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# Calculate the standard cell potentials of galvanic cell in which the following reactions take place:

3.4     Calculate the standard cell potentials of galvanic cell in which the following reactions take place:

$2Cr(s)+3Cd^{2+}(aq)\rightarrow 2Cr^{3+}(aq)+3Cd$

Calculate the $\Delta _{r}G^{e}$ and equilibrium constant of the reactions.

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The galvanic cell of the given reaction is shown below:-

The standard electrode potential of Cr and Cd can be found in table of standard electrode potential.

So, we get  :

$E^{\circ} = E^{\circ}_R\ -\ E^{\circ} _L$

$= -0.40\ -\ (-0.74)$

$=\ 0.34\ V$

Now

$\Delta G_r^{\circ}\ = -\ nFE_{cell}^{\circ}$

Putting values :

$\Delta G_r^{\circ}\ = -\ 6\times96487\times 0.34$

$= -196.83\ KJ\ mol^{-1}$

Now for finding equlilibrium constant we have :

$log\ k = \frac{-\Delta G _r^{\circ}}{2.303\times R\times T}$

or                                         $log\ k = 34.496$

or                                             $K = 3.13\times10^34$

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