Discussion
The ΔrG° of the galvanic cell in which the following cell reaction takes place,
2Cr(s) + 3Cd2+(aq) → 2Cr3+(aq) + 3Cd(s), is
(E°Cr3+/Cr = -0.74 V and E°Cd2+/Cd = -0.40 V )
Answer: A
\(\Delta_{r}G^\circ\) is -196.86 kJ mol-1.
Chromium is oxidised (anode) and cadmium ions are reduced (cathode). Six electrons are transferred in the balanced reaction.
\[ \begin{aligned} E^\circ_{cell} &= -0.40 - (-0.74) = 0.34 \text{ V} \\ \Delta_{r}G^\circ &= -nFE^\circ_{cell} \\ &= -6 \times 96500 \times 0.34 \\ &= -196860 \text{ J mol}^{-1} \end{aligned} \]
The cell EMF is positive, so the reaction is spontaneous and \(\Delta_{r}G^\circ\) must be negative, ruling out all the positive values. -96.50 kJ mol-1 does not use the 0.34 V EMF with six electrons.
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