What is the correct equation for pressure in terms of volume as per Boyle's Law?

Boyle's Law describes the relationship between the pressure and volume of a gas at constant temperature. It states that the pressure of a given mass of gas is inversely proportional to its volume when the temperature is held constant. This relationship can be mathematically expressed as:

[ P \propto \frac{1}{V} ]

This indicates that if the volume increases, the pressure decreases, and vice versa, as long as the temperature remains constant. In order to express this relationship in equation form, we introduce a constant ( k ) (which depends on the amount of gas and the temperature). Thus, we can write the equation as:

[ P = \frac{k}{V} ]

This clearly shows that pressure ( P ) is equal to a constant ( k ) divided by volume ( V ), aligning perfectly with the choice indicating that pressure is inversely proportional to volume.

The other options do not accurately reflect Boyle’s Law: ( P = kV ) suggests direct proportionality, which is incorrect in this context; ( P = kT ) indicates that pressure is proportional to temperature, not volume; and ( P = nRT ) relates pressure to the number of moles, the gas constant,