Zn = -0.76 V, E°_Cu^2+ — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Understand the Relative Nature of Electrode Potentials An absolute electrode potential of a single half-cell cannot be measured directly because a oxidation or reduction half-reaction cannot occur in isolation. Therefore, all standard reduction potentials ($E^\circ$) are measured relative to a reference electrode. By international convention, the Standard Hydrogen Electrode (S.H.E.), corresponding to the half-cell reaction: $$\ce{2H^+(aq) + 2e^- -> H2(g)}$$ is assigned a standard reduction potential of exactly $0.00\text{ V}$ at all temperatures. Step 2 - Analyze the Effect of Shifting the Reference Scale If the potential of the Standard Hydrogen Electrode is arbitrarily redefined from $0.00\text{ V}$ to a new value of $1.00\text{ V}$: $$\Delta E_{\text{ref}} = +1.00\text{ V}$$ Because every individual electrode potential is measured relative to this reference, redefining the reference shifts the measured potential of all other electrodes by the exact same constant value: $$E^\circ_{\text{new}} = E^\circ_{\text{old}} + \Delta E_{\text{ref}}$$ Using the given standard values where S.H.E. is $0.00\text{ V}$ ($E^\circ_{\ce{Zn^2+/Zn}} = -0.76\text{ V}$ and $E^\circ_{\ce{Cu^2+/Cu}} = +0.34\text{ V}$): * **New potential of the Copper electrode:** $$E^\circ_{\ce{Cu^2+/Cu, new}} = +0.34\text{ V} + 1.00\text{ V} = 1.34\text{ V}$$ * **New potential of the Zinc electrode:** $$E^\circ_{\ce{Zn^2+/Zn, new}} = -0.76\text{ V} + 1.00\text{ V} = +0.24\text{ V}$$ Step 3 - Calculate the Potential of the Zn-Cu Cell on Both Scales The electromotive force or standard potential of a galvanic cell ($E^\circ_{\text{cell}}$) is the difference between the reduction potentials of the cathode and the anode: $$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$$ In a Zn-Cu galvanic cell, copper has the higher reduction potential and acts as the cathode, while zinc has the lower reduction potential and acts as the anode. * **On the standard scale (S.H.E. = 0.00 V):** $$E^\circ_{\text{cell}} = E^\circ_{\ce{Cu^2+/Cu}} - E^\circ_{\ce{Zn^2+/Zn}}$$ $$E^\circ_{\text{cell}} = 0.34\text{ V} - (-0.76\text{ V}) = 1.10\text{ V}$$ * **On the new scale (S.H.E. = 1.00 V):** $$E^\circ_{\text{cell, new}} = E^\circ_{\ce{Cu^2+/Cu, new}} - E^\circ_{\ce{Zn^2+/Zn, new}}$$ $$E^\circ_{\text{cell, new}} = 1.34\text{ V} - 0.24\text{ V} = 1.10\text{ V}$$ Step 4 - Evaluate the Options and Conclude Mathematically, if a constant $C$ is added to both electrode potentials, it cancels out completely when calculating the difference: $$E^\circ_{\text{cell, new}} = (E^\circ_{\text{cathode}} + C) - (E^\circ_{\text{anode}} + C) = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = E^\circ_{\text{cell}}$$ * **Option (A) is correct:** The observed voltage of the Zn-Cu cell remains unchanged at $+1.10\text{ V}$ because cell potential is a difference of two values on the same scale. * **Option (B) is incorrect:** A value of $-1.10\text{ V}$ would mean the spontaneous cell reaction reversed or became non-spontaneous, which is physically impossible just by changing the mathematical reference point. * **Option (C) is incorrect:** A value of $0.0\text{ V}$ implies the cell is at equilibrium and cannot produce any voltage. * **Option (D) is incorrect:** The voltage is not indeterminate; it can be precisely calculated as $+1.10\text{ V}$. $$\text{Correct Option: } \boxed{A}$$