Final answer:
The minimum external potential to begin the deposition of copper metal onto the cathode in an electrolytic cell with 1 M Cu²⁺ solution is slightly over +0.337 V, the standard electrode potential for Cu²⁺ reduction.
Step-by-step explanation:
The student is asking about the minimum external potential required to cause the deposition of copper metal onto the cathode in an electrolytic cell.
From the information provided, we know that the standard electrode potential for the half-reaction Cu²⁺ (aq) + 2e→ Cu(s) under standard conditions is +0.337 V. This indicates the potential difference required to drive the reduction of copper ions to solid copper at the cathode if all conditions are standard, including 1 M concentration.
However, if we have a 1 M Cu²⁺ solution and want to deposit copper, we can refer to the provided data indicating an initial cell voltage greater than the standard electrode potential expressed as E°. This is because initially, the concentration quotient Q (ratio of concentrations of products to reactants) is less than 1, which would necessitate a higher potential to start the electrodeposition.
As the composition changes and reaction proceeds, the need for external potential might decrease. But to initiate the deposition, the potential will at minimum need to be the standard electrode potential of +0.337 V, probably slightly more to overcome overpotential and other resistance in the system. Therefore, the minimum external potential required to start the electroplating process is estimated to be just over +0.337 V.