A voltaic cell consists of a Pb/Pb²⁺ half-cell and a Cu/Cu²⁺ half-cell at 25°C. The initial concentrations of Pb²⁺ and Cu²⁺ are 0.0500 M and 1.50 M, respectively. c. What are the concentrations of Pb²⁺ and Cu²⁺ when the cell potential falls to 0.35 V?

검증된 단계별 안내

Identify the standard reduction potentials for both half-cells. For Pb, the reaction is Pb^2+ + 2e^- \(\rightarrow\) Pb, and for Cu, the reaction is Cu^2+ + 2e^- \(\rightarrow\) Cu.

Write the overall cell reaction by combining the two half-reactions. Make sure to balance the electrons in the half-reactions.

Use the Nernst equation to relate the cell potential to the ion concentrations. The Nernst equation is E = E^0 - (RT/nF) \(\ln\) Q, where E is the cell potential, E^0 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 the Faraday constant, and Q is the reaction quotient.

Calculate the reaction quotient Q using the initial concentrations of Pb^2+ and Cu^2+. Q is given by the expression Q = [Pb^2+]/[Cu^2+]^2.

Solve the Nernst equation for the new concentrations of Pb^2+ and Cu^2+ when the cell potential is 0.35 V. Rearrange the equation to isolate the terms involving the concentrations and solve for the unknowns.

비슷한 문제에 대한 검증된 영상 답변:

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 and reduction at the cathode, creating a flow of electrons that generates an electric current. Understanding the roles of the half-cells and the overall cell reaction is crucial for analyzing the cell's behavior under different conditions.

Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products in a redox reaction. It allows for the calculation of the cell potential at non-standard conditions, taking into account temperature and concentration changes. This equation is essential for determining how the concentrations of Pb2+ and Cu2+ will change as the cell operates and the potential decreases.

Standard Electrode Potentials

Standard electrode potentials are measured voltages that indicate the tendency of a half-cell to gain or lose electrons under standard conditions. Each half-cell has a specific standard potential, which is used to calculate the overall cell potential. Knowing the standard potentials for the Pb and Cu half-cells is necessary to understand how the cell operates and how the potential changes as the reaction proceeds.

A voltaic cell consists of a Pb/Pb2+ half-cell and a Cu/Cu2+ half-cell at 25°C. The initial concentrations of Pb2+ and Cu2+ are 0.0500 M and 1.50 M, respectively. c. What are the concentrations of Pb2+ and Cu2+ when the cell potential falls to 0.35 V?