A voltaic cell consists of a Zn/Zn²⁺ half-cell and a Ni/Ni²⁺ half-cell at 25 °C. The initial concentrations of Ni²⁺ and Zn²⁺ are 1.50 M and 0.100 M, respectively. c. What are the concentrations of Ni²⁺ and Zn²⁺ when the cell potential falls to 0.45 V?

검증된 단계별 안내

Identify the half-reactions for the voltaic cell: Zn -> Zn^{2+} + 2e^- and Ni^{2+} + 2e^- -> Ni.

Write the Nernst equation for the cell: E = E^0 - (RT/nF) * ln(Q), where Q is the reaction quotient.

Calculate the standard cell potential (E^0) using standard reduction potentials: E^0 = E^0_{cathode} - E^0_{anode}.

Set up the expression for the reaction quotient Q: Q = [Zn^{2+}]/[Ni^{2+}].

Substitute the given cell potential (0.45 V) and solve the Nernst equation for the concentrations of Ni^{2+} and Zn^{2+}.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

주요 개념

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

Electrochemical Cells

Electrochemical cells, such as voltaic cells, convert chemical energy into electrical energy through redox reactions. In a voltaic cell, oxidation occurs at the anode (where Zn is oxidized to Zn2+) and reduction occurs at the cathode (where Ni2+ is reduced to Ni). Understanding the flow of electrons and the role of each half-cell is crucial for analyzing cell behavior and potential.

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 is essential for calculating the cell potential at non-standard conditions.

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 voltaic cell in question, Q is calculated using the concentrations of Zn2+ and Ni2+ ions. As the reaction proceeds, the concentrations change, affecting Q and consequently the cell potential, which is critical for determining the concentrations when the potential drops to a specific value.

A voltaic cell consists of a Zn/Zn2+ half-cell and a Ni/Ni2+ half-cell at 25 °C. The initial concentrations of Ni2+ and Zn2+ are 1.50 M and 0.100 M, respectively. c. What are the concentrations of Ni2+ and Zn2+ when the cell potential falls to 0.45 V?