Give the formula to calculate the equilibrium constant $K_C$ of any electrochemical cell.
(N/A) At equilibrium,the cell potential $E_{cell} = 0$.
According to the Nernst equation:
$E_{cell} = E^{\circ}_{cell} - \frac{RT}{nF} \ln Q_c$
At equilibrium,$Q_c = K_C$ and $E_{cell} = 0$.
Substituting these values:
$0 = E^{\circ}_{cell} - \frac{RT}{nF} \ln K_C$
$E^{\circ}_{cell} = \frac{RT}{nF} \ln K_C$
For a reaction at $298 \ K$,this simplifies to:
$E^{\circ}_{cell} = \frac{0.0591}{n} \log K_C$
Therefore,the formula for $K_C$ is:
$\log K_C = \frac{n E^{\circ}_{cell}}{0.0591}$
According to the Nernst equation:
$E_{cell} = E^{\circ}_{cell} - \frac{RT}{nF} \ln Q_c$
At equilibrium,$Q_c = K_C$ and $E_{cell} = 0$.
Substituting these values:
$0 = E^{\circ}_{cell} - \frac{RT}{nF} \ln K_C$
$E^{\circ}_{cell} = \frac{RT}{nF} \ln K_C$
For a reaction at $298 \ K$,this simplifies to:
$E^{\circ}_{cell} = \frac{0.0591}{n} \log K_C$
Therefore,the formula for $K_C$ is:
$\log K_C = \frac{n E^{\circ}_{cell}}{0.0591}$
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