Which one of the following has a potential more than zero

Options

A. `Pt,(1)/(2)H_(2)(1atm)|HCl(1M)`
B. `Pt,(1)/(2)H_(2)(1atm)|HCl(2M)`
C. `Pt,(1)/(2)H_(2)(1atm)|HCl(0.1M)`
D. `Pt,(1)/(2)H_(2)(1atm)|HCl(0.5M)`

Answer

To determine which of the given options has a potential greater than zero, we will use the Nernst equation:

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

For simplicity, we often use the logarithmic form:

\[ E_{cell} = E^{\circ} - \frac{0.0591}{n} \log Q \]

Where:
- \( E_{cell} \) is the cell potential,
- \( E^{\circ} \) is the standard cell potential,
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( n \) is the number of moles of electrons exchanged,
- \( F \) is Faraday's constant,
- \( Q \) is the reaction quotient.

### Step-by-Step Solution:

1. **Identify the Options**:
We have four options to evaluate:
- Option 1: \( H_2 \) at 118 and \( HCl \) at 1M
- Option 2: \( H_2 \) at 18 and \( HCl \) at 2M
- Option 3: \( H_2 \) at 18 and \( HCl \) at 0.1M
- Option 4: \( H_2 \) at 18 and \( HCl \) at 0.5M

2. **Calculate for Option 1**:
- For \( H_2 \) at 118 and \( HCl \) at 1M:
\[ E_{cell} = 0.0591/2 \cdot \log(1) = 0.0591/2 \cdot 0 = 0 \]
- This potential is not greater than 0.

3. **Calculate for Option 2**:
- For \( H_2 \) at 18 and \( HCl \) at 2M:
\[ E_{cell} = 0.0591/2 \cdot \log(2) = 0.0591/2 \cdot 0.3010 \approx 0.0089 \]
- This potential is slightly greater than 0.

4. **Calculate for Option 3**:
- For \( H_2 \) at 18 and \( HCl \) at 0.1M:
\[ E_{cell} = 0.0591/2 \cdot \log(0.1) = 0.0591/2 \cdot (-1) \approx -0.0295 \]
- This potential is less than 0.

5. **Calculate for Option 4**:
- For \( H_2 \) at 18 and \( HCl \) at 0.5M:
\[ E_{cell} = 0.0591/2 \cdot \log(0.5) = 0.0591/2 \cdot (-0.3010) \approx -0.0089 \]
- This potential is also less than 0.

6. **Conclusion**:
After evaluating all options, we find that only Option 2 has a potential that is slightly greater than 0.

### Final Answer:
**Option 2** is the correct answer as it has a potential slightly greater than 0.