Chemistry

Problem

A manufacturer wants to create a standard-condition galvanic cell whose standard cell potential is as close as possible to

+1.10\,\text{V}

, while using only the half-reactions in the table below. Any given half-reaction may be used once, reversed if necessary, and multiplied by an integer as required for electron balance. Standard reduction potentials (

25\,^{\circ}\text{C}

): 1. Ag⁺(aq) + e⁻ → Ag(s)

E^\circ = +0.80\,\text{V}

2. Fe3⁺(aq) + e⁻ → Fe2⁺(aq)

E^\circ = +0.77\,\text{V}

3. I2(s) + 2 e⁻ → 2 I⁻(aq)

E^\circ = +0.54\,\text{V}

4. Zn2⁺(aq) + 2 e⁻ → Zn(s)

E^\circ = -0.76\,\text{V}

(a) Identify a pair of half-reactions from the table that, when combined appropriately, produces an overall

E^\circ_{\text{cell}}

whose magnitude is the closest to

+1.10\,\text{V}

. State which half-reaction is written as a reduction and which is written as an oxidation. (b) Balance the chosen half-reactions for electrons, combine them into a single overall redox equation, and calculate the exact value of

E^\circ_{\text{cell}}

. (c) Compute the corresponding standard free-energy change

\Delta G^\circ

(in kJ mol⁻¹) for the balanced overall reaction from part (b). (d) Evaluate whether the cell you designed meets the manufacturer’s target to within

\pm 0.05\,\text{V}

. If the target is not met, propose a justification for why no combination of the provided half-reactions can achieve an

E^\circ_{\text{cell}}

within that tolerance.

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