Which of the following is expected to possess the largest root mean square speed at the same temperature?

Options

A. `H_(2)S`
B. `NH_(3)`
C. `SO_(2)`
D. `CO_(2)`

Explanation

To determine which molecule possesses the largest root mean square (RMS) speed at the same temperature, we can use the formula for root mean square speed:

\[ u_{rms} = \sqrt{\frac{3RT}{M}} \]

Where:
- \( u_{rms} \) = root mean square speed
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin
- \( M \) = molar mass of the gas in kg/mol

### Step-by-Step Solution:

1. **Understand the Relationship**: The root mean square speed is inversely proportional to the square root of the molar mass (\( M \)). This means that as the molar mass decreases, the root mean square speed increases.

2. **List the Molar Masses**: We need to calculate the molar mass of each given molecule:
- **H2S (Hydrogen Sulfide)**:
- Molar mass = \( 2 \times 1 + 32 = 34 \, \text{g/mol} \)
- **NH3 (Ammonia)**:
- Molar mass = \( 14 + 3 \times 1 = 17 \, \text{g/mol} \)
- **SO2 (Sulfur Dioxide)**:
- Molar mass = \( 32 + 2 \times 16 = 64 \, \text{g/mol} \)
- **CO2 (Carbon Dioxide)**:
- Molar mass = \( 12 + 2 \times 16 = 44 \, \text{g/mol} \)

3. **Compare Molar Masses**: Now we have the molar masses:
- H2S: 34 g/mol
- NH3: 17 g/mol
- SO2: 64 g/mol
- CO2: 44 g/mol

4. **Identify the Lowest Molar Mass**: Among the calculated molar masses, NH3 has the lowest molar mass (17 g/mol).

5. **Conclusion**: Since the root mean square speed is inversely proportional to the square root of the molar mass, NH3 will have the highest root mean square speed at the same temperature.

### Final Answer:
**NH3 (Ammonia)** is expected to possess the largest root mean square speed at the same temperature.

---