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Chapter 17: Problem 20

Tell whether this statement is true or false. If false, rewrite it to make it a correct statement: The value of an electrode potential changes when the half-reaction is multiplied by a factor. That is, \(E^{\circ}\) for \(\mathrm{Li}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Li}\) is different from that for \(2 \mathrm{Li}^{+}+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Li}\).

Short Answer

Expert verified
False. Electrode potentials are independent of reaction scaling.

Step by step solution

01

Understanding Electrode Potentials

Electrode potentials, denoted as \(E^{\circ}\), are standard reduction potentials measured under standard conditions. They are intrinsic to the chemical reaction itself and do not depend on the stoichiometry or number of electrons involved in the half-reaction.
02

Analyzing the Given Statement

The problem suggests that multiplying a half-reaction by a factor alters its electrode potential. We'll explore if this claim is correct by considering that \(E^{\circ}\) values are intensive properties and should remain unchanged by scaling the reaction.
03

Evaluating the Half-Reactions

Consider the initial reaction: \(\mathrm{Li}^{+} + \mathrm{e}^{-} \rightarrow \mathrm{Li}\), with a potential \(E^{\circ}\). Multiplying this reaction by 2 does not change the potential: \(2\mathrm{Li}^{+} + 2\mathrm{e}^{-} \rightarrow 2\mathrm{Li}\) also has the same \(E^{\circ}\). The potential value remains the same irrespective of the coefficients.
04

Conclusion on Statement Validity

The statement that the electrode potential changes with the reaction's scaling is false. Electrode potentials are independent of the stoichiometric coefficients in the reaction. Hence, the correct statement should be: The value of an electrode potential \(E^{\circ}\) remains unchanged when a half-reaction is multiplied by a factor.

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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 measure of the tendency of a chemical species to gain electrons and be reduced. It tells us how easily a species can undergo a reduction reaction.
These values are often represented as standard reduction potentials, denoted by \(E^{\circ}\).
It is important to note that these potentials are compared to a standard hydrogen electrode, which is assigned a potential of zero.
  • Higher \(E^{\circ}\) indicates a greater tendency to be reduced.
  • Reduction potentials are intensive properties, meaning they do not change with the amount of substance.
  • These values help predict the direction of electrochemical reactions.
Understanding how reduction potentials work allows us to figure out which way electrons will flow in a reaction, making it essential for solving electrochemical problems.
Standard Conditions
Standard conditions are specific conditions under which electrode potentials are measured. This ensures consistency across various measurements and allows us to accurately compare different reactions.
These conditions include:
  • Temperature of 25掳C (298 K).
  • Concentration of 1 M for any dissolved substances.
  • Pressure of 1 atm for any gases involved.
By maintaining these fixed conditions, we can ensure that the \(E^{\circ}\) values are consistent and reliable.
This also allows scientists and students to compare and utilize these values when predicting the favorability of electrochemical reactions.
Stoichiometry
Stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. It uses coefficients in balanced equations to show how much of each substance is involved.
However, for electrode potentials, stoichiometry does not alter the value of \(E^{\circ}\).
This might seem counterintuitive because stoichiometry affects the amounts and ratios of substances, but the intrinsic nature of electrode potentials remains unchanged.
  • Electrode potentials are about the inherent energy needed for reduction, not the amount reacting.
  • Multiplying coefficients in a half-reaction will not affect the potential value.
Understanding this distinction is key to avoiding mistakes when working with electrochemical reactions.
Half-Reaction
A half-reaction describes either the oxidation or reduction part of a redox reaction.
It focuses only on one side of the electron transfer process, making it easier to study the individual components.
  • Reduction half-reactions involve gaining electrons.
  • Oxidation half-reactions involve losing electrons.
Half-reactions are useful because they allow us to consider the separate processes occurring in a redox reaction.
By focusing on one aspect, scientists and students can more clearly analyze and calculate important properties like electrode potentials.
When combining half-reactions, it鈥檚 crucial to ensure that the electrons gained and lost are balanced, but this balancing does not affect the electrode potential value.

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Most popular questions from this chapter

Explain how galvanizing iron stops corrosion of the underlying iron.

The major reduction half-reaction occurring in the cell in which molten \(\mathrm{Al}_{2} \mathrm{O}_{3}\) and molten aluminum salts are electrolyzed is \(\mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}(\mathrm{s})\). The cell operates at \(5.0 \mathrm{~V}\) and \(1.0 \times 10^{5} \mathrm{~A} .\) Calculate the mass \((\mathrm{g})\) of aluminum metal produced in \(8.0 \mathrm{~h}\).

Make a drawing showing the principal parts of (a) a voltaic cell: show the anode, the cathode, the direction of electron movement outside the cell, and the direction of ion movement inside the cell. (b) a standard hydrogen electrode: describe the components of the electrode and explain how it works.

Copper can reduce silver ion to metallic silver, a reaction that could, in principle, be used in a battery. $$ \mathrm{Cu}(\mathrm{s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s}) $$ (a) Write equations for the half-reactions involved. (b) Which half-reaction is an oxidation and which is a reduction? Which half- reaction occurs in the anode compartment and which takes place in the cathode compartment?

In principle, a battery could be made from aluminum metal and chlorine gas. (a) Write a balanced equation for the reaction that would occur in a battery using \(\mathrm{Al}^{3+}(\mathrm{aq}) \mid \mathrm{Al}(\mathrm{s})\) and \(\mathrm{Cl}_{2}(\mathrm{~g}) \mid \mathrm{Cl}^{-}(\) aq \()\) half-cells. (b) Identify the half-reaction at the anode and at the cathode. Do electrons flow from the \(\mathrm{Al}\) electrode when the cell does work? Explain. (c) Calculate the standard potential, \(E_{\text {cell }}^{\circ}\), for the battery.
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