Under what condition is `E_("cell")^(@)=0` or `Delta_(r)G=0`?

Explanation

To determine the conditions under which \( E^\circ_{\text{cell}} = 0 \) or \( \Delta_r G = 0 \), we can analyze the relationship between the electromotive force (EMF) of a cell and the Gibbs free energy change of a reaction. Here’s a step-by-step solution:

### Step 1: Understand the Definitions
- **Electromotive Force (EMF)**, \( E^\circ_{\text{cell}} \): This is the voltage or potential difference of a galvanic cell under standard conditions. It indicates the driving force behind the electrochemical reaction.
- **Gibbs Free Energy Change**, \( \Delta_r G \): This is the change in free energy associated with a chemical reaction. It indicates the spontaneity of a reaction.

### Step 2: Relationship Between EMF and Gibbs Free Energy
The relationship between the EMF of a cell and the Gibbs free energy change is given by the equation:
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