JEE MAIN - Chemistry (2017 - 8th April Morning Slot - No. 22)
What is the standard reduction potential (Eo) for Fe3+ $$ \to $$ Fe ?
Given that :
Fe2+ + 2e$$-$$ $$ \to $$ Fe; $$E_{F{e^{2 + }}/Fe}^o$$ = $$-$$0.47 V
Fe3+ + e$$-$$ $$ \to $$ Fe2+; $$E_{F{e^{3 + }}/F{e^{2 + }}}^o$$ = +0.77 V
Given that :
Fe2+ + 2e$$-$$ $$ \to $$ Fe; $$E_{F{e^{2 + }}/Fe}^o$$ = $$-$$0.47 V
Fe3+ + e$$-$$ $$ \to $$ Fe2+; $$E_{F{e^{3 + }}/F{e^{2 + }}}^o$$ = +0.77 V
$$-$$ 0.057 V
+ 0.057 V
+ 0.30 V
$$-$$ 0.30 V
Explanation
For the given reaction :
Fe3+ + e$$-$$ $$ \to $$ Fe2+; $$E_{F{e^{3 + }}/F{e^{2 + }}}^o$$ = +0.77 V
$$\Delta $$Go = -nFEo
$$ \Rightarrow $$ $$\Delta G_1^o = - \left( 1 \right)F\left( {0.77} \right)$$ = -0.77F
For the following reaction :
Fe2+ + 2e$$-$$ $$ \to $$ Fe; $$E_{F{e^{2 + }}/Fe}^o$$ = $$-$$0.47 V
$$\Delta G_2^o = - \left( 2 \right)F\left( {-0.47} \right)$$ = 0.47$$ \times $$2F
Overall reaction :
Fe3+ + 3e$$-$$ $$ \to $$ Fe;
$$\Delta G_3^o = - 3FE_3^o$$
$$ \Rightarrow $$ $$\Delta G_1^o$$ + $$\Delta G_2^o$$ = $$ 3FE_3^o$$
$$ \Rightarrow $$ -0.77F + 0.47$$ \times $$2F = $$ 3FE_3^o$$
$$ \Rightarrow $$ $$E_3^o = - {{0.17} \over 3}$$ = -0.057 V
Fe3+ + e$$-$$ $$ \to $$ Fe2+; $$E_{F{e^{3 + }}/F{e^{2 + }}}^o$$ = +0.77 V
$$\Delta $$Go = -nFEo
$$ \Rightarrow $$ $$\Delta G_1^o = - \left( 1 \right)F\left( {0.77} \right)$$ = -0.77F
For the following reaction :
Fe2+ + 2e$$-$$ $$ \to $$ Fe; $$E_{F{e^{2 + }}/Fe}^o$$ = $$-$$0.47 V
$$\Delta G_2^o = - \left( 2 \right)F\left( {-0.47} \right)$$ = 0.47$$ \times $$2F
Overall reaction :
Fe3+ + 3e$$-$$ $$ \to $$ Fe;
$$\Delta G_3^o = - 3FE_3^o$$
$$ \Rightarrow $$ $$\Delta G_1^o$$ + $$\Delta G_2^o$$ = $$ 3FE_3^o$$
$$ \Rightarrow $$ -0.77F + 0.47$$ \times $$2F = $$ 3FE_3^o$$
$$ \Rightarrow $$ $$E_3^o = - {{0.17} \over 3}$$ = -0.057 V
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