Question

Equilibrium constant (\(K_c\)) is related to \(E^\circ_{cell}\), but not to \(E_{cell}\). Why ?

Hint:

Remember the important relation: \[ E^\circ_{cell}=\frac{0.0591}{n}\log K \] Only the standard cell potential is related to the equilibrium constant.

Answer 1

Concept: The standard cell potential and equilibrium constant are thermodynamically related through the Gibbs energy change. The relation is: \[ \Delta G^\circ=-nFE^\circ_{cell} \] and \[ \Delta G^\circ=-RT\ln K \] Combining these equations, \[ E^\circ_{cell} = \frac{0.0591}{n}\log K \] Thus, the equilibrium constant depends only on the standard cell potential.

Explanation: The standard cell potential is measured under standard conditions:

• Concentration \(=1\,M\)

• Pressure \(=1\,atm\)

• Temperature \(=298\,K\)
Therefore, \(E^\circ_{cell}\) is a constant characteristic of the reaction. On the other hand, \[ E_{cell} \] changes with concentration and reaction conditions according to the Nernst equation. Since equilibrium constant is also a fixed quantity for a given temperature, it can be related only to the constant standard cell potential and not to the variable cell potential.

Final Answer \[ \boxed{ K_c \text{ is related to } E^\circ_{cell} \text{ because both refer to standard equilibrium conditions.} } \] \[ \boxed{ E_{cell} \text{ changes with concentration and hence cannot be directly related to } K_c. } \]