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: (A)

Equilibrium constant is 1

Answer 2

The Nernst equation relates the cell potential ($E_{cell}$) to the standard cell potential ($E^\circ$) and the reaction quotient ($Q$):

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

Where:

• $R$ is the ideal gas constant
• $T$ is the temperature in Kelvin
• $n$ is the number of moles of electrons transferred
• $F$ is Faraday's constant

For $E_{cell} = E^\circ$, it implies $\frac{RT}{nF} \ln Q = 0$, which means $\ln Q = 0$, hence $Q=1$. So, the cell potential equals standard cell potential when the reaction quotient is 1.

The relationship between $E^\circ$ and the equilibrium constant $K$ is $E^\circ = \frac{RT}{nF} \ln K$.

If $K=1$, then $\ln K = 0$, which means $E^\circ = 0$.

If $E^\circ = 0$, then the condition $E_{cell} = E^\circ$ becomes $E_{cell} = 0$.

$E_{cell} = 0$ is the condition for equilibrium. At equilibrium, $Q=K$.

Since $K=1$, at equilibrium $Q=1$.

Therefore, if the equilibrium constant $K=1$, then $E^\circ=0$, and at equilibrium, $E_{cell}=0$. This satisfies $E_{cell}=E^\circ$.