MCQ
Standard electrode potentials for a few half cells are mentioned below :
$
\begin{array}{l}
E_{Cu^{2+} / Cu}^{o}=0.34 V, E_{Zn^{2+} / Zn}^{o}=-0.76 V \\
E_{Ag^{+} / Ag}^{o}=0.80 V, E_{Mg^{2+} / Mg}^{o}=-2.37 V
\end{array}
$
Which one of the following cells gives the most negative value of $\Delta G ^{ o }$ ?
  • $Zn \left| Zn ^{2+}(1 M ) \| Ag ^{+}(1 M )\right| Ag$
  • B
    $Zn \left| Zn ^{2+}(1 M )\right|\left| Mg ^{2+}(1 M )\right| Mg$
  • C
    $Ag \left| Ag ^{+}(1 M )\right|\left| Mg ^{2+}(1 M )\right| Mg$
  • D
    $Cu \left| Cu ^{2+}(1 M ) \| Ag ^{+}(1 M )\right| Ag$

Answer

Correct option: A.
$Zn \left| Zn ^{2+}(1 M ) \| Ag ^{+}(1 M )\right| Ag$
(A)
$
\begin{array}{l} 
\because \Delta G^{\circ}=-nFE^{\circ} \\
\text { Option (1) } E^{\circ}=0.8+0.76 \\
=1.56 V \\
\therefore \Delta G^{\circ}=-2 \times F \times 1.56 \\
=-3.12 V
\end{array}
$
$
\begin{array}{c}
\text { Option (2) } E^{\circ}=-2.37+0.76 \\
=-1.61 V \\
\therefore \Delta G^{\circ}=-2 \times F \times(-1.61) \\
=+3.22 V
\end{array}
$
$
\begin{array}{c}
\text { Option (3) } \begin{aligned}
E^{\circ} & =-2.37-0.8 \\
& =-3.17 V \\
\therefore \Delta G^{\circ}=-2 & \times F \times(-3.17) \\
& =+6.34
\end{aligned}
\end{array}
$
Option (4)
$
\begin{aligned}
E^{\circ} & =0.8-0.34 \\
& =0.46 V
\end{aligned}
$
$
\begin{aligned}
\Delta G^{\circ} & =-2 \times F \times 0.46 \\
& =-0.92 V
\end{aligned}
$

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