When the volume of a gas decreases, the pressure of the gas increases, assuming that the temperature and number of moles of the gas are held constant. This relationship is described by Boyle's Law, which states that at constant temperature, the pressure and volume of a gas are inversely proportional. Mathematically, this can be represented by the equation PV = k, where P is the pressure of the gas, V is the volume of the gas, and k is a constant. As the volume of a gas decreases, the pressure increases in order to maintain the constant value of k.
It's important to note that this relationship applies only to an ideal gas, which is a theoretical concept of a gas that does not take into account the interactions between gas molecules or the compressibility factor. In reality, gases deviate from the ideal behavior, so PV = k is only an approximation. Additionally, the temperature also plays a role in the gas behavior and in order to properly use Boyle's Law, you must hold temperature constant.