A voltaic cell is constructed that uses the following reaction and operates at 298 K: Zn(s) + Ni²⁺(aq) → Zn²⁺(aq) + Ni(s) (b) What is the emf of this cell when [Ni²⁺] = 3.00 M and [Zn²⁺] = 0.100 M? (c) What is the emf of the cell when [Ni²⁺] = 0.200 M and [Zn²⁺] = 0.900 M?

검증된 단계별 안내

Identify the half-reactions for the zinc and nickel in the cell. For zinc: Zn(s) → Zn^{2+}(aq) + 2e^{-}, and for nickel: Ni^{2+}(aq) + 2e^{-} → Ni(s).

Write the overall cell reaction by combining the half-reactions: Zn(s) + Ni^{2+}(aq) → Zn^{2+}(aq) + Ni(s).

Calculate the standard cell potential (E°) using standard reduction potentials. E° = E°_{cathode} - E°_{anode}. Look up the standard reduction potentials for Ni^{2+}/Ni and Zn^{2+}/Zn.

Use the Nernst equation to find the cell potential under non-standard conditions: E = E° - (RT/nF) \(\ln\)(Q), where Q is the reaction quotient, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, and F is the Faraday constant.

Calculate Q, the reaction quotient, using the concentrations given: Q = \(\frac{[Zn^{2+}\)]}{[Ni^{2+}]} = \(\frac{0.900}{0.200}\). Substitute this value into the Nernst equation to find the emf of the cell.

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주요 개념

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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, generating a flow of electrons that can be harnessed for electrical work. Understanding the components and functioning of these cells is essential for calculating their electromotive force (emf).

Nernst Equation

The Nernst equation relates the cell potential (emf) 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 emf under 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. It is calculated using the formula Q = [products]/[reactants], where the concentrations are raised to the power of their coefficients in the balanced equation. In the context of the Nernst equation, Q helps determine how the cell potential changes as the reaction progresses towards equilibrium.

A voltaic cell is constructed that uses the following reaction and operates at 298 K: Zn(s) + Ni2+(aq) → Zn2+(aq) + Ni(s) (b) What is the emf of this cell when [Ni2+] = 3.00 M and [Zn2+] = 0.100 M? (c) What is the emf of the cell when [Ni2+] = 0.200 M and [Zn2+] = 0.900 M?