A real gas obeying van der Waal equation will resemble ideal gas if the

Options

A. (a) constants a and b both are small
B. (b) a is large and b is small
C. (c) a is small and b is larger
D. (d) constants a and b both are large

Explanation

To solve the question, we need to analyze the conditions under which a real gas, described by the van der Waals equation, behaves like an ideal gas.

### Step-by-Step Solution:

1. **Understanding the Ideal Gas Equation**:
The ideal gas equation is given by:
\[ PV = nRT \]
where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature.

2. **Understanding the Van der Waals Equation**:
The van der Waals equation for real gases is expressed as:
\[ \left(P + \frac{a n^2}{V^2}\right)(V - nb) = nRT \]
Here, \( a \) accounts for the attractive forces between gas molecules, and \( b \) accounts for the volume occupied by the gas molecules themselves.

3. **Conditions for Ideal Behavior**:
- For a real gas to behave like an ideal gas, the effects of intermolecular forces (represented by \( a \)) and the volume occupied by gas molecules (represented by \( b \)) must be negligible.
- This means that both \( a \) and \( b \) should be small.

4. **Conclusion**:
Therefore, a real gas will resemble an ideal gas when the values of the van der Waals constants \( a \) and \( b \) are both small. This leads us to conclude that the correct condition is when both \( a \) and \( b \) are small.

### Answer:
A real gas obeying the van der Waals equation will resemble an ideal gas if the values of the van der Waals constants \( a \) and \( b \) are both small.

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