An electrochemical cell is based on these two half-reactions:
Ox: Sn(s) → Sn²⁺(aq, 2.00 M) + 2 e^–
Red: ClO₂(g, 0.100 atm) + e^– → ClO₂^–(aq, 2.00 M)
Calculate the cell potential at 25 °C.

Verified step by step guidance

1. Write the balanced overall cell reaction by combining the oxidation and reduction half-reactions. Ensure that the number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction.
2. Use the Nernst equation to calculate the cell potential. The Nernst equation is given by: \( E = E^\circ - \frac{RT}{nF} \ln Q \), where \( E^\circ \) is the standard cell potential, \( R \) is the gas constant (8.314 J/mol·K), \( T \) is the temperature in Kelvin, \( n \) is the number of moles of electrons transferred, \( F \) is the Faraday constant (96485 C/mol), and \( Q \) is the reaction quotient.
3. Calculate the standard cell potential (\( E^\circ \)) using the standard reduction potentials of the two half-reactions. The standard cell potential is the difference between the standard reduction potential of the cathode and the anode: \( E^\circ = E^\circ_{cathode} - E^\circ_{anode} \).
4. Determine the reaction quotient (\( Q \)) using the concentrations and partial pressures given in the problem. For the reaction quotient, use the expression \( Q = \frac{[products]}{[reactants]} \), considering the stoichiometry of the balanced overall reaction.
5. Substitute the values of \( E^\circ \), \( R \), \( T \), \( n \), \( F \), and \( Q \) into the Nernst equation to find the cell potential (\( E \)).

Key Concepts

Electrochemical Cells

Electrochemical cells convert chemical energy into electrical energy through redox reactions. They consist of two half-cells, each containing an electrode and an electrolyte. The oxidation half-reaction occurs at the anode, while the reduction half-reaction takes place at the cathode. The cell potential, or electromotive force (EMF), is the driving force for the flow of electrons from the anode to the cathode.

Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products involved in the half-reactions. 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 the cell potential under non-standard conditions.

Standard Reduction Potentials

Standard reduction potentials (E°) are measured under standard conditions (1 M concentration, 1 atm pressure, and 25 °C) and indicate the tendency of a species to gain electrons. Each half-reaction has a specific E° value, which can be found in tables. The overall cell potential can be calculated by subtracting the anode potential from the cathode potential, providing insight into the feasibility and direction of the electrochemical reaction.