Question

Why is $ k $ constant in Boyle’s law?

Answer 1

Hint: Ideal gases behave in a particular manner and the relation between the physical attributes of ideal gases are governed by a certain set of laws called the ideal gas laws. One such law is Boyle's law that establishes a relationship between the pressure and volume of an ideal gas.

Complete Step By Step Answer:
Boyle's law of ideal gases is based on experimental observations such as application of pressure leads to compression of the volume and a decrease in external pressure allows expansion of volume of the gas.
Thus, this law states that the pressure and volume are inversely proportional quantities for an ideal gas. On increasing pressure volume decreases and vice versa. The relation can be expressed as follows:
 $ P\alpha \dfrac{1}{V} $
On removing the proportionality sign we get,
 $ PV = k $
The product of pressure and volume remains a constant equal to $ k $ as the measurement of volume and pressure of an ideal gas is done for a fixed amount of gas at a particular temperature. Under such conditions, the increase in pressure nullifies the decrease in volume and the product always comes out to be equal to a constant value.
The ideal gas equation expresses the actual value of this constant $ k $ :
 $ PV = k = nRT $
 $ \Rightarrow $ Thus, $ k $ is a constant because the product of pressure and volume remains unchanged at constant temperature and for a mixed amount of gas.

Note:
Boyle’s law is only followed under specific ranges of temperature and pressure and most real gases show significant deviation from this law due to the presence of intermolecular forces of attraction in between their particles which is ignored in ideal gases.