reaction
The cathode is the electrode where reduction occurs in an electrolysis process. The ions in solution gain electrons to form atoms or molecules, a process termed reduction.

In our electrolysis examples:
  • For NiBr鈧, Ni虏鈦 ions gain electrons to form nickel metal (Ni).
  • For AlF鈧, Al鲁鈦 ions receive electrons to produce aluminum metal (Al).
  • For MnI鈧, Mn虏鈦 ions gain electrons and form manganese metal (Mn).
This reaction forms the solid elemental form of the metal present in the solution at the cathode.
Anode Reaction
The anode is where oxidation occurs during electrolysis and involves the loss of electrons.

When analyzing reactions at the anode, we look for the ion that wants to lose electrons the most. This is shown by the lower standard electrode potential value compared to the cathodic reaction. In these electrolysis examples:
  • For NiBr鈧 solution, Br鈦 ions are oxidized to form bromine gas (Br鈧).
  • In AlF鈧 solution, F鈦 ions lose electrons to form fluorine gas (F鈧).
  • For MnI鈧 solution, I鈦 ions are oxidized to produce iodine gas (I鈧).
Anode reactions are essential as they release gaseous forms of the non-metal ions in the electrolytic cell.
Half-Reactions
Half-reactions provide detailed insight into the separate processes taking part in electrolysis 鈥 reduction and oxidation.

Half-reactions break down the overall electrolysis reaction into two simpler processes. You can see which species get reduced and which get oxidized.
  • In a solution of NiBr鈧, the half-reactions are:
    Reduction: Ni虏鈦 + 2e鈦 鈫 Ni
    Oxidation: 2Br鈦 鈫 Br鈧 + 2e鈦
  • For AlF鈧:
    Reduction: Al鲁鈦 + 3e鈦 鈫 Al
    Oxidation: 2F鈦 鈫 F鈧 + 2e鈦
  • With MnI鈧:
    Reduction: Mn虏鈦 + 2e鈦 鈫 Mn
    Oxidation: 2I鈦 鈫 I鈧 + 2e鈦
Understanding and writing half-reactions helps in grasping the complete picture of electrochemical processes in a systematic manner.

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Most popular questions from this chapter

A solution at \(25^{\circ} \mathrm{C}\) contains \(1.0 M \mathrm{Cd}^{2+}, 1.0 M \mathrm{Ag}^{+}, 1.0 \mathrm{M}\) \(\mathrm{Au}^{3+},\) 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.

What is electrochemistry? What are redox reactions? Explain the difference between a galvanic and an electrolytic cell.

Balance the following oxidation鈥搑eduction reactions that occur in basic solution using the half-reaction method. a. \(\mathrm{PO}_{3}^{3-}(a q)+\mathrm{MnO}_{4}^{-}(a q) \rightarrow \mathrm{PO}_{4}^{3-}(a q)+\mathrm{MnO}_{2}(s)\) b. \(\operatorname{Mg}(s)+\mathrm{OCl}^{-}(a q) \rightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s)+\mathrm{Cl}^{-}(a q)\) c. \(\mathrm{H}_{2} \mathrm{CO}(a q)+\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}+(a q) \rightarrow\) $$\mathrm{HCO}_{3}(a q)+\mathrm{Ag}(s)+\mathrm{NH}_{3}(a q)$$

Balance the following oxidation鈥搑eduction reactions that occur in acidic solution using the half-reaction method. a. \(\mathrm{Cr}(s)+\mathrm{NO}_{3}^{-}(a q) \rightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{NO}(g)\) b. \(\mathrm{CH}_{3} \mathrm{OH}(a q)+\mathrm{Ce}^{4+}(a q) \rightarrow \mathrm{CO}_{2}(a q)+\mathrm{Ce}^{3+}(a q)\) c. \(\mathrm{SO}_{3}^{2-}(a q)+\mathrm{MnO}_{4}^{-}(a q) \rightarrow \mathrm{SO}_{4}^{2-}(a q)+\mathrm{Mn}^{2+}(a q)\)

An aqueous solution of an unknown salt of ruthenium is electrolyzed by a current of 2.50 A passing for 50.0 min. If 2.618 g Ru is produced at the cathode, what is the charge on the ruthenium ions in solution?
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