Given the following standard reduction potentials at 25^\circ\text{C}: \text{Al}^{3+}_{\te… — JAMB UTME

Given the following standard reduction potentials at

25^\circ\text{C}

\text{Al}^{3+}_{\text{(aq)}} + 3\text{e}^- \rightarrow \text{Al}_{\text{(s)}} \quad E^\circ = -1.66\text{ V}

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

Calculate the standard electromotive force ( $E^\circ_{\text{cell}}$ ), in volts, of the galvanic cell formed by coupling these two half-cells.

Answer: 2 V

Answer

The standard electromotive force (

E^\circ_{\text{cell}}

) of the galvanic cell is

2.00\text{ V}

The standard electromotive force of a galvanic cell is defined as

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

. Since copper has a higher standard reduction potential (

+0.34\text{ V}

) than aluminium (

-1.66\text{ V}

), reduction occurs at the copper electrode (cathode) and oxidation occurs at the aluminium electrode (anode). Evaluating the potential difference yields

E^\circ_{\text{cell}} = 0.34\text{ V} - (-1.66\text{ V}) = 2.00\text{ V}

Step-by-Step Solution

Determine which half-cell undergoes reduction (cathode) and which undergoes oxidation (anode).

Copper is the cathode (

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

) and aluminium is the anode (

E^\circ = -1.66\text{ V}

The half-cell with the higher standard reduction potential spontaneously undergoes reduction at the cathode.

Apply the formula for calculating standard electromotive force (

E^\circ_{\text{cell}}

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

The cell EMF is the standard potential difference between the reduction half-reaction and the oxidation half-reaction.

Perform the subtraction to evaluate

E^\circ_{\text{cell}}

E^\circ_{\text{cell}} = 0.34 - (-1.66) = 2.00\text{ V}

Subtracting a negative quantity is mathematically equivalent to adding its positive value.

Key Concept

Calculation of standard cell potential (

E^\circ_{\text{cell}}

) from standard electrode reduction potentials.

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