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 solve the question of which gas possesses the largest root mean square speed at the same temperature, we can follow these steps:

### Step 1: Understand the formula for root mean square speed
The root mean square speed (U_rms) of a gas is given by the formula:
\[ U_{rms} = \sqrt{\frac{3RT}{M}} \]
where:
- \( R \) is the gas constant,
- \( T \) is the temperature,
- \( M \) is the molar mass of the gas.

### Step 2: Identify the relationship between U_rms and molar mass
From the formula, we can see that U_rms 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.

### Step 3: Calculate the molar mass of each gas
Now, we will calculate the molar mass of each gas provided in the options.

1. **H2S (Hydrogen Sulfide)**:
- Molar mass = (2 × atomic mass of H) + (1 × atomic mass of S)
- Molar mass = (2 × 1) + (32) = 34 g/mol

2. **NH3 (Ammonia)**:
- Molar mass = (1 × atomic mass of N) + (3 × atomic mass of H)
- Molar mass = (14) + (3 × 1) = 17 g/mol

3. **SO2 (Sulfur Dioxide)**:
- Molar mass = (1 × atomic mass of S) + (2 × atomic mass of O)
- Molar mass = (32) + (2 × 16) = 64 g/mol

4. **CO2 (Carbon Dioxide)**:
- Molar mass = (1 × atomic mass of C) + (2 × atomic mass of O)
- Molar mass = (12) + (2 × 16) = 44 g/mol

### Step 4: Compare the molar masses
Now we can list the molar masses we calculated:
- H2S: 34 g/mol
- NH3: 17 g/mol
- SO2: 64 g/mol
- CO2: 44 g/mol

### Step 5: Determine the order of molar masses
Arranging these in order from least to greatest:
1. NH3: 17 g/mol (least)
2. H2S: 34 g/mol
3. CO2: 44 g/mol
4. SO2: 64 g/mol (greatest)

### Step 6: Determine the order of U_rms
Since U_rms is inversely proportional to the square root of molar mass, the gas with the lowest molar mass will have the highest U_rms. Therefore, the order of U_rms from highest to lowest is:
1. NH3 (highest U_rms)
2. H2S
3. CO2
4. SO2 (lowest U_rms)

### Conclusion
Thus, the gas expected to possess the largest root mean square speed at the same temperature is **NH3 (Ammonia)**.