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Chapter 18: Problem 40

Which of the following oxidations will occur in the presence of \(\mathrm{H}_{2}\) gas under standard conditions? a. \(\mathrm{Zn}^{2+}\) to \(\mathrm{Zn}\) b. \(\mathrm{Fe}^{2+}\) to \(\mathrm{Fe}^{3+}\) c. \(\mathrm{Cr}(\mathrm{OH})_{3}\) to \(\mathrm{CrO}_{4}^{2-}\) d. Ni to Ni \(^{2+}\)

Short Answer

Expert verified
Answer: b. Fe虏鈦� to Fe鲁鈦�

Step by step solution

01

Recall the standard reduction potential of hydrogen gas

Under standard conditions, the standard reduction potential (E掳) of hydrogen gas is 0 V.
02

Write the half-cell reactions for each option

Here are the half-cell reactions for each option: a. \(\mathrm{Zn}^{2+} + 2 \mathrm{e}^{-} \rightarrow \mathrm{Zn}\) b. \(\mathrm{Fe}^{2+} + \mathrm{e}^{-} \rightarrow \mathrm{Fe}^{3+}\) c. \(\mathrm{Cr}(\mathrm{OH})_{3} + 3 \mathrm{H}_{2} \mathrm{O} + 6 \mathrm{e}^{-} \rightarrow \mathrm{CrO}_{4}^{2-} + 12 \mathrm{H}^{+}\) d. \(\mathrm{Ni} \rightarrow \mathrm{Ni}^{2+} + 2 \mathrm{e}^{-}\)
03

Compare the standard reduction potentials

For each of the half-reactions listed, we need to compare their standard reduction potentials (E掳) with the E掳 of hydrogen gas (0 V). a. E掳(Zn虏鈦�/Zn) = -0.76 V < 0 V, so this reduction will not be favored. b. E掳(Fe鲁鈦�/Fe虏鈦�) = 0.77 V > 0 V, so this reduction is favored and Fe虏鈦� will be oxidized to Fe鲁鈦�. c. E掳(CrO鈧劼测伝/Cr(OH)鈧�) = -0.41 V < 0 V, so this reduction will not be favored. d. E掳(Ni虏鈦�/Ni) = -0.23 V < 0 V, so this reduction will not be favored.
04

Identify the oxidation that will occur

Based on our comparisons, only the oxidation in option b has a favorable reduction potential, so this is the correct answer: Which of the following oxidations will occur in the presence of \(\mathrm{H}_{2}\) gas under standard conditions? b. \(\mathrm{Fe}^{2+}\) to \(\mathrm{Fe}^{3+}\)

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Key Concepts

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

Standard Reduction Potentials
The standard reduction potential is a measure of the tendency of a chemical species to gain electrons and be reduced. Under standard conditions, these potentials are measured in volts (V). Here, hydrogen gas is used as the reference with a potential of 0 V.
This means that other reactions are compared against the reduction potential of hydrogen.

Understanding these potentials helps to predict which substances can be reduced when paired together.
If a substance has a higher standard reduction potential than hydrogen, it is more likely to gain electrons than hydrogen.
  • A positive potential indicates a strong tendency to be reduced.
  • A negative potential suggests a weaker tendency to gain electrons.
These values are crucial in determining which oxidation and reduction reactions will occur under given conditions.
Oxidation Reactions
Oxidation involves the loss of electrons by a molecule, atom, or ion.
In the context of the exercise, we are looking at scenarios where specific ions might oxidize.
The reverse of reduction potentials can help in understanding oxidation.
  • An oxidation reaction will occur if its reverse has a lower reduction potential than that of the substance it is paired with.
  • The lower the reduction potential of the opposite reaction, the more favorable the oxidation.
For example, in the exercise, the oxidation of \( \text{Fe}^{2+} \rightarrow \text{Fe}^{3+} \) is favorable due to this principle.
The potential comparisons guide us to identify which ions will lose electrons under standard conditions.
Half-Cell Reactions
Half-cell reactions describe either the oxidation or reduction half of a redox reaction.
Each part of a redox equation can be separated into a half-cell reaction, capturing either the gain or loss of electrons.
  • Reduction half-cell: Shows a species gaining electrons.
  • Oxidation half-cell: Represents the loss of electrons.
Understanding and writing these reactions is vital.
They allow for easy comparison of standard reduction potentials.

In the provided example, each possible reaction is evaluated individually by its half-cell form.
This separation allows for an organized approach to determining which redox reactions are feasible.

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A magnesium battery can be constructed from an anode of magnesium metal and a cathode of molybdenum sulfide, \(\mathrm{Mo}_{3} \mathrm{S}_{4} .\) The standard reduction potentials of the electrode half-reactions are $$\mathrm{Mg}^{2+}(a q)+2 \mathrm{e}^{-} \rightarrow \mathrm{Mg}(s) \quad E^{\circ}=-2.37 \mathrm{V}$$ \(\mathrm{Mg}^{2+}(a q)+\mathrm{Mo}_{3} \mathrm{S}_{4}(s)+2 \mathrm{e}^{-} \rightarrow \mathrm{MgMo}_{3} \mathrm{S}_{4}(s) \quad E^{\circ}=?\) a. If the standard cell potential for the battery is \(1.50 \mathrm{V}\) what is the value of \(E^{\circ}\) for the reduction of \(\mathrm{Mo}_{3} \mathrm{S}_{4} ?\) b. What are the apparent oxidation states of Mo in \(\mathrm{Mo}_{3} \mathrm{S}_{4}\) and in \(\mathrm{MgMo}_{3} \mathrm{S}_{4} ?\) "c. The electrolyte in the battery contains a complex magnesium salt, \(\mathrm{Mg}\left(\mathrm{AlCl}_{3} \mathrm{CH}_{3}\right)_{2} .\) Why is it necessary to include \(\mathrm{Mg}^{2+}\) ions in the electrolyte?
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