According to Boyle's Law, how are pressure and volume of a gas related?

Boyle's Law states that for a given amount of gas at a constant temperature, the pressure and volume of the gas are inversely related. This means that as the volume of a gas increases, the pressure decreases, and vice versa, as long as the temperature remains constant. Mathematically, this relationship is often expressed as ( P \propto \frac{1}{V} ), where ( P ) represents pressure and ( V ) represents volume.

This inverse relationship makes intuitive sense; when a gas occupies a larger volume, its molecules have more space to move around, which reduces the number of collisions with the walls of the container, thereby lowering the pressure. Conversely, decreasing the volume compresses the gas, increasing the frequency of these collisions and thus increasing the pressure. This foundational principle is crucial in understanding gas behaviors under varying conditions in physical chemistry.

The other options describe different relationships that do not align with Boyle's Law. For example, the idea of direct proportionality does not hold true in this case, nor does the concept of equal quantities or no relationship at all, as both pressure and volume are critically interconnected through this law.