Question

Assertion: At Boyle’s Temperature, the compressibility factors of a gas approaches unity.
Reason: At Boyle’s temperature the real gases obey ideal gas laws.
A.Both Assertion and reason are correct and the reason is the correct explanation for the assertion
B.Both Assertion and reason are correct and the reason is not the correct explanation for the assertion
C.Assertion is correct but the reason is incorrect
D.Assertion is incorrect but the reason is correct

Answer 1

Hint: Compressibility Factor can be understood as a correction factor which identifies the deviation of a real gas from an ideal gas. It can be mathematically understood as the ratio of the molar volume of a real gas to the molar volume of an ideal gas at constant values of temperature and pressure.

Complete Step-by-Step Answer:

Before we move forward with the solution of this question, let us first understand some important basic concepts.
Boyle’s temperature can be understood at the temperature at which any real gas would exhibit the values of an ideal gas. The value of Boyle’s temperature is unique to every gas. This means that at this temperature, the given real gas would obey the ideal gas law, i.e. \[PV = nRT\]
Once we reach Boyle’s Temperature, all the correction factors approach the value of 1. To explain this, let us first understand that the deviations of the values of the properties of the real gases are monitored by implementing various correction factors. These correction factors enable us to understand how much the values of the properties are deviating in comparison to an ideal gas. When the gas is at its Boyle’s temperature, it begins to behave like an ideal gas. Hence, all these correction factors become obsolete and approach the value of unity. Compressibility ratio is one such correction factor, and hence at Boyle’s temperature, it too approaches unity.
Hence, both Assertion and reason are correct and the reason is the correct explanation for the assertion

Hence, Option A is the correct option

Note: Boyle temperature (TB) is related to the Vander Waals constant a, b as given below. At this temperature, the attractive and repulsive forces acting on the gas particles arrive at a balance for a real gas. \[\left[ {TB = \dfrac{a}{{Rb}}} \right]\]