1 mole of a diatomic gas present in 10 L vessel at certain temperature exert a pressure of 0.96 atm. Under similar conditions an ideal gas exerted 1.0 atm pressure. If volume of gas molecule is negligible, then find the value of van der Waals' constant ''a'' (in atm `L^(2)//mol^(2)`).

Explanation

To solve the problem, we will use the Van der Waals equation for real gases and the given data to find the value of the Van der Waals constant "a".

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Pressure of the real gas, \( P_{real} = 0.96 \, \text{atm} \)
- Pressure of the ideal gas, \( P_{ideal} = 1.0 \, \text{atm} \)
- Number of moles, \( n = 1 \, \text{mol} \)
- Volume of the gas, \( V = 10 \, \text{L} \)

2. **Write the Van der Waals Equation**:
The Van der Waals equation for real gases is given by:
\[ P_{ideal} = P_{real} + \frac{a n^2}{V^2} \]

3. **Substitute the Known Values**:
Substitute the known values into the equation:
\[ 1.0 = 0.96 + \frac{a (1)^2}{(10)^2} \]

4. **Simplify the Equation**:
Rearranging the equation gives:
\[ 1.0 - 0.96 = \frac{a}{100} \]
\[ 0.04 = \frac{a}{100} \]

5. **Solve for "a"**:
Multiply both sides by 100 to isolate "a":
\[ a = 0.04 \times 100 \]
\[ a = 4 \, \text{atm} \cdot \text{L}^2/\text{mol}^2 \]

### Final Answer:
The value of the Van der Waals constant "a" is \( 4 \, \text{atm} \cdot \text{L}^2/\text{mol}^2 \).

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