The efficiency of a cell is 60%.i ts cell reaction is A(s) + B power(2+)(aq)=A power (2+)(aq)+B; ∆H=-240kj. The standard electrode potential of the cell

To determine the standard electrode potential of the cell reaction you've provided, we need to consider a few key concepts from electrochemistry. The efficiency of the cell, which is 60% in this case, indicates how effectively the cell converts chemical energy into electrical energy. However, to find the standard electrode potential, we primarily focus on the thermodynamic aspects of the reaction.

Understanding the Reaction

The cell reaction is given as:

A(s) + B²⁺(aq) = A²⁺(aq) + B

Here, A is a solid reactant, and B²⁺ is an aqueous ion. The products are A²⁺ in solution and solid B. The change in enthalpy (∆H) for this reaction is -240 kJ, indicating that the reaction is exothermic, meaning it releases energy.

Relating Enthalpy to Electrode Potential

The standard electrode potential (E°) can be related to the Gibbs free energy change (∆G) of the reaction using the following equation:

∆G = -nFE°

Where:

• ∆G is the Gibbs free energy change.
• n is the number of moles of electrons transferred in the reaction.
• F is the Faraday constant (approximately 96485 C/mol).
• E° is the standard electrode potential.

Calculating Gibbs Free Energy Change

To find ∆G, we can use the relationship between enthalpy and Gibbs free energy:

∆G = ∆H - T∆S

However, we need the entropy change (∆S) to calculate this accurately. If we assume that the reaction occurs at standard conditions (298 K) and that we don't have specific entropy values, we can simplify our approach by using the given enthalpy change directly for a rough estimate.

Assuming n and Finding E°

For this reaction, let’s assume that 2 moles of electrons are transferred (this is common for reactions involving divalent ions). Thus, n = 2. Now we can rearrange the equation for E°:

E° = -∆G / (nF)

Since we don't have ∆G directly, we can approximate it using ∆H. If we take ∆H = -240 kJ, we convert this to joules:

∆H = -240,000 J

Now, substituting into the equation:

E° = -(-240,000 J) / (2 * 96485 C/mol)

E° = 240,000 J / 192970 C/mol

E° ≈ 1.24 V

Final Thoughts

The calculated standard electrode potential for the cell reaction is approximately 1.24 V. This value indicates a strong driving force for the reaction under standard conditions. Keep in mind that the actual potential may vary based on concentration, temperature, and other factors, but this gives you a solid foundation for understanding how to approach these types of electrochemical problems.