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)

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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