Which of the following gases will have the highest `RMS` velocity at `25^(@)C`?

Options

A. Oxygen
B. Carbon dioxide
C. Sulphur dioxide
D. Carbon monoxide

Answer

To determine which gas has the highest RMS (Root Mean Square) velocity at 25°C, we can follow these steps:

### Step 1: Understand the formula for RMS velocity
The RMS velocity (v_rms) of a gas is given by the formula:
\[ v_{rms} = \sqrt{\frac{3RT}{M_w}} \]
Where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin,
- \( M_w \) is the molecular weight of the gas.

### Step 2: Identify the relationship between RMS velocity and molecular weight
From the formula, we can see that RMS velocity is inversely proportional to the square root of the molecular weight:
\[ v_{rms} \propto \frac{1}{\sqrt{M_w}} \]
This means that a lower molecular weight will result in a higher RMS velocity.

### Step 3: Calculate the molecular weights of the given gases
Now, we will calculate the molecular weights of the gases provided in the question:

1. **Oxygen (O₂)**:
- Molecular weight = \( 16 \times 2 = 32 \) g/mol

2. **Carbon Dioxide (CO₂)**:
- Molecular weight = \( 12 + (16 \times 2) = 12 + 32 = 44 \) g/mol

3. **Sulfur Dioxide (SO₂)**:
- Molecular weight = \( 32 + (16 \times 2) = 32 + 32 = 64 \) g/mol

4. **Carbon Monoxide (CO)**:
- Molecular weight = \( 12 + 16 = 28 \) g/mol

### Step 4: Compare the molecular weights
Now that we have the molecular weights:
- O₂: 32 g/mol
- CO₂: 44 g/mol
- SO₂: 64 g/mol
- CO: 28 g/mol

### Step 5: Identify the gas with the lowest molecular weight
Among the calculated molecular weights, Carbon Monoxide (CO) has the lowest molecular weight of 28 g/mol.

### Step 6: Conclusion
Since Carbon Monoxide has the lowest molecular weight, it will have the highest RMS velocity at 25°C. Therefore, the answer is:
**Carbon Monoxide (CO)**.

### Final Answer
The gas with the highest RMS velocity at 25°C is **Carbon Monoxide (CO)**.

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