`Pt(H_(2))(p_(1))|H^(o+)(1M)|(H_(2))(p_(2)),Pt` cell reaction will be exergonic if

Options

A. `p_(1) = p_(2)`
B. `p_(1) gt p_(2)`
C. `p_(2) gt p_(1)`
D. `p_(1) = 1atm`

Answer

To determine the condition under which the cell reaction represented by the standard hydrogen electrode will be exergonic, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Exergonic Reactions**:
- An exergonic reaction is one that releases energy, which corresponds to a negative change in Gibbs free energy (ΔG < 0).

2. **Relationship Between ΔG and Cell Potential (E)**:
- The relationship between Gibbs free energy and the cell potential is given by the equation:
\[ \Delta G^0 = -nFE^0_{cell} \]
- Here, \( n \) is the number of moles of electrons transferred, \( F \) is Faraday's constant, and \( E^0_{cell} \) is the standard cell potential.

3. **Condition for Exergonic Reaction**:
- For the reaction to be exergonic (ΔG < 0), it is necessary that:
\[ E^0_{cell} > 0 \]

4. **Using the Nernst Equation**:
- The Nernst equation relates the standard cell potential to the actual cell potential:
\[ E_{cell} = E^0_{cell} - \frac{0.0591}{n} \log \frac{[products]}{[reactants]} \]
- In this case, we need to evaluate the pressures of hydrogen gas (H₂) and the concentration of hydrogen ions (H⁺).

5. **Identifying the Reaction**:
- The half-reaction can be represented as:
\[ H_2 \rightleftharpoons 2H^+ + 2e^- \]
- The pressures are given as \( p_1 \) for H₂ and \( p_2 \) for H⁺.

6. **Setting Up the Nernst Equation**:
- For the given cell, we can express the Nernst equation as:
\[ E_{cell} = E^0_{cell} - \frac{0.0591}{2} \log \frac{p_1}{p_2} \]
- To ensure \( E_{cell} \) is positive, we need:
\[ E^0_{cell} - \frac{0.0591}{2} \log \frac{p_1}{p_2} > 0 \]

7. **Condition for \( p_1 \) and \( p_2 \)**:
- Rearranging gives us:
\[ \frac{0.0591}{2} \log \frac{p_1}{p_2} < E^0_{cell} \]
- This implies that for \( E_{cell} \) to be positive, \( \frac{p_1}{p_2} \) must be greater than 1, leading to:
\[ p_1 > p_2 \]

### Conclusion:
Thus, the cell reaction will be exergonic if \( p_1 > p_2 \).