Derivation of the Equilibrium Constant from the Nernst Equation
The Nernst equation relates the electrode potential of a reaction to its standard electrode potential,
temperature, and reaction quotient. From this equation, we can derive the equilibrium constant (K) of
a reaction.
Nernst Equation:
E = E° - (RT/nF) ln(Q)
At Equilibrium:
At equilibrium, the reaction quotient Q becomes the equilibrium constant K, and the cell potential E
is zero:
0 = E° - (RT/nF) ln(K)
Solving for K:
Rearranging the equation:
ln(K) = (nF E°) / (RT)
Taking the exponential on both sides:
K = exp(nF E° / RT)
Conclusion:
The equilibrium constant K is related to the standard electrode potential E° of the reaction. For a
spontaneous reaction (positive E°), K is greater than 1, indicating a product-favored equilibrium.
The Nernst equation relates the electrode potential of a reaction to its standard electrode potential,
temperature, and reaction quotient. From this equation, we can derive the equilibrium constant (K) of
a reaction.
Nernst Equation:
E = E° - (RT/nF) ln(Q)
At Equilibrium:
At equilibrium, the reaction quotient Q becomes the equilibrium constant K, and the cell potential E
is zero:
0 = E° - (RT/nF) ln(K)
Solving for K:
Rearranging the equation:
ln(K) = (nF E°) / (RT)
Taking the exponential on both sides:
K = exp(nF E° / RT)
Conclusion:
The equilibrium constant K is related to the standard electrode potential E° of the reaction. For a
spontaneous reaction (positive E°), K is greater than 1, indicating a product-favored equilibrium.
