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The standard e.m.f. of a cell, involving one electron change is found to be 0.591 V at $25^{\circ}C$ . The equilibrium constant of the reaction is $\left ( F= 96,500\: C\: mol^{-1} ,R= 8.314 JK^{-1}mol^{-1}\right )$

Option 1)
$1.0\times 10^{1}$

Option 2)
$1.0\times 10^{5}$

Option 3)
$1.0\times 10^{10}$

Option 4)
$1.0\times 10^{30}$

Answers (1)

best_answer

As we learnt in

Electrode Potential(Nerst Equation) -

$M^{n+}(aq)+ne^{-}\rightarrow M(s)$

- wherein

$E_{(M^{n+}/M)}=E_{(M^{n+}/M)}^{0}-\frac{RT}{nf}ln\frac{[M]}{[M^{n+}]}$

$[M^{n+}]$ is concentration of species

F= 96487 C $moi^{-1}$

R= 8.314 $JK^{-1}moi^{-1}$

T= Temperature in kelvin

$E_{cell}=E^{\circ}_{cell}-\frac{0.0591}{n}logK_{c}$

$0=0.591-\frac{0.0591}{1}logK_{c}$

$\Rightarrow -0.591=-0.0591\, logK_{c}$

$\Rightarrow logK_{c}=\frac{0.591}{0.0591}=10$

$\therefore \; \; K_{c}=antilog\, 10=1\times 10^{10}$

Option 1)

$1.0\times 10^{1}$

This option is incorrect.

Option 2)

$1.0\times 10^{5}$

This option is incorrect.

Option 3)

$1.0\times 10^{10}$

This option is correct.

Option 4)

$1.0\times 10^{30}$

This option is incorrect.

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prateek

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