An MnO₂(s)/Mn²⁺(aq) electrode in which the pH si 10.24 is prepared. Find the [Mn²⁺] necessary to lower the potential of the half-cell to 0.00 V (at 25°C)

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Identify the half-reaction for the MnO2(s)/Mn2+(aq) electrode: \( \text{MnO}_2(s) + 4\text{H}^+(aq) + 2\text{e}^- \rightarrow \text{Mn}^{2+}(aq) + 2\text{H}_2\text{O}(l) \).

Use the Nernst equation to relate the cell potential to the concentrations and pH: \( E = E^0 - \frac{RT}{nF} \ln Q \), where \( Q \) is the reaction quotient.

Determine the standard reduction potential \( E^0 \) for the half-reaction from a standard reduction potential table.

Calculate the reaction quotient \( Q \) using \( Q = \frac{[\text{Mn}^{2+}]}{[\text{H}^+]^4} \). Given \( \text{pH} = 10.24 \), find \( [\text{H}^+] = 10^{-10.24} \).

Set \( E = 0.00 \) V and solve the Nernst equation for \( [\text{Mn}^{2+}] \) to find the concentration necessary to achieve the desired potential.

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주요 개념

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Nernst Equation

The Nernst Equation relates the reduction potential of an electrochemical cell to the concentrations of the reactants and products. It is expressed as E = E° - (RT/nF) ln(Q), where E is the cell potential, E° is the standard potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday's constant, and Q is the reaction quotient. This equation is essential for calculating the potential of the half-cell under non-standard conditions.

pH and its Effect on Electrochemical Reactions

pH is a measure of the hydrogen ion concentration in a solution, which can significantly influence the behavior of electrochemical reactions. In this case, a pH of 10.24 indicates a basic environment, affecting the solubility and speciation of manganese ions. Understanding how pH alters the equilibrium of the MnO2/Mn2+ system is crucial for determining the necessary concentration of Mn2+ to achieve the desired potential.

Equilibrium and Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative concentrations of products and reactants at any point in a reaction. For the MnO2/Mn2+ half-cell, Q can be expressed as [Mn2+]/[MnO2]. At equilibrium, Q equals the equilibrium constant (K), and changes in concentration will shift the equilibrium position according to Le Chatelier's principle. This concept is vital for understanding how to manipulate [Mn2+] to achieve a specific cell potential.

An MnO2(s)/Mn2+(aq) electrode in which the pH si 10.24 is prepared. Find the [Mn2+] necessary to lower the potential of the half-cell to 0.00 V (at 25°C)