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. b. What is the cell potential when the concentration of Ni²⁺ has fallen to 0.500 M?

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 potential: E = E^0 - \(\frac{RT}{nF}\) \(\ln\) Q, where Q is the reaction quotient.

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

Determine the reaction quotient (Q) using the concentrations: Q = \(\frac{[Zn^{2+}\)]}{[Ni^{2+}]}.

Substitute the values into the Nernst equation to find the cell potential at the given concentrations.

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주요 개념

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Nernst Equation

The Nernst Equation relates the cell 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 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 us to calculate the 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 voltaic cell. It indicates the tendency of the cell to drive an electric current through an external circuit. The potential is influenced by the concentrations of the reactants and products, and it can change as the reaction proceeds, which is crucial for understanding how the cell operates over time.

Half-Cell Reactions

In a voltaic cell, half-cell reactions occur at the anode and cathode, where oxidation and reduction take place, respectively. For the Zn|Zn2+ half-cell, zinc is oxidized to Zn2+, while in the Ni|Ni2+ half-cell, Ni2+ is reduced to nickel. Understanding these half-cell reactions is essential for calculating the overall cell potential and determining how changes in concentration affect the cell's performance.

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. b. What is the cell potential when the concentration of Ni2+ has fallen to 0.500 M?