Boyles Law Formulas and Examples
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:
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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:
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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
FAQs on Boyles Law Formula
1. What are some of the examples of Boyle's Law Formula?
Boyle’s law has a number of applications and some of the examples of the same can be provided as follows:
Breathing is the medium of survival for humans. But how the breathing process takes place is through Boyle’s law. During breathing, the air is inhaled into the lungs and they get filled in and expanded. This in turn causes an increase in the volume of air in the lungs and the pressure gets reduced. But during the process of exhalation there is a decrease in the volume of air and hence resulting in the squeezing of the lungs due to the increase in pressure observed.
Another instance is seen in the packed carbonated drinks where a mixture of carbon dioxide and water is sealed in a packet. While the bottle is sealed it cannot be compressed due to the air molecules that have been tightly packed in. But when the bottle is opened these air molecules tend to get free and hence making it easier to compress and exert pressure on the gas molecule.
2. What are the limitations to Boyle's Law Formula?
One of the biggest limitations to Boyle's Law Formula is that it can only be applied to ideal gases. The law holds good only at high temperature and pressure at a very low value. The law does not work when there is the presence of high-pressure values. The merchandise of pressure and volume does not remain constant at high pressures instead it shows a small increase. This increase takes place due to a rise that is seen within the volume due to which it is caused by repulsive forces among the molecules.
3. What is Boyle's Law statement?
According to Boyle’s law, it is seen that at a constant temperature and mass the volume of the given amount of gas will stay inversely proportional to the pressure. In other words, it can also be said that if the temperature and mass of a given gas are kept constant then the volume of that gas will be decreasing with an increase in the pressure. Boyle’s law is one of the most important gas laws that explain an inverse relationship between pressure and volume. This law was provided by one of the pioneer founders of modern experimental chemistry, an English chemist named Robert Boyle in 1662. While experimenting on gases and studying the deviating behavior of gas in the variable environment, Robert Boyle introduced Boyle's law.
4. What is the relationship between pressure and volume as provided by Boyle's Law Formula?
Consider a sample of gas in a one-liter container. We already know that the pressure exerted on the container due to the gas will be the sum of the collisions of the particles, divided by the surface area of the container, and can be expressed as follows:
\[F = \frac{\sum F_{col}}{A}\]
We also have an idea about the volume which is related to the surface area and that if the volume decreases then the surface area will also automatically decrease as well. From these two relations, it is quite obvious that as the volume decreases the total pressure is going to increase. This hence leads to Boyle’s law formula such as follows:
\[P \alpha \frac{1}{V}\]
This proportionality helps us solve a lot of problems that are related to the changes in pressure and volume in a closed system. For example, in a piston full of oxygen it is obvious that as the piston will be compressed the pressure will go on increasing.
5. Why do students need to learn more about Boyle's Law Formula?
Boyle's Law Formula is an important part of the syllabus and is also considered to be one of the most used formulae in not only Physics but also in Chemistry where not only are the question put during Class 11 and 12 exams but is also put during the IIT JEE Mains exams and other such competitive exams. In order to revise all the concepts that are related to Boyle's Law Formula, students can now also access the Vedantu Revision notes for Chemistry.
