What is the pH of the solution in the cathode compartment of the following cell if the measured cell potential at 25 °C is 0.58 V? (Refer to Appendix B for standard reduction potentials.) (a) 8.0(b) 4.5(c) 2.2(d) 3.0

Verified step by step guidance

1. Identify the half-reactions occurring at the anode and cathode using standard reduction potentials from Appendix B.
2. Write the overall cell reaction by combining the half-reactions, ensuring that electrons are balanced.
3. Use the Nernst equation: $E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q$, where $E_{cell}$ is the measured cell potential, $E^\circ_{cell}$ 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.
4. Rearrange the Nernst equation to solve for the reaction quotient $Q$: $Q = e^{\frac{nF(E^\circ_{cell} - E_{cell})}{RT}}$.
5. Determine the concentration of H+ ions in the cathode compartment from the reaction quotient $Q$, and calculate the pH using the formula $pH = -\log[H^+]$.

Key Concepts

Nernst Equation

The Nernst Equation relates the cell potential to the concentrations of the reactants and products in an electrochemical cell. It allows for the calculation of the cell potential under non-standard conditions, taking into account temperature and concentration. 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.

pH and Hydrogen Ion Concentration

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration: pH = -log[H+]. A lower pH indicates a higher concentration of hydrogen ions, which corresponds to a more acidic solution. Understanding the relationship between pH and [H+] is crucial for interpreting the conditions in the cathode compartment of the electrochemical cell.

Standard Reduction Potentials

Standard reduction potentials are values that indicate the tendency of a species to gain electrons and be reduced, measured under standard conditions (1 M concentration, 1 atm pressure, and 25 °C). These potentials are used to predict the direction of electron flow in electrochemical cells. By comparing the standard reduction potentials of the half-reactions involved, one can determine the overall cell potential and the feasibility of the reaction.