What will be the $E_{cell}^{\circ}$ from following half cell reactions ? $Fe^{3+}(aq)+e^{-}\rightarrow Fe^{2+}(aq)$, $E^{\circ}=+0.77~V$ and $Zn^{2+}(aq)+2e^{-}\rightarrow Zn(s)$, $E^{\circ}=-0.76~V$

Question

Accepted Answer

To determine the standard cell potential ($E_{cell}^{\circ}$) for the given electrochemical cell, we need to consider the two half-cell reactions and their standard electrode potentials ($E^{\circ}$).

The given half-cell reactions are:

1. $ Fe^{3+}(aq) + e^{-} \rightarrow Fe^{2+}(aq) $, with $ E^{\circ} = +0.77 \, \text{V} $
2. $ Zn^{2+}(aq) + 2e^{-} \rightarrow Zn(s) $, with $ E^{\circ} = -0.76 \, \text{V} $

To find the overall cell potential, we need to identify which half-reaction will act as the anode (oxidation) and which will act as the cathode (reduction).

1. **Cathode Reaction (Reduction):** The reaction with the more positive electrode potential will occur as the reduction at the cathode. Here, $ Fe^{3+}(aq) + e^{-} \rightarrow Fe^{2+}(aq) $ with $ E^{\circ} = +0.77 \, \text{V} $ is the reduction reaction.

2. **Anode Reaction (Oxidation):** The reaction with the less positive (or more negative) electrode potential will occur as the oxidation at the anode. Here, the reverse of $ Zn^{2+}(aq) + 2e^{-} \rightarrow Zn(s) $ is $ Zn(s) \rightarrow Zn^{2+}(aq) + 2e^{-} $ with $ E^{\circ} = +0.76 \, \text{V} $ (since oxidation is the reverse of reduction, we change the sign).

The standard cell potential is calculated using the formula:
$$ E_{cell}^{\circ} = E_{cathode}^{\circ} - E_{anode}^{\circ} $$

Substituting the values:
$$ E_{cell}^{\circ} = (+0.77 \, \text{V}) - (-0.76 \, \text{V}) $$
$$ E_{cell}^{\circ} = 0.77 \, \text{V} + 0.76 \, \text{V} $$
$$ E_{cell}^{\circ} = 1.53 \, \text{V} $$

Therefore, the correct answer is Option 2: 1.53 V.

**Explanation for Incorrect Options:**

1. **Option 1 (0.01 V):** This value is incorrect because it does not account for the correct addition of the electrode potentials. The calculation clearly shows that the sum of the potentials is 1.53 V, not 0.01 V.

2. **Option 3 (-1.53 V):** This option is incorrect because the cell potential cannot be negative when calculated as the difference between a positive and a negative potential, as shown in the calculation.

3. **Option 4 (2.30 V):** This value is incorrect because it overestimates the cell potential. The correct calculation based on the given electrode potentials results in 1.53 V, not 2.30 V.

In conclusion, the correct standard cell potential for the given reactions is 1.53 V, which supports Option 2 as the correct answer.