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Chapter 21: Problem 47

Use the following half-reactions to write three spontaneous reactions, calculate \(E_{\text {cell }}^{\circ}\) for each reaction, and rank the strengths of the oxidizing and reducing agents: (1) \(\mathrm{Au}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Au}(s)\) \(E^{\circ}=1.69 \mathrm{~V}\) (2) \(\mathrm{N}_{2} \mathrm{O}(g)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \longrightarrow \mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \quad E^{\circ}=1.77 \mathrm{~V}\) (3) \(\mathrm{Cr}^{3+}(a q)+3 \mathrm{e}^{-} \longrightarrow \mathrm{Cr}(s) \quad E^{\circ}=-0.74 \mathrm{~V}\)

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01

Identify Half-Reactions and Standard Potentials

List the given half-reactions along with their standard reduction potentials (

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Key Concepts

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

half-reactions
A half-reaction is a part of a redox (reduction-oxidation) reaction. In an electrochemical cell, the overall reaction can be split into two half-reactions: one for the reduction process and one for the oxidation process.
Each half-reaction shows either the gain or loss of electrons. For example, in our exercise, \[\text {Au}^{+}(a q)+\text {e}^{-} \to \text {Au}(s) \] is a reduction half-reaction because it involves the gain of an electron by Au+.
Understanding half-reactions helps in balancing redox equations and calculating cell potentials.
  • Write down each half-reaction.
  • Ensure electron loss and gain are balanced.
standard reduction potential
The standard reduction potential (\(E_{\text {red}}^{\text {°}}\) ) is a measure of the tendency of a chemical species to be reduced, i.e., gain electrons. These potentials are measured under standard conditions (25°C, 1 M concentration, 1 atm pressure).
By comparing potentials, we can predict which species are stronger oxidizing agents. Higher values of \(E_{\text {red}}^{\text {°}}\) indicate stronger tendencies to be reduced.
For example, in our exercise: \(E_{\text {red}}^{\text {°}}\) = 1.77 V for \(\text {N}_2 \text {O}(g) + 2 \text {H}^+(a q) + 2 \text {e}^- \to \text {N}_2(g) + \text {H}_2 \text {O}(l)\) is higher than that of Au+ and Cr3+.
Remember:
  • Identify standard reduction potentials from tables.
  • Higher values mean stronger natural reduction tendencies.
oxidizing agents
An oxidizing agent is a substance that gains electrons in a redox reaction, causing another substance to be oxidized. In simple terms, it gets reduced and helps the oxidation of another substance.
In the provided half-reactions, we can identify oxidizing agents by looking at the reduction potentials. Higher potential means a better oxidizing agent. For instance, \(\text {N}_2O\text {(g)}\) in our exercise has the highest reduction potential (\(1.77 V\)), making it the strongest oxidizing agent among the given species.
Steps to identify:
  • Compare the standard reduction potential values.
  • Higher potential means a stronger oxidizing agent.
reducing agents
A reducing agent is a substance that loses electrons in a redox reaction, causing another substance to be reduced. It gets oxidized and helps in reduction.
In the given exercise, Cr3+ can act as a reducing agent because it can lose electrons to form metallic chromium. The lowest standard potential (\(-0.74 V\)) indicates it is a strong reducer.
Remember,
  • Lower reduction potential values mean better reducing agents.
  • Identify substances that lose electrons in half-reactions.
spontaneous reactions
A spontaneous reaction occurs without needing external energy. In electrochemistry, a reaction is spontaneous if the overall cell potential (\({E_{\text {cell}}}^{\text {°}}\)) is positive.
To calculate \({E_{\text {cell}}}^{\text {°}}\), you need to subtract the reduction potential of the anode (lower number) from that of the cathode (higher number): \[\text {E}_{\text {cell}}^{\text {°}} = E_{\text {cathode}}^{\text {°}} – E_{\text {anode}}^{\text {°}}\]Calculating these for our reactions allows ranking the strengths of oxidizing and reducing agents and identifying the spontaneity of the reaction.
  • Ensure cathode potential is higher for spontaneous reactions.
  • Calculate step-by-step.

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Most popular questions from this chapter

Define oxidation and reduction in terms of electron transfer and change in oxidation number.

What purpose does the salt bridge serve in a voltaic cell, and how does it accomplish this purpose?

An inexpensive and accurate method of measuring the quantity of electricity flowing through a circuit is to pass the current through a solution of a metal ion and weigh the metal deposited. A silver electrode immersed in an Ag \(^{+}\) solution weighs \(1.7854 \mathrm{~g}\) before the current has passed and weighs \(1.8016 \mathrm{~g}\) after the current has passed. How many coulombs have passed?

A voltaic cell is constructed with an \(\mathrm{Ag} / \mathrm{Ag}^{+}\) half- cell and a \(\mathrm{Pb} / \mathrm{Pb}^{2+}\) half-cell. The silver electrode is positive. (a) Write balanced half-reactions and the overall cell reaction. (b) Diagram the cell, labeling electrodes with their charges and showing the directions of electron flow in the circuit and of cation and anion flow in the salt bridge.

Why must an electrochemical process involve a redox reaction?
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