Question

Given below are the half-cell reactions $Mn ^{2+}+2 e ^{-} \rightarrow Mn ; E ^{\circ}=-1.18 \,V$ $\left( Mn ^{3+}+ e ^{-} \rightarrow Mn ^{2+}\right) ; E ^{\circ}=+1.51 \,V$ The $ E ^{\circ} $ for $3 \,Mn ^{2+} \rightarrow Mn +2 Mn ^{3+}$ will be

• A. $-2.69\, V$; the reaction will not occur
• B. $- 2.69\, V$; the reaction will occur
• C. $-2.69 \,V$; the reaction will occur
• D. $- 0.33\, V$; the reaction will occur

Answer 1

The Correct Option is A

(1) $ Mn ^{2+}+2 e \rightarrow Mn ; E ^{\circ}=-1.18 V $;

$\Delta G _{1}^{\circ}=-2 F (-1.18)=2.36 F $

(2) $ Mn ^{3+}+ e \rightarrow Mn ^{2+} ; E ^{\circ}=+1.51 \,V$ ;

$\Delta G _{2}^{\circ}=- F (1.51)=-1.51 \,F$
$(1)-2 \times (2)$
$3 Mn ^{2+} \rightarrow Mn +2 Mn ^{3+} $ ;

$\Delta G _{3}^{\circ} =\Delta G _{1}^{\circ}-2 \Delta G _{2}^{\circ} $
$=[2.36-2(-1.51)] F $
$=(2.36+3.02) F $
$=5.38 \,F$

But $ \Delta G_{3}^{\circ}=-2 FE ^{\circ}$
$\Rightarrow 5.38 F =-2 FE ^{\circ}$
$\Rightarrow E ^{\circ}=-2.69 \,V$

As $E ^{\circ}$ value is negative reaction is non spontaneous