Question

The cell potential becomes equal to E⁰ when

• A. Equilibrium constant is 1
• B. Equilibrium constant is 10
• C. Equilibrium constant is 100
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

The Nernst equation describes the relationship between the cell potential (E), the standard cell potential (E⁰), and the reaction quotient (Q):

$E_{cell} = E^0_{cell} - \frac{RT}{nF} \ln Q$

Where:

• $E_{cell}$ is the cell potential under non-standard conditions.
• $E^0_{cell}$ is the standard cell potential.
• R is the ideal gas constant.
• T is the temperature in Kelvin.
• n is the number of moles of electrons transferred in the balanced redox reaction.
• F is Faraday's constant.
• Q is the reaction quotient.

For $E_{cell}$ to be equal to $E^0_{cell}$, the term $\frac{RT}{nF} \ln Q$ must be zero. Since R, T, n, and F are non-zero constants (assuming T > 0 K), the only way for the term to be zero is if $\ln Q = 0$.

If $\ln Q = 0$, then $Q = e^0 = 1$.

Therefore, the cell potential becomes equal to E⁰ when the reaction quotient (Q) is 1. The options provided are about the equilibrium constant K, but this condition is always Q=1, regardless of the value of $E^0_{cell}$ or K.