At Boyle's temperature the value of compressibility factro `Z = (PV_(m(//RT = V_(real)//V_(ideal))` has a value of 1 over a wide range of pressure. This is due to the fact that in the van der Waal's equation

Options

A. The constant ‘a’ is negligible and not ‘b’
B. The constant ‘b’ is negligible and not ‘a’
C. Both the constant ‘a’ and ‘b’ are negligible
D. The effect produced due to the molecular attraction compensates the effect produced due to the molecular volume

Explanation

To solve the question regarding Boyle's temperature and the compressibility factor \( Z \) in the context of the van der Waals equation, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Compressibility Factor**:
The compressibility factor \( Z \) is defined as:
\[ Z = \frac{PV_m}{RT} \]
where \( P \) is the pressure, \( V_m \) is the molar volume, \( R \) is the universal gas constant, and \( T \) is the temperature.

2. **Definition of Boyle's Temperature**:
Boyle's temperature is defined as the temperature at which a real gas behaves like an ideal gas over a range of pressures. At this temperature, the compressibility factor \( Z \) approaches 1.

3. **Van der Waals Equation**:
The van der Waals equation for real gases is given by:
\[ \left( P + \frac{a n^2}{V^2} \right)(V - nb) = nRT \]
where \( a \) and \( b \) are the van der Waals constants that account for intermolecular forces and the volume occupied by gas molecules, respectively.

4. **Behavior at Boyle's Temperature**:
At Boyle's temperature, the effects of the van der Waals constants \( a \) and \( b \) become negligible. This means that the intermolecular forces and the volume occupied by the gas molecules do not significantly affect the behavior of the gas.

5. **Reduction to Ideal Gas Law**:
When \( a \) and \( b \) are negligible, the van der Waals equation simplifies to:
\[ PV = nRT \]
This is the ideal gas equation, which implies that:
\[ Z = \frac{PV}{RT} = 1 \]

6. **Conclusion**:
Therefore, at Boyle's temperature, the compressibility factor \( Z \) equals 1 because the van der Waals constants \( a \) and \( b \) are negligible, allowing the gas to behave ideally.

### Final Answer:
At Boyle's temperature, the value of compressibility factor \( Z = 1 \) over a wide range of pressure due to the fact that in the van der Waals equation, the constants \( a \) and \( b \) become negligible, leading the equation to approximate the ideal gas law.