Laws of Gases: Boyle's Law

In studying the laws of gases there are different variables that we need to consider.  These are the volume, pressure, temperature, and the number of moles.  Volume is the amount of space occupied by a three-dimensional object as measured in cubic units (such as quarts and liter).  Pressure is the force applied in a given area, usually has the unit of atmosphere (atm), millimeter of  Mercury (mm Hg), torr, Pascal (Pa), kilopascal (kPa). Temperature is the degree of hotness and coldness measured on the definite scale such as Kelvin, ^oF and ^oC.  In solving problems related to gases, kelvin always is used.  Number of moles refer to the amount of substance, the unit is mol.

Boyle's Law

Robert Boyle is a British chemist who investigated the relationship between pressure and volume at constant temperature.  He used the J- shaped tube in studying the relationship between pressure and volume, he observed that adding pressure to the open end of the J-shaped tube at constant temperature will cause the decrease in the volume as shown in the figure below:

Boyle's law therefore can be stated as " if the volume of a fixed amount of gas is inversely proportional to volume at constant temperature." Inversely proportional mean that if you increase the pressure the volume will decrease or if the pressure is decreased the volume is increased.  If the relationship will be plotted in a graph, the graph will look like the figure below:

The mathematical equation that will express the inverse relationship between pressure and volume is

where ∝ is means proportional to.  We can change ∝ to an equal sign, 

where k₁ is the proportionality constant.   Arranging the equation:

This means that the product of pressure and volume at constants temperature is constant.

Using Boyle's Law we can predict the new pressure if there is a change in volume and at the same time volume can also be predicted if the pressure is also changed provided the temperature is not changed..  Since P₁V₁ = k, therefore P₂V₂ = k, combining both, the formula will be

P₁V₁ = P₂V₂

Using the above equation as the mother equation we can already formulate formulas for calculating P₁, V₁, P₂ and V₂.

These are the formulas: