Problem 20 - Chemistry The Molecular Science

Question

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 \(2 \mathrm{Li}^{+}+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Li}\).

Step-by-Step Solution

Answer

False. Electrode potentials are independent of reaction scaling.

Step 1: 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.

Step 2: 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.

Step 3: 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.

Step 4: 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.

Key Concepts

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°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’s crucial to ensure that the electrons gained and lost are balanced, but this balancing does not affect the electrode potential value.