Cell Potentials and Spontaneity

Detailed Explanations

A. Workflow: E⦵_cell, direction, and feasibility (standard conditions)

1. Write down the two E⦵ values from the data booklet (both are reductions).
2. The more positive E⦵ stays as reduction → cathode.
3. The other half-equation is reversed → oxidation at anode.
4. Calculate: E⦵_cell = E⦵_cathode - E⦵_anode
5. Interpret the sign:
   • E⦵_cell > 0: feasible under standard conditions
   • E⦵_cell < 0: not feasible under standard conditions (reverse is feasible)

Mini example: If E⦵(Cu²⁺/Cu) = +0.34 and E⦵(Zn²⁺/Zn) = -0.76, then Cu is the cathode and E⦵_cell = 0.34-(-0.76) = +1.10 V.

B. What the sign means (and what it does not mean)

• E⦵_cell > 0: feasible under standard conditions.
• E⦵_cell < 0: not feasible under standard conditions (the reverse reaction would be feasible).

But:

• changing concentration / pressure / temperature can change feasibility (this is why cells can be rechargeable or vary in voltage).

Link to energetics wording (optional but useful): Δ G⦵ = -nFE⦵_cell.

C. Worked method you can reuse (30-second structure)

Write this sequence every time:

1. “More positive reduction potential is the cathode.”
2. “Other half-cell is the anode.”
3. “ E⦵_cell = E⦵_cathode - E⦵_anode = …”
4. “Since E⦵_cell is [positive/negative], the forward reaction is [feasible/not feasible] under standard conditions.”

D. Limits of feasibility predictions

A positive E⦵_cell is a thermodynamic prediction for the reaction as written under standard conditions. It does not guarantee an observable rate: activation energy, passivation or another kinetic barrier may make a feasible reaction very slow. Actual concentration, gas pressure and temperature may also differ from standard conditions, so the actual cell potential need not equal E⦵_cell.

E. Qualitative concentration effects

For a reduction written as Ox + ne⁻ ⇌ Red, increasing the concentration of the oxidised aqueous species generally favours reduction and makes the electrode potential more positive. Increasing the concentration of the reduced aqueous species generally opposes reduction and makes it less positive. Use the actual half-equation to identify which side is changed; do not memorise “higher concentration means higher potential” without naming the species.