Understanding Spontaneity of Redox Reactions

A reaction is spontaneous if the cell potential (E°_cell) is positive. For the reaction X + Y²⁺ → X²⁺ + Y, it represents the oxidation of X and reduction of Y²⁺. The standard cell potential is calculated as:

$E_{cell}=E_Y^{\circ }-E_X^{\circ }$

where E°_Y is the reduction potential of Y²⁺/Y and E°_X is the reduction potential of X²⁺/X. For spontaneity, E°_cell > 0, which requires E°_Y > E°_X. This means Y²⁺ must be a stronger oxidizing agent (higher reduction potential) than X²⁺.

Step-by-Step Solution:

Step 1: List the given reduction potentials:

• E° for Zn²⁺/Zn = -0.76 V
• E° for Ni²⁺/Ni = -0.23 V
• E° for Fe²⁺/Fe = -0.44 V

Step 2: Analyze each option by calculating E°_cell = E°_Y - E°_X:

• Option 1: X = Ni, Y = Fe → E°_cell = E°_Fe - E°_Ni = (-0.44) - (-0.23) = -0.21 V (Not spontaneous)
• Option 2: X = Zn, Y = Ni → E°_cell = E°_Ni - E°_Zn = (-0.23) - (-0.76) = +0.53 V (Spontaneous)
• Option 3: X = Fe, Y = Zn → E°_cell = E°_Zn - E°_Fe = (-0.76) - (-0.44) = -0.32 V (Not spontaneous)
• Option 4: X = Ni, Y = Zn → E°_cell = E°_Zn - E°_Ni = (-0.76) - (-0.23) = -0.53 V (Not spontaneous)

Step 3: Final Answer: Only Option 2 (X = Zn, Y = Ni) gives a positive E°_cell, so the reaction is spontaneous in this case.

Related Topics:

• Electrochemical Series
• Standard Reduction Potential
• Spontaneity of Redox Reactions
• Galvanic Cells

Key Formulae and Theory:

The standard cell potential for a reaction is given by:

$E_{cell}=E_{cathode}^{\circ }-E_{anode}^{\circ }$

where E°_cathode is the reduction potential of the species being reduced and E°_anode is the reduction potential of the species being oxidized. A positive E°_cell indicates a spontaneous reaction under standard conditions. The relationship between cell potential and Gibbs free energy is:

$\mathrm{\Delta }{G}^{\circ }=-nF{E}_{cell}^{\circ }$

where n is the number of electrons transferred, F is the Faraday constant, and ΔG° is the standard Gibbs free energy change. A negative ΔG° (which corresponds to a positive E°_cell) signifies a spontaneous process.