Calculate the standard reduction potential for Ba2+ (aq) + 2 e- -> Ba(s) given that ∆G° = 16.7 kJ for the reaction Ba2+(aq) + 2Cl-(aq) -> BaCl2(s). Use any necessary data from Appendices B and D.

Verified step by step guidance

1. Step 1: Understand the relationship between Gibbs free energy change (\( \Delta G^\circ \)) and the standard cell potential (\( E^\circ \)). The equation that relates these two is \( \Delta G^\circ = -nFE^\circ \), where \( n \) is the number of moles of electrons transferred, and \( F \) is the Faraday constant (approximately 96485 C/mol).
2. Step 2: Identify the number of electrons transferred in the reduction half-reaction. For the reaction \( \text{Ba}^{2+} (aq) + 2e^- \rightarrow \text{Ba}(s) \), \( n = 2 \) electrons are transferred.
3. Step 3: Rearrange the equation \( \Delta G^\circ = -nFE^\circ \) to solve for \( E^\circ \). This gives \( E^\circ = -\frac{\Delta G^\circ}{nF} \).
4. Step 4: Substitute the given \( \Delta G^\circ = 16.7 \text{ kJ} \) into the equation. Remember to convert \( \Delta G^\circ \) from kJ to J by multiplying by 1000, so \( \Delta G^\circ = 16700 \text{ J} \).
5. Step 5: Calculate \( E^\circ \) using the values: \( n = 2 \), \( F = 96485 \text{ C/mol} \), and \( \Delta G^\circ = 16700 \text{ J} \). Substitute these into the equation \( E^\circ = -\frac{16700}{2 \times 96485} \) to find the standard reduction potential.

Key Concepts

Standard Reduction Potential

Standard reduction potential (E°) is a measure of the tendency of a chemical species to acquire electrons and be reduced. It is measured in volts and is determined under standard conditions (1 M concentration, 1 atm pressure, and 25°C). A higher E° value indicates a greater likelihood of reduction occurring, which is crucial for understanding electrochemical reactions.

Gibbs Free Energy and its Relation to E°

Gibbs free energy (∆G) is a thermodynamic potential that indicates the spontaneity of a reaction. The relationship between Gibbs free energy and standard reduction potential is given by the equation ∆G° = -nFE°, where n is the number of moles of electrons transferred, F is Faraday's constant, and E° is the standard reduction potential. This relationship allows us to calculate E° from known values of ∆G°.

Electrochemical Cell Reactions

Electrochemical cells consist of oxidation and reduction half-reactions. In the given reaction, Ba2+ is reduced to Ba(s), while the overall process involves the formation of BaCl2 from Ba2+ and Cl-. Understanding how to balance these half-reactions and relate them to standard potentials is essential for calculating the overall cell potential and determining the feasibility of the reaction.