Vanderwaal gas constant 'a' value is very high for the following gas

Options

A. `SO_2`
B. He
C. `O_2`
D. `CO_2`

Answer

To determine which gas has the highest Van der Waals constant 'a', we need to analyze the molecular weights of the given gases. The Van der Waals constant 'a' is directly related to the intermolecular forces of attraction, which are influenced by the molecular weight of the gas. Here’s how to approach the problem step by step:

### Step 1: Understand the Van der Waals Constant 'a'
The Van der Waals constant 'a' indicates the strength of the intermolecular forces of attraction between gas molecules. A higher value of 'a' means stronger intermolecular forces.

### Step 2: Identify the Gases and Their Molecular Weights
We need to find the molecular weights of the gases provided:
- **Sulfur Dioxide (SO2)**:
- Sulfur (S) = 32 g/mol
- Oxygen (O) = 16 g/mol
- Molecular weight of SO2 = 32 + (16 × 2) = 32 + 32 = **64 g/mol**

- **Helium (He)**:
- Helium = 4 g/mol
- Molecular weight of He = **4 g/mol**

- **Oxygen (O2)**:
- Oxygen (O) = 16 g/mol
- Molecular weight of O2 = 16 × 2 = **32 g/mol**

- **Carbon Dioxide (CO2)**:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- Molecular weight of CO2 = 12 + (16 × 2) = 12 + 32 = **44 g/mol**

### Step 3: Compare the Molecular Weights
Now, we compare the molecular weights calculated:
- SO2 = 64 g/mol
- He = 4 g/mol
- O2 = 32 g/mol
- CO2 = 44 g/mol

### Step 4: Determine the Highest Molecular Weight
From the comparison:
- The highest molecular weight is for **Sulfur Dioxide (SO2)** at 64 g/mol.

### Step 5: Conclusion
Since the Van der Waals constant 'a' is directly proportional to the molecular weight, the gas with the highest molecular weight will have the highest value of 'a'. Therefore, the correct answer is:
- **Option A: Sulfur Dioxide (SO2)**