A galvanic cell has a silver electrode in contact with 0.050 M AgNO3 and a copper electrode in contact with 1.0 M Cu(NO3)2. (a) Write a balanced equation for the cell reaction, and calculate the cell potential at 25 °C.

Verified step by step guidance

1. Identify the half-reactions for the silver and copper electrodes. Silver undergoes reduction: \( \text{Ag}^+ + e^- \rightarrow \text{Ag} \). Copper undergoes oxidation: \( \text{Cu} \rightarrow \text{Cu}^{2+} + 2e^- \).
2. Balance the electrons in the half-reactions. Multiply the silver half-reaction by 2 to balance the electrons: \( 2\text{Ag}^+ + 2e^- \rightarrow 2\text{Ag} \).
3. Combine the balanced half-reactions to write the overall balanced cell reaction: \( 2\text{Ag}^+ + \text{Cu} \rightarrow 2\text{Ag} + \text{Cu}^{2+} \).
4. Use the Nernst equation to calculate the cell potential: \( E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q \), where \( E^\circ_{cell} \) 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.
5. Calculate the standard cell potential \( E^\circ_{cell} \) using standard reduction potentials: \( E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} \). Look up the standard reduction potentials for silver and copper and substitute them into the equation.

Key Concepts

Galvanic Cell

A galvanic cell is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two electrodes, an anode and a cathode, immersed in electrolyte solutions. The flow of electrons from the anode to the cathode generates an electric current, and the cell potential can be calculated using standard reduction potentials.

Standard Reduction Potentials

Standard reduction potentials are measured voltages that indicate the tendency of a chemical species to gain electrons and be reduced. Each half-reaction has a specific potential, and these values can be found in standard tables. The overall cell potential is determined by subtracting the anode potential from the cathode potential, allowing for the prediction of the direction of electron flow and the feasibility of the reaction.

Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products at non-standard conditions. It accounts for temperature and concentration changes, allowing for the calculation of the cell potential under specific conditions. The equation is given by 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.