Boyle’s law: Pressure and volume

Boyle’s law (named after Robert Boyle, a 17th-century English scientist) describes the pressure-volume relationship of gases if you keep the temperature and amount of the gas constant. The law states that there’s an inverse relationship between the volume and air pressure (the collision of the gas particles with the inside walls of the container): As the volume decreases, the pressure increases, and vice versa. He determined that the product of the pressure and the volume is a constant (k):

PV = k

Suppose you have a cylinder that contains a certain volume of gas at a certain pressure. When you decrease the volume, the same number of gas particles is now contained in a much smaller space, and the number of collisions increases significantly.

Therefore, the pressure is greater.

Now consider a case where you have a gas at a certain pressure (P₁) and volume (V₁). If you change the volume to some new value (V₂), the pressure also changes to a new value (P₂). You can use Boyle’s Law to describe both sets of conditions:

P₁V₁ = k

P₂V₂ = k

The constant, k, is going to be the same in both cases, so you can say the following, if the temperature and amount of gas don’t change:

P₁V₁ = P₂V₂

This equation is another statement of Boyle’s Law — and it’s really a more useful one, because you normally deal with changes in pressure and volume.

If you know three of the preceding quantities, you can calculate the fourth one. For example, suppose that you have 5.00 liters of a gas at 1.00 atm pressure, and then you decrease the volume to 2.00 liters. What’s the new pressure? Use the formula.

Substitute 1.00 atm for P₁, 5.00 liters for V₁, and 2.00 liters

for V₂, and then solve for P₂: