A voltaic cell employs the following redox reaction: Sn²⁺(aq) + Mn(s) → Sn(s) + Mn²⁺(aq) Calculate the cell potential at 25 °C under each set of conditions. c. [Sn²⁺] = 2.00 M; [Mn²⁺] = 0.0100 M

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Identify the half-reactions for the redox process. The oxidation half-reaction is: \(Mn(s) \rightarrow Mn^{2+}(aq) + 2e^-\) and the reduction half-reaction is: \(Sn^{2+}(aq) + 2e^- \rightarrow Sn(s)\).

Write the Nernst equation for the cell potential, \(E_{cell} = E^\circ_{cell} - \frac{0.0592}{n} \log \frac{[\text{Products}]}{[\text{Reactants}]}\), where \(n\) is the number of moles of electrons transferred in the balanced equation.

Determine the standard cell potential, \(E^\circ_{cell}\), using standard reduction potentials from a table: \(E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}\).

Substitute the concentrations of \(Sn^{2+}\) and \(Mn^{2+}\) into the Nernst equation. For this problem, use \([Sn^{2+}] = 2.00 \text{ M}\) and \([Mn^{2+}] = 0.0100 \text{ M}\).

Calculate the logarithmic term in the Nernst equation, \(\log \frac{[Mn^{2+}]}{[Sn^{2+}]}\), and then compute the cell potential, \(E_{cell}\), at 25 °C.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Redox Reactions

Redox reactions involve the transfer of electrons between two species, where one species is oxidized (loses electrons) and the other is reduced (gains electrons). In the given reaction, Sn2+ is reduced to Sn, while Mn is oxidized to Mn2+. Understanding the oxidation states and the flow of electrons is crucial for analyzing the cell's behavior.

Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products in a redox reaction. It is expressed as E = E° - (RT/nF) ln(Q), where E° is the standard cell 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 allows for the calculation of cell potential under non-standard conditions.

Cell Potential

Cell potential, or electromotive force (EMF), is the measure of the energy per unit charge available from a redox reaction in a voltaic cell. It indicates the tendency of the cell to drive the reaction forward. A positive cell potential signifies a spontaneous reaction, while a negative value indicates non-spontaneity. The cell potential can vary with concentration changes, which is why it is essential to consider the specific concentrations given in the problem.

A voltaic cell employs the following redox reaction: Sn2+(aq) + Mn(s) → Sn(s) + Mn2+(aq) Calculate the cell potential at 25 °C under each set of conditions. c. [Sn2+] = 2.00 M; [Mn2+] = 0.0100 M