Consider the standard reduction potentials for the following two half-cell reactions: \tex… — JAMB UTME

Consider the standard reduction potentials for the following two half-cell reactions:

\text{Zn}^{2+}(aq) + 2e^- \rightarrow \text{Zn}(s) \quad E^\circ = -0.76\text{ V}

\text{Fe}^{3+}(aq) + 3e^- \rightarrow \text{Fe}(s) \quad E^\circ = -0.04\text{ V}

What is the standard cell potential (

E^\circ_{\text{cell}}

), in volts, for the spontaneous redox reaction represented by the balanced chemical equation:

3\text{Zn}(s) + 2\text{Fe}^{3+}(aq) \rightarrow 3\text{Zn}^{2+}(aq) + 2\text{Fe}(s)

Answer: 0.72 V

Answer

The standard cell potential for the spontaneous reaction is +0.72 V.

To calculate the standard cell potential (

E^\circ_{\text{cell}}

), identify the cathode (reduction) and anode (oxidation) processes from the balanced chemical equation. Iron(III) ions are reduced to iron metal at the cathode (

E^\circ = -0.04\text{ V}

), while zinc metal is oxidized to zinc ions at the anode (

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

). Using

E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}

, we calculate

E^\circ_{\text{cell}} = -0.04\text{ V} - (-0.76\text{ V}) = +0.72\text{ V}

. Because standard electrode potential is an intensive property, the stoichiometric coefficients (3 for Zn and 2 for Fe³⁺) do not alter the half-cell potentials.

Step-by-Step Solution

Determine the oxidation and reduction species from the overall equation

Zinc is oxidized at the anode (

\text{Zn} \rightarrow \text{Zn}^{2+} + 2e^-

), and

\text{Fe}^{3+}

is reduced at the cathode (

\text{Fe}^{3+} + 3e^- \rightarrow \text{Fe}

The equation shows elemental Zn losing electrons to form

\text{Zn}^{2+}

and

\text{Fe}^{3+}

gaining electrons to form Fe.

Recall that standard electrode potential is an intensive property

The values

E^\circ(\text{Zn}^{2+}/\text{Zn}) = -0.76\text{ V}

and

E^\circ(\text{Fe}^{3+}/\text{Fe}) = -0.04\text{ V}

remain unchanged regardless of stoichiometric coefficients.

Potential measures electrical potential energy per unit charge, which does not depend on the total amount of substance reacting.

Calculate the standard cell potential using

E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}

E^\circ_{\text{cell}} = -0.04\text{ V} - (-0.76\text{ V}) = +0.72\text{ V}

Subtracting the anode reduction potential from the cathode reduction potential yields the net electromotive force of the spontaneous cell.

Key Concept

Standard Cell Potential Calculation and Independence of E° from Stoichiometric Coefficients

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic