The standard reduction potentials for aluminium and nickel half-cells at 25^\circ\text{C} … — JAMB UTME

The standard reduction potentials for aluminium and nickel half-cells at

25^\circ\text{C}

are given below:

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

\text{Ni}^{2+}(aq) + 2e^- \rightarrow \text{Ni}(s) \quad E^\circ = -0.25\text{ V}

Calculate the standard electromotive force ( $E^\circ_{\text{cell}}$ ) in volts for the spontaneous reaction between these two half-cells.

Answer: 1.41 V

The standard electromotive force (

E^\circ_{\text{cell}}

) for the spontaneous galvanic cell reaction is +1.41 V.

For a spontaneous electrochemical reaction, the standard cell electromotive force (

E^\circ_{\text{cell}}

) must be positive. The half-reaction with the more positive standard reduction potential (

\text{Ni}^{2+}/\text{Ni}

-0.25\text{ V}

) proceeds as a reduction at the cathode. The half-reaction with the less positive potential (

\text{Al}^{3+}/\text{Al}

-1.66\text{ V}

) proceeds as an oxidation at the anode. Calculating

E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} = -0.25\text{ V} - (-1.66\text{ V}) = +1.41\text{ V}

. Because

E^\circ

is an intensive property, the stoichiometric coefficients used to balance electrons (

2\text{Al} + 3\text{Ni}^{2+} \rightarrow 2\text{Al}^{3+} + 3\text{Ni}

) do not affect the numerical values of the half-cell potentials.

Determine which electrode undergoes reduction (cathode) and which undergoes oxidation (anode)

Nickel ion reduction occurs at the cathode (

E^\circ = -0.25\text{ V}

), and aluminium metal oxidation occurs at the anode (

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

A galvanic cell operates spontaneously (

E^\circ_{\text{cell}} > 0

) when the half-cell with the more positive standard reduction potential acts as the cathode.

State the equation for standard cell potential

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

The cell potential measures the potential difference between the reduction half-reaction and the oxidation half-reaction under standard conditions.

Substitute the reduction potential values into the equation

E^\circ_{\text{cell}} = -0.25\text{ V} - (-1.66\text{ V}) = +1.41\text{ V}

Standard electrode potentials are intensive properties; hence, balancing electron stoichiometry does not scale

E^\circ

values.

Calculating standard cell electromotive force (

E^\circ_{\text{cell}}

) and predicting spontaneity from standard reduction potentials

Question