Mathematically, Boyle's Law can be expressed as:
P₁V₁ = P₂V₂
Where P₁ and V₁ represent the initial pressure and volume of the gas, and P₂ and V₂ represent the final pressure and volume of the gas.
If the volume increases (V₂ > V₁) while the temperature remains constant, then the pressure must decrease (P₂ < P₁) in order to maintain the equality of the product of pressure and volume.
This relationship can be understood in terms of the behavior of gas particles. When the volume of the container increases, the gas particles have more space to move around. This means that they collide with the walls of the container less frequently, resulting in a decrease in the overall pressure.
In summary, if the volume of a gas sealed container increases while the temperature stays the same, the pressure of the gas will decrease.