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

The standard reduction potentials for gallium and nickel half-reactions at

25^\circ\text{C}

are given below:

\text{Ga}^{3+}(aq) + 3e^- \rightarrow \text{Ga}(s) \quad E^\circ = -0.56\text{ V}

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

What is the standard electromotive force (

E^\circ_{\text{cell}}

) for the spontaneous reaction between these two electrochemical systems?

+0.31\text{ V}

For a redox reaction to be spontaneous under standard conditions, the cell potential (

E^\circ_{\text{cell}}

) must be positive. In the electrochemical series, species with higher reduction potentials undergo reduction (cathode). Comparing

-0.25\text{ V}

(nickel) and

-0.56\text{ V}

(gallium), nickel has the higher potential and acts as the cathode. Applying

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

yields

-0.25\text{ V} - (-0.56\text{ V}) = +0.31\text{ V}

Identify cathode and anode based on standard reduction potentials for spontaneity

Cathode:

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

(

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

), Anode:

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

(

E^\circ = -0.56\text{ V}

)

The half-cell with the more positive (less negative) standard reduction potential undergoes reduction at the cathode in a spontaneous cell.

Calculate the standard cell potential using

E^\circ_{\text{cell}} = E^\circ_{\text{reduction}} - E^\circ_{\text{oxidation}}

E^\circ_{\text{cell}} = -0.25\text{ V} - (-0.56\text{ V}) = +0.31\text{ V}

Standard electromotive force is the difference between the reduction potential of the cathode and the reduction potential of the anode.

Standard Cell Potential and Reaction Spontaneity

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