Yes, at equilibrium, the cell potential (E_cell) becomes zero. This happens because the forward and reverse reactions occur at the same rate, meaning there is no net flow of electrons.

Why is E_cell = 0 at equilibrium?

1. Gibbs Free Energy and Cell Potential
   The relationship between Gibbs free energy (ΔG) and cell potential is:

   ΔG=−nFEcell\Delta G = -nFE_{\text{cell}}At equilibrium, ΔG = 0, so:

   0=−nFEcell0 = -nFE_{\text{cell}}Since n (number of electrons) and F (Faraday’s constant) are nonzero, the only way this equation holds true is if E_cell = 0.

2. Nernst Equation
   The Nernst equation is:

   Ecell=Ecell∘−0.0591nlog⁡QE_{\text{cell}} = E^\circ_{\text{cell}} – \frac{0.0591}{n} \log QAt equilibrium, Q = K (equilibrium constant), so:

   0=Ecell∘−0.0591nlog⁡K0 = E^\circ_{\text{cell}} – \frac{0.0591}{n} \log KThis shows that the standard electrode potential (E°_cell) determines the equilibrium constant, but at equilibrium itself, E_cell = 0.

What does this mean in practical terms?

• A galvanic cell (battery) stops producing electricity once equilibrium is reached.
• If a reaction reaches equilibrium, there is no net movement of electrons, meaning the cell is no longer useful for electrical work.

So, the simple answer is: Yes, E_cell is zero at equilibrium, and this is why batteries eventually stop working!