To determine the cell potential when connecting the Sn⁴⁺ | Sn²⁺ couple with the Cr³⁺ | Cr couple, we need to apply the concept of standard electrode potentials. The cell potential (E_cell) can be calculated using the formula:
Understanding Standard Electrode Potentials
Standard electrode potential is a measure of the tendency of a chemical species to be reduced, measured in volts (V). A positive value indicates a greater tendency to gain electrons (be reduced), while a negative value indicates a lesser tendency.
Identifying the Half-Reactions
We have two half-reactions based on the given standard electrode potentials:
- For the Sn⁴⁺ | Sn²⁺ couple:
- Reduction: Sn⁴⁺ + 2e⁻ → Sn²⁺, E° = +0.15 V
- For the Cr³⁺ | Cr couple:
- Reduction: Cr³⁺ + 3e⁻ → Cr, E° = -0.74 V
Determining the Overall Cell Reaction
In a galvanic cell, the half-reaction with the higher standard electrode potential will occur as a reduction, while the one with the lower potential will occur as an oxidation. Therefore:
- Oxidation (Cr): Cr → Cr³⁺ + 3e⁻, E° = +0.74 V (reverse the sign)
- Reduction (Sn): Sn⁴⁺ + 2e⁻ → Sn²⁺, E° = +0.15 V
Balancing the Electrons
Before we can add these half-reactions, we need to ensure that the number of electrons lost in oxidation equals the number gained in reduction. The least common multiple of 2 and 3 is 6, so we multiply the half-reactions accordingly:
- Oxidation: 2Cr → 2Cr³⁺ + 6e⁻
- Reduction: 3Sn⁴⁺ + 6e⁻ → 3Sn²⁺
Calculating the Cell Potential
Now, we can find the overall cell potential by adding the standard electrode potentials of the two half-reactions:
E_cell = E°(reduction) + E°(oxidation)
E_cell = (+0.15 V) + (+0.74 V) = +0.89 V
Final Answer
Thus, the cell potential when connecting the Sn⁴⁺ | Sn²⁺ couple with the Cr³⁺ | Cr couple is +0.89 V. The correct answer is B. +0.89V.
