There is quite a relation between pressure and volume and is provided by a formula. This formula was given by Robert Boyle in 1660. He is also rightly known as the Father of Modern Chemistry who has worked both in the fields of chemistry and physics. A book named The Spring and Weight of the Air is the one in which he had mentioned the various experiments that he had conducted using a vacuum pump and has also mentioned this relation between volume and pressure which is also called Boyle’s law.
Boyle’s Law Formula
According to this experimental gas law, the pressure of a given mass of an ideal gas is inversely proportional to its volume at a constant temperature. An important point to note here is that the amount of ideal gas (i.e., number of moles) is kept fixed and a constant temperature is maintained. Under this condition, the pressure of the gas will tend to increase if we decrease the volume of the container and vice-versa.
Mathematically, it can be expressed as:
()
Where ‘P’ is the pressure exerted by the gas and ‘V’ is the Volume of the container.
Graphically, we can observe the behaviour of the curve as follows:
()
You can see how the value of Pressure decreases when the Volume is increased or vice-versa.
In order to understand it better, let us go through a simple example:
Example: If 20[c{m^3}] gas at 1 atm. is expanded to 50 [c{m^3}] at constant T, then what is the final pressure
Options:
(a) [20 times frac{1}{{50}}]
(b) [50 times frac{1}{{20}}]
(c) [1 times frac{1}{{20}} times 50]
(d) None of these
Answer: (a)
Solution:
At constant [T,{P_1}{V_1} = {P_2}{V_2}]
[1 times 20 = {P_2} times 50]; [{P_2} = frac{{20}}{{50}} times 1]
We hope you have understood, how to apply the Boyle’s Law Formula. Now in order to test your understanding, try and solve the Question by yourself.
Example: An ideal gas exerts a pressure of 3atm in a 3L container. The container is at a temperature of 298K. What will be the final pressure if the volume of the container changes to 2L?
Options:
(a) 2 atm
(b) 3.5 atm
(c) 4.5 atm
(d) 4 atm
Answer: (c)
Solution:
Boyle’s law can be written as follows:
[{P_1}{V_1} = {P_2}{V_2}]
Use the given volumes and the initial pressure to solve for the final pressure.
(3atm)(3L)=(2L)P2
P2=4.5atm