The standard reduction potentials for iron and copper half-cells are given as follows: \te… — JAMB UTME

The standard reduction potentials for iron and copper half-cells are given as follows:

\text{Fe}^{2+}(aq) + 2e^- \rightarrow \text{Fe}(s) \quad E^\circ = -0.44\text{ V}

\text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s) \quad E^\circ = +0.34\text{ V}

What is the standard electromotive force ( $E^\circ_{\text{cell}}$ ) for the overall reaction $\text{Fe}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Fe}^{2+}(aq) + \text{Cu}(s)$ , and is the reaction spontaneous under standard conditions?

$+0.78\text{ V}$ , spontaneousCevap
B
$-0.78\text{ V}$ , non-spontaneous
C
$-0.10\text{ V}$ , non-spontaneous
D
$+0.10\text{ V}$ , spontaneous

Cevap

The standard electromotive force (

E^\circ_{\text{cell}}

) is

+0.78\text{ V}

, and the reaction is spontaneous.

In the given reaction,

\text{Cu}^{2+}

ions are reduced to copper metal at the cathode (

E^\circ = +0.34\text{ V}

), while

\text{Fe}

metal is oxidized to

\text{Fe}^{2+}

ions at the anode (

E^\circ = -0.44\text{ V}

). Using the standard formula

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

, we calculate

E^\circ_{\text{cell}} = +0.34\text{ V} - (-0.44\text{ V}) = +0.78\text{ V}

. Because the cell potential is positive, the reaction is spontaneous under standard conditions.

Adım Adım Çözüm

Identify the reduction and oxidation half-reactions

Cathode (reduction):

\text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s)

with

E^\circ_{\text{cathode}} = +0.34\text{ V}

. Anode (oxidation):

\text{Fe}(s) \rightarrow \text{Fe}^{2+}(aq) + 2e^-

with

E^\circ_{\text{anode}} = -0.44\text{ V}

Copper ions gain electrons (reduction at cathode) while iron metal loses electrons (oxidation at anode).

Calculate the standard cell potential (

E^\circ_{\text{cell}}

)

E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = +0.34\text{ V} - (-0.44\text{ V}) = +0.78\text{ V}

The cell potential is the difference between the reduction potential of the cathode species and that of the anode species.

Determine reaction spontaneity

Since

E^\circ_{\text{cell}} = +0.78\text{ V} > 0

, the reaction is spontaneous.

A positive standard cell potential indicates a thermodynamically feasible (spontaneous) redox reaction under standard conditions.

Anahtar Kavram

Standard Cell Potential and Reaction Spontaneity

Tahmini Süre:1m 15s

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