The correct increasing order of Vanderwaal constant 'b' for `H_(2) , O_(2) , CO_(2) ` , He gases is

Options

A. `H_(2) lt He lt O_(2) lt CO_(2)`
B. `He lt H_2 lt O_2 lt CO_2`
C. `He lt H_2 lt CO_2 lt O_2`
D. `CO_(2) lt O_(2) lt He lt H_(2)`

Explanation

To determine the correct increasing order of the Van der Waals constant 'b' for the gases \( H_2 \), \( O_2 \), \( CO_2 \), and He, we need to understand what the constant 'b' represents. The Van der Waals constant 'b' is related to the volume occupied by the gas particles and is indicative of the size of the gas molecules. A larger molecular size results in a larger value of 'b'.

### Step-by-Step Solution:

1. **Identify the Molecular Sizes**:
- \( H_2 \) (Hydrogen) has the smallest molecular size.
- \( He \) (Helium) is a noble gas and is also quite small, but slightly larger than \( H_2 \).
- \( O_2 \) (Oxygen) has a larger molecular size than both \( H_2 \) and \( He \).
- \( CO_2 \) (Carbon Dioxide) has the largest molecular size among the four gases.

2. **Rank the Gases by Size**:
- The order of increasing size is:
- \( H_2 \) < \( He \) < \( O_2 \) < \( CO_2 \)

3. **Relate Size to Van der Waals Constant 'b'**:
- Since 'b' is directly related to the size of the molecules, we can conclude that:
- The smaller the molecule, the smaller the value of 'b'.
- Therefore, the increasing order of 'b' will follow the same order as the increasing size of the molecules.

4. **Write the Increasing Order of 'b'**:
- Based on the sizes identified, the increasing order of the Van der Waals constant 'b' is:
- \( H_2 < He < O_2 < CO_2 \)

### Final Answer:
The correct increasing order of Van der Waals constant 'b' for \( H_2 \), \( O_2 \), \( CO_2 \), and He is:
\[ H_2 < He < O_2 < CO_2 \]