JEE Main On 8 April 2017 Question 22
Question: What is the standard reduction potential $ (E{}^\circ ) $ for $ F{e^{3+}}\to Fe $ ? Given that: $ F{e^{2+}}+2{e^{-}}\to Fe;E^o _{F{e^{2+}}/Fe}=-0.47V $ $ F{e^{3+}}+{e^{-}}\to F{e^{2+}};E^o _{F{e^{3+}}/F{e^{2+}}}=+0.77V $ [JEE Online 08-04-2017]
Options:
A) -0.057 V
B) + 0.30 V
C) - 0.30 V
D) + 0.057 V
Show Answer
Answer:
Correct Answer: A
Solution:
Calculate $\Delta G^{\circ}$ for each half-reaction:
For $\mathrm{Fe}^{3+}+\mathrm{e}^{-} \rightarrow \mathrm{Fe}^{2+}$ :
$$ \Delta G_1^{\circ}=-n_1 F E_1^{\circ}=-1 \times 96485 \times 0.77=-74293.45 \mathrm{~J} / \mathrm{mol} $$
For $\mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \rightarrow \mathrm{Fe}$ :
$$ \Delta G_2^{\circ}=-n_2 F E_2^{\circ}=-2 \times 96485 \times(-0.47)=90615.8 \mathrm{~J} / \mathrm{mol} $$
Total $\Delta G^{\circ}$ :
$$ \Delta G_{\text {total }}^{\circ}=\Delta G_1^{\circ}+\Delta G_2^{\circ}=-74293.45+90615.8=16322.35 \mathrm{~J} / \mathrm{mol} $$
Calculate $E^{\circ}$ for $\mathrm{Fe}^{3+} \rightarrow \mathrm{Fe}$ :
$$ E^{\circ}=-\frac{\Delta G_{\text {total }}^{\circ}}{n F}=-\frac{16322.35}{3 \times 96485} \approx-0.057 \mathrm{~V} $$
The standard reduction potential is -0.057 V .
BETA
