Question

Assertion: At Boyle temperature, the compressibility factor of a real gas,$\text{ Z}>\text{1 }$.
Reason: All the gases tend to approach a value$\text{ Z= 1 }$when the pressure of gas approaches to zero value at any temperature.
A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C) Assertion is correct but Reason is incorrect
D) Assertion is incorrect but Reason is correct

Answer 1

Hint: Boyle's law states that at a constant temperature pressure is proportional to the volume of a gas. That is,
 $\text{ PV = constant }$
The ideal gas equation is obtained by combining the gas laws. Thus gas behaves ideally at Boyle's temperature.

Complete step by step answer:
The ideal gas equation is stated as the $\text{ PV = nRT }$
The compressibility factor ‘Z’ is a ratio of the molar volume of gas to the molar volume of an ideal gas at the temperature and pressure.
According to Boyle’s law, the pressure exerted by the mass of an ideal gas is inversely proportional to the volume of the gas at a constant temperature in a closed system. Mathematically Boyle’s law can be stated as,
\[\text{ P}\propto \text{ }\dfrac{\text{1}}{\text{V}}\text{ }\]
Where P is the pressure of the gas and V is the volume of the gas. The ideal gas equation is obtained by combining Boyle’s law, Charles law, and Avogadro’s law. At Boyle’s temperature gas behaves as an ideal gas.
Gases that behave ideally have a molar volume of gas equal to the molar volume of an ideal gas. Thus compressibility factor for an ideal gas is $\text{ Z= 1 }$. At Boyle’s temperature the compressibility factor of a real gas $\text{ Z}\ge \text{ 1 }$. Thus the given statement is correct as at Boyle’s temperature gas behaves as an ideal gas.
Value of the compressibility factor approaches towards 1 when the pressure of gas approaches zero. When the value of $\text{ Z= 1 }$all gases behaves ideally. This statement is correct. But this is not a reason.
Thus both assertion and reason are correct but the reason is not the correct explanation for the assertion.

Hence, (B) is the correct option.

Note: the value of the compressibility factor ‘Z’ used to determine the behavior of gas:
1. When $\text{ Z =1 }$ the pressure of gas approaches towards zero and thus gas behaves ideally.
2. When$\text{ Z}<\text{1 }$ the gas has an intermediate pressure. This is because the intermolecular forces of attraction reduce the volume than the ideal gas. A gas behaves like a real gas.
3. When $\text{ Z}>\text{1 }$ the gas experiences high pressure and intermolecular repulsive forces increase. This leads to a greater volume than the actual ideal gas values. Here gas behaves like a real gas.