1. Tardigrade
  2. Question
  3. Chemistry
  4. For the given cell ; Cu ( s )| Cu 2+( C 1 M ) | Cu 2+( C 2 M )| Cu ( s ) change in Gibbs energy (Δ G) is negative, if

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Q. For the given cell ;
$Cu ( s )\left| Cu ^{2+}\left( C _{1} M \right) \| Cu ^{2+}\left( C _{2} M \right)\right| Cu ( s )$ change in Gibbs energy $(\Delta G)$ is negative, if

JEE MainJEE Main 2020Electrochemistry

Solution:

$\Delta G=-n \,F\, E_{\text{cell}}$

$\Delta G$ is negative, if $E_{\text{cell}}$ is positive

Anode: $ Cu ( s ) \to Cu^{+2}(C_{1})+2e^{-} : E^{\circ}$

$\frac{ \text { Cathode }: Cu ^{+2}\left( C _{2}\right)+2 e ^{-} \to Cu ( S ): - E ^{\circ}}{\text { Cell reaction }: Cu ^{+2}\left( C _{2}\right) \longrightarrow Cu ^{+2}\left( C _{1}\right) E _{ cen }^{\circ}=0}$

$E _{\text {cell }}= E _{ cell }^{\circ}-\frac{2.303 RT }{ nF } \log \,Q$

$E _{\text {cell }}=0-\frac{2.303 RT }{ nF } \log \left(\frac{ C _{1}}{ C _{2}}\right)$

$E _{\text {cell }}>\,0$:

if $\frac{ C _{1}}{ C _{2}}<\,1 $

$\Rightarrow C _{1}<\, C _{2}$