# Why is k constant in Boyle's law?

Jan 9, 2015

Boyle's law was first formulated as an experimental gas law which described how the pressure of a gas decreased when the volume of said gas increased.

A more formal description of Boyle's law states that the pressure exerted by a mass of ideal gas is inversely proportional to the volume it occupies if temperature and amount of gas remain unchanged.

Mathematically, this can be written as

$P$ $\alpha \frac{1}{V}$, or $P V = \text{constant}$

This is where a $k$ is usually seen, as it is often used to describe a constant value. So the $k$ you are referring to is

$P V = \text{constant} = k$

This can be easily derived from the ideal gas law, $P V = n R T$, for the conditions specified by Boyle's law.

We need to keep the amount of gas, which represents the number of moles, and the temperature constant. Since $R$ is a constant already, the ideal gas law becomes

$P V = n R T = k$

Therefore, $k$ must be constant in order to allow for a relationship to be set between pressure and volume.