A voltaic cell that uses the reaction PdCl₄^2-(aq) + Cd(s) → Pd(s) + 4 Cl^-(aq) + Cd²⁺(aq) has a measured standard cell potential of +1.03 V. (b) By using data from Appendix E, determine E°_red for the reaction involving Pd.

Verified step by step guidance

1. Identify the half-reactions involved in the voltaic cell. The given overall reaction is: \[ \text{PdCl}_4^{2-} (aq) + \text{Cd} (s) \rightarrow \text{Pd} (s) + 4 \text{Cl}^- (aq) + \text{Cd}^{2+} (aq) \].
2. Write the oxidation and reduction half-reactions. The oxidation half-reaction is: \[ \text{Cd} (s) \rightarrow \text{Cd}^{2+} (aq) + 2e^- \]. The reduction half-reaction is: \[ \text{PdCl}_4^{2-} (aq) + 2e^- \rightarrow \text{Pd} (s) + 4 \text{Cl}^- (aq) \].
3. Use the standard cell potential equation: \[ E^\circ_{\text{cell}} = E^\circ_{\text{red}} (\text{cathode}) - E^\circ_{\text{red}} (\text{anode}) \]. Here, \( E^\circ_{\text{cell}} = +1.03 \text{ V} \).
4. Look up the standard reduction potential for the cadmium half-reaction from Appendix E: \( E^\circ_{\text{red}} (\text{Cd}^{2+}/\text{Cd}) \).
5. Rearrange the equation to solve for \( E^\circ_{\text{red}} (\text{PdCl}_4^{2-}/\text{Pd}) \): \[ E^\circ_{\text{red}} (\text{PdCl}_4^{2-}/\text{Pd}) = E^\circ_{\text{cell}} + E^\circ_{\text{red}} (\text{Cd}^{2+}/\text{Cd}) \].

Key Concepts

Voltaic Cell

A voltaic cell, also known as a galvanic cell, is an electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two half-cells, each containing an electrode and an electrolyte. The flow of electrons from the anode to the cathode generates an electric current, and the cell potential (E°) is a measure of the driving force behind the reaction.

Standard Reduction Potential (E°red)

Standard reduction potential (E°red) is a measure of the tendency of a chemical species to gain electrons and be reduced, measured under standard conditions (1 M concentration, 1 atm pressure, and 25°C). Each half-reaction has a specific E°red value, which can be used to calculate the overall cell potential of a voltaic cell. A higher E°red indicates a greater likelihood of reduction occurring.

Nernst Equation

The Nernst equation relates the cell potential of an electrochemical cell to the concentrations of the reactants and products involved in the redox reaction. It allows for the calculation of the cell potential under non-standard conditions and is expressed as E = E° - (RT/nF)ln(Q), where Q is the reaction quotient. Understanding this equation is crucial for analyzing how changes in concentration affect the cell potential.