First slide

Standard EMF of a cell

Question

The standard reduction potential for ${Zn}^{2 +} / Zn, {Ni}^{2 +} / Ni and {Fe}^{2 +} / Fe are - 0 .76, - 0 .23$ and -0.44 V respectively. The reaction $X + Y^{2 +} ⟶ X^{2 +} + Y$ will be spontaneous if

Moderate

A

$X = Ni, Y = F$
B

$X = Ni, Y = Zn$
C

$X = Fe, Y = Zn$
D

$X = Zn, Y = Ni$

Solution

A cell reaction is spontaneous, if ${ΔG}^{\circ} < 0$
Since,    ${ΔG}^{\circ} = - {nF}_{cell}^{\circ}$
Thus, $E_{cell}^{\circ} > 0$
$E_{cell}^{\circ} = E_{oxi}^{\circ} + E_{Red}^{\circ}$
(a) X = Ni, Y = Fe
$Ni + {Fe}^{2 +} ⟶ {Ni}^{2 +} + Fe$
   $\begin{aligned} E_{Ni / {Ni}^{2 +}}^{o} = 0 .23 V \\ {E^{\circ}}_{{Fe}^{2 +} / Fe} = - 0 .44 V \end{aligned}$
Thus, $E_{cell}^{\circ} = E_{Ni / {Ni}^{2 +}}^{\circ} + E_{{Fe}^{2 +} / Fe}^{\circ}$
=-0.21 V $E_{cell}^{\circ} < 0,$ reaction is non-spontaneous.
(b) X = Ni, Y = Zn,
$Ni + {Zn}^{2 +} ⟶ {Ni}^{2 +} + Zn$
   $E_{Ni / {Ni}^{2 +}} = 0 .23 V, E_{{Zn}^{2 +} / Zn}^{\circ} = - 0 .76 V$
$E_{cell}^{\circ} = - 0 .53 V$
   $E_{cell}^{α} < 0$ reaction is non- spontaneous.
(c ) $X = Fe, Y = Zn, Fe + {Zn}^{2 +} ⟶ {Fe}^{2 +} + Zn$
   $E_{cell}^{\circ} = E_{Fe / {Fe}^{2 +}}^{\circ} + E_{{Zn}^{2 +} / Zn}^{\circ} = 0 .44 - 0 .76 = - 0 .32 V$
$E_{cell}^{\circ} < 0$ , reaction is non- spontaneous.
(d) $X = Zn, Y = Ni$
$Zn + {Ni}^{2 +} ⟶ {Zn}^{2 +} + Ni$
   $E_{cell}^{\circ} = E_{Zn / {Zn}^{2 +}}^{\circ} + E_{{Ni}^{2 +} / Ni}^{\circ} = 0 .76 - 0 .23 = 0 .53 V$
The reaction is spontaneous.

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