# Boyle's law

An animation showing the relationship between pressure and volume.The amount and temperature of the gas are constant.

Boyle's law (also called Mariotte's law and the Boyle-Mariotte law) is a law about ideal gases.

The law can be stated as follows:[1]

For a fixed amount of an ideal gas kept at a fixed temperature, P (pressure) and V (volume) are inversely proportional.

In other words, the volume of a constant mass of ideal gas at a constant temperature is inversely proportional to its pressure.[2]

In symbols, the law is:

${\displaystyle P\propto {\frac {1}{V}}}$

or

${\displaystyle PV=k}$

where P is the pressure of the gas, V is the volume of the gas, and k is a constant.

For a given mass of gas at a constant temperature, the product of the pressure and the volume is a constant. As the volume decreases, the pressure increases in proprotion, and vice versa. For example, when the pressure halves, the volume doubles.

Suppose you have a tank that contains a certain volume of gas at a certain pressure. When you decrease the volume of the tank, the same number of gas particles is now contained in a smaller space. Therefore, the number of collisions increases. Therefore, the pressure is greater.[3]

Imagine you have a gas at a certain pressure (P1) and volume (V1). If you change the pressure to a new value (P2), the volume changes to a new value (V2). We can use Boyle's law to describe both sets of conditions:[3]

${\displaystyle P_{1}V_{1}=k}$
${\displaystyle P_{2}V_{2}=k}$

The constant, k, is the same in both cases, so we can say the following:[3]

${\displaystyle P_{1}V_{1}=P_{2}V_{2}}$

Example: The pressure of a gas is 3 atm and the volume is 5 litres. If the pressure is reduced to 2 atm, what is the volume?

${\displaystyle P_{1}V_{1}=P_{2}V_{2}}$
${\displaystyle V_{2}={\frac {P_{1}V_{1}}{P_{2}}}}$
${\displaystyle V_{2}={\frac {3*5}{2}}}$
${\displaystyle V_{2}={\frac {15}{2}}}$
${\displaystyle V_{2}=7.5}$

∴ The volume will be 7.5 litres.

The law was found by Robert Boyle in 1662, and afterwards independently by Edme Mariotte in 1679.[2][4][5]

## References

1. Levine, Ira N. (2009). Physical Chemistry (Sixth ed.). New York: McGraw-Hill. p. 10. ISBN 978–0–07–253862–5 Check |isbn= value: invalid character (help).
2. Daintith, John, ed. (2008). A Dictionary of Chemistry (Sixth ed.). Oxford: Oxford University Press. p. 82. ISBN 978-0-19-920463-2.
3. Moore, John T. (2010). Chemistry Essentials For Dummies. New Jersey: John Wiley & Sons, Inc. p. 163. ISBN 978-0-470-61836-3.
4. Ganot, Adolphe; Atkinson, Edmund (1883). Éléments de Physique [Elementary Treatise on Physics] (Eleventh ed.). London: Longmans, Green, and Co. p. 142.
5. West, John B. (2005-01-01), "Robert Boyle's landmark book of 1660 with the first experiments on rarified air", Journal of Applied Physiology, 98 (1), pp. 31–39, doi:10.1152/japplphysiol.00759.2004