Question

$\boxed{E_{cell} = E_{cell}^{\circ} - \frac{0.0591}{n}log Q}$

at equilibrium $\Delta g = 0 \Rightarrow E_{cell} = 0$

so

$\boxed{E_{cell}^{\circ} = \frac{0.0591}{n}log K_{eq}}$

Answer 1

The equations provided relate cell potential to standard cell potential and the equilibrium constant. They are derived from the Nernst equation and the relationship between Gibbs free energy and cell potential.

Answer 2

The boxed equations represent fundamental relationships in electrochemistry:

1. Nernst Equation: The first equation, $E_{cell} = E_{cell}^{\circ} - \frac{0.0591}{n}log Q$, is the Nernst equation. It relates the cell potential ($E_{cell}$) to the standard cell potential ($E_{cell}^{\circ}$), the number of moles of electrons transferred in the cell reaction ($n$), and the reaction quotient ($Q$). The reaction quotient is a measure of the relative amounts of reactants and products present in a reaction at any given time.

2. Equilibrium Condition: The statement "at equilibrium $\Delta g = 0 \Rightarrow E_{cell} = 0$" indicates that at equilibrium, the change in Gibbs free energy ($\Delta g$) is zero, which implies that the cell potential ($E_{cell}$) is also zero. This is a key concept because it links thermodynamics and electrochemistry.

3. Standard Cell Potential and Equilibrium Constant: The second boxed equation, $E_{cell}^{\circ} = \frac{0.0591}{n}log K_{eq}$, relates the standard cell potential ($E_{cell}^{\circ}$) to the equilibrium constant ($K_{eq}$) for the cell reaction. This equation is derived from the Nernst equation by setting $E_{cell} = 0$ and $Q = K_{eq}$ at equilibrium. It shows that the standard cell potential is directly proportional to the logarithm of the equilibrium constant. A larger $K_{eq}$ indicates a more spontaneous reaction under standard conditions.

In summary, these equations are essential for understanding and calculating cell potentials under various conditions and for relating them to the equilibrium constant of the cell reaction.