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E⊖Cell of Z...

Question

$E_{C e l l}^{⊖}$ of $Z n / Z n^{2 +} | | C u^{2 +} / C u$ is $1.10$ V at $25^{o}$ C, the equilibrium constant for the reaction, $Z n + C u^{2 +} ⇌ C u + Z n^{2 +}$ is approximately of the order of:

10^{- 28}

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10^{+ 37}

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10^{- 18}

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10^{17}

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Solution

The correct option is B $10^{+ 37}$
The given cell reaction is :- $Z n + {C u}^{2 +} ⇌ C u + {Z n}^{2 +}$
Given, $E^{0}$ cell for $Z n / {Z n}^{2 +} 11 {C u}^{2 +} / C u = 1.1 v a t 25^{0} c$
Now, we have
${△ G}^{0} = - n F E^{0} c e l l = - R T l n K_{e q}$
where, $E^{0} c e l l$ = EMF of cell
$n =$ no. of $e^{-} s$ transferred
$F =$ Faraday's constant $= 96500 c$
$R =$ Gas const. , $T =$ temp.
At, $25^{0} c$
$\Rightarrow l n K_{e q} = {(\frac{R T}{n F})}^{- 1} E^{0} c e l l$
$\Rightarrow l n K_{e q} = (\frac{n F}{R T}) E^{0} c e l l$
$\Rightarrow l o g K_{e q} = (h / 0.0591) E^{0} c e l l$
$\Rightarrow l o g K_{e q} = \frac{2}{0.0591} \times 1.1$
$\Rightarrow l o g K_{e q} = 37.22$
$\Rightarrow K_{e q} = 10^{37.22}$

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