Question

is this electrolytic cell thermodynamically favorable or thermodynamically unfavorable?
pb + cu²⁺ → pb²⁺ + cu
e°_cell = 0.47 v
the reaction is favorable because the ecell value is negative.
the reaction is favorable because the ecell value is positive.
the reaction is unfavorable because the ecell value is negative.
the reaction is unfavorable because the ecell value is positive.

Explanation:

To determine if an electrochemical reaction (for an electrolytic or galvanic cell) is thermodynamically favorable, we use the standard cell potential (\(E^\circ_{\text{cell}}\)). A positive \(E^\circ_{\text{cell}}\) indicates a thermodynamically favorable (spontaneous) reaction, while a negative \(E^\circ_{\text{cell}}\) indicates an unfavorable (non - spontaneous) reaction. Here, \(E^\circ_{\text{cell}} = 0.47\space V\), which is positive. So we analyze each option:

• Option 1: Says the reaction is favorable because \(E_{\text{cell}}\) is negative. But our \(E_{\text{cell}}\) is positive, and a negative \(E_{\text{cell}}\) would mean unfavorable. So this is wrong.
• Option 2: States the reaction is favorable because \(E_{\text{cell}}\) is positive. This matches our knowledge about the relationship between \(E^\circ_{\text{cell}}\) and thermodynamic favorability.
• Option 3: Claims the reaction is unfavorable because \(E_{\text{cell}}\) is negative. But our \(E_{\text{cell}}\) is positive, so this is incorrect.
• Option 4: Says the reaction is unfavorable because \(E_{\text{cell}}\) is positive. A positive \(E_{\text{cell}}\) means favorable, so this is wrong.

Answer:

B. The reaction is favorable because the Ecell value is positive.