van der Waal's equation of state of a gas takes into account

Options

A. the intermolecular forces only
B. the size of the molecule only
C. both the intermolecular forces and the size of the molecule
D. the velocity of the molecules only

Answer

To answer the question regarding what the Van der Waals equation of state of a gas takes into account, we can break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding the Van der Waals Equation**:
The Van der Waals equation is given by:
\[ \left( P + \frac{a}{V^2} \right) (V - b) = RT \]
where \( P \) is the pressure, \( V \) is the volume, \( T \) is the temperature, \( R \) is the universal gas constant, and \( a \) and \( b \) are the Van der Waals constants.

2. **Intermolecular Forces**:
The term \( a \) in the equation accounts for the attractive forces between the molecules. In an ideal gas, we assume no intermolecular forces; however, real gases experience these forces, which affect the pressure exerted by the gas.

3. **Volume of Molecules**:
The term \( b \) represents the volume occupied by the gas molecules themselves. In an ideal gas, we consider the gas molecules as point particles with no volume, but in reality, they have a finite size that affects the overall volume available for the gas to occupy.

4. **Conclusion**:
The Van der Waals equation takes into account both the intermolecular forces (through the constant \( a \)) and the size of the molecules (through the constant \( b \)). Therefore, the correct answer to the question is that the Van der Waals equation considers both intermolecular forces and the size of molecules.

### Final Answer:
The Van der Waals equation of state of a gas takes into account **both intermolecular forces and the size of molecules**.

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