# Boyle’s Law

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## What is Boyle’s Law?

Boyle’s law is a gas law which states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant. Boyle’s law was put forward by the Anglo-Irish chemist Robert Boyle in the year 1662.

For a gas, the relationship between volume and pressure (at constant mass and temperature) can be expressed mathematically as follows.

P ∝ (1/V)

Where P is the pressure exerted by the gas and V is the volume occupied by it. This proportionality can be converted into an equation by adding a constant, k.

P = k*(1/V) ⇒ PV = k

The pressure v/s volume curve for a fixed amount of gas kept at constant temperature is illustrated below.

It can be observed that a straight line is obtained when the pressure exerted by the gas (P) is taken on the Y-axis and the inverse of the volume occupied by the gas (1/V) is taken on the X-axis.

## Formula and Derivation

As per Boyle’s law, any change in the volume occupied by a gas (at constant quantity and temperature) will result in a change in the pressure exerted by it. In other words, the product of the initial pressure and the initial volume of a gas is equal to the product of its final pressure and final volume (at constant temperature and number of moles). This law can be expressed mathematically as follows:

P1V1 = P2V2

Where,

• P1 is the initial pressure exerted by the gas
• V1 is the initial volume occupied by the gas
• P2 is the final pressure exerted by the gas
• V2 is the final volume occupied by the gas

This expression can be obtained from the pressure-volume relationship suggested by Boyle’s law. For a fixed amount of gas kept at a constant temperature, PV = k. Therefore,

P1V1 = k (initial pressure * initial volume)

P2V2 = k (final pressure * final volume)

∴ P1V1 = P2V2

This equation can be used to predict the increase in the pressure exerted by a gas on the walls of its container when the volume of its container is decreased (and its quantity and absolute temperature remain unchanged).

## Examples of Boyle’s Law

When a filled balloon is squeezed, the volume occupied by the air inside the balloon decreases. This is accompanied by an increase in the pressure exerted by the air on the balloon, as a consequence of Boyle’s law. As the balloon is squeezed further, the increasing pressure eventually pops it. An illustration describing the increase in pressure that accompanies a decrease in the volume of a gas is provided below.

If a scuba diver rapidly ascends from a deep zone towards the surface of the water, the decrease in the pressure can cause the gas molecules in his/her body to expand. These gas bubbles can go on to cause damage to the diver’s organs and can also result in death. This expansion of the gas caused by the ascension of the scuba diver is another example of Boyle’s law. Another similar example can be observed in the deep-sea fish that die after reaching the surface of the water (due to the expansion of dissolved gasses in their blood).

## Solved Exercises on Boyle’s Law

Exercise 1

A fixed amount of a gas occupies a volume of 1L and exerts a pressure of 400 kPa on the walls of its container. What would be the pressure exerted by the gas if it is completely transferred into a new container having a volume of 3 liters (assuming the temperature and quantity of gas remains constant)?

Given,

Initial volume (V1) = 1L

Initial pressure (P1) = 400 kPa

Final volume (V2) = 3L

As per Boyle’s law, P1V1 = P2V2 ⇒ P2 = (P1V1)/V2

P2 = (1L * 400 kPa)/3L = 133.33 kPa

Therefore, the gas exerts a pressure of 133.33 kPa on the walls of the 3-liter container.

Exercise 2

A gas exerts a pressure of 3 kPa on the walls of container 1. When container 1 is emptied into a 10-liter container, the pressure exerted by the gas increases to 6 kPa. Find the volume of container 1. Assume that the temperature and quantity of the gas remain constant.

Given,

Initial pressure, P1 = 3kPa

Final pressure, P2 = 6kPa

Final volume, V2 = 10L

According to Boyle’s law, V1 = (P2V2)/P1

V1 = (6 kPa * 10 L)/3 kPa = 20 L

Therefore, the volume of container 1 is 20 L.

## Frequently Asked Questions – FAQs

### How does Boyle’s law work?

Boyle’s law is a gas law that states that a gas’s pressure and volume are inversely proportional. When the temperature is kept constant, as volume increases, pressure falls and vice versa.

### Why is Boyle law important?

Boyle’s law is significant because it explains how gases behave. It proves beyond a shadow of a doubt that gas pressure and volume are inversely proportional. When you apply pressure on a gas, the volume shrinks and the pressure rises.

### What is the formula for Boyle’s gas law?

The empirical relation asserts that the pressure (p) of a given quantity of gas changes inversely with its volume (v) at constant temperature; i.e., pv = k, a constant, as proposed by physicist Robert Boyle in 1662.

### What is a good example of Boyle’s Law?

A balloon is a good example of Boyle’s law in action. The balloon is inflated by blowing air into it; the pressure of the air pulls on the rubber, causing the balloon to expand. When one end of the balloon is compressed, the pressure within rises, causing the un-squeezed section of the balloon to expand outward.

### Can Boyle’s law be experimentally proven?

Boyle’s law is a connection between pressure and volume. It asserts that under constant temperature, the pressure of a specific quantity of gas is inversely proportional to its volume. It is possible to prove the law empirically. The paper discusses a syringe-based experimental approach for verifying the law.

Gases have various properties which we can observe with our senses, including the gas pressure, temperature, mass, and the volume which contains the gas. Careful, scientific observation has determined that these variables are related to one another, and the values of these properties determine the state of the gas.

In the mid 1600’s, Robert Boyle studied the relationship between the pressure p and the volume V of a confined gas held at a constant temperature. Boyle observed that the product of the pressure and volume are observed to be nearly constant. The product of pressure and volume is exactly a constant for an ideal gas.

p * V = constant

This relationship between pressure and volume is called Boyle’s Law in his honor. For example, suppose we have a theoretical gas confined in a jar with a piston at the top. The initial state of the gas has a volume equal to 4.0 cubic meters and the pressure is 1.0 kilopascal. With the temperature and number of moles held constant, weights are slowly added to the top of the piston to increase the pressure. When the pressure is 1.33 kilopascals the volume decreases to 3.0 cubic meters. The product of pressure and volume remains a constant (4 x 1.0 = 3 x 1.33333 ). Here is a computer animation of this process:

Boyle’s Law is a basic law in chemistry describing the behavior of a gas held at a constant temperature. The law, discovered by Robert A. Boyle in 1662, states that at a fixed temperature, the volume of gas is inversely proportional to the pressure exerted by the gas. In other words, when a gas is pumped into an enclosed space, it will shrink to fit into that space, but the pressure that gas puts on the container will increase.

Perhaps a more straightforward way is to say Boyle’s law is the relationship between pressure and volume. Mathematically, Boyle’s law can be written as pV=k, where p is the pressure of the gas, V is the volume of the gas, and k is a constant.

An example of Boyle’s law in action can be seen in a balloon. Air is blown into the balloon; the pressure of that air pushes on the rubber, making the balloon expand. If one end of the balloon is squeezed, making the volume smaller, the pressure inside increased, making the un-squeezed part of the balloon expand out. There is a limit to how much the air/gas can be compressed, however, because eventually the pressure becomes so great that it causes the balloon to break.

### Boyle’s Law: Volume and Pressure

#### Learning Objective

• Apply Boyle’s Law using mathematical calculations.

#### Key Points

• According to Boyle’s Law, an inverse relationship exists between pressure and volume.
• Boyle’s Law holds true only if the number of molecules (n) and the temperature (T) are both constant.
• Boyle’s Law is used to predict the result of introducing a change in volume and pressure only, and only to the initial state of a fixed quantity of gas.
• The relationship for Boyle’s Law can be expressed as follows: P1V1 = P2V2, where P1 and V1 are the initial pressure and volume values, and P2 and V2 are the values of the pressure and volume of the gas after change.

#### Terms

• isothermin thermodynamics, a curve on a p-V diagram for an isothermal process
• Boyle’s lawthe absolute pressure and volume of a given mass of confined gas are inversely proportional, while the temperature remains unchanged within a closed system
• ideal gasa theoretical gas composed of a set of randomly-moving, non-interacting point particles

### Boyle’s Law

Boyle’s Law (sometimes referred to as the Boyle-Mariotte Law) states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, provided the temperature remains unchanged within a closed system. This can be stated mathematically as follows:

P1V1=P2V2

### History and Derivation of Boyle’s Law

The law was named after chemist and physicist Robert Boyle, who published the original law in 1662. Boyle showed that the volume of air trapped by a liquid in the closed short limb of a J-shaped tube decreased in exact proportion to the pressure produced by the liquid in the long part of the tube.

Boyle’s LawAn animation of Boyle’s Law, showing the relationship between volume and pressure when mass and temperature are held constant.

The trapped air acted much like a spring, exerting a force opposing its compression. Boyle called this effect “the spring of the air” and published his results in a pamphlet with that title. The difference between the heights of the two mercury columns gives the pressure (76 cm = 1 atm), and the volume of the air is calculated from the length of the air column and the tubing diameter.

The law itself can be stated as follows: for a fixed amount of an ideal gas kept at a fixed temperature, P (pressure) and V (volume) are inversely proportional—that is, when one doubles, the other is reduced by half.

Remember that these relations hold true only if the number of molecules (n) and the temperature (T) are both constant.Interactive: The Volume-Pressure RelationshipGases can be compressed into smaller volumes. How does compressing a gas affect its pressure? Run the model, then change the volume of the containers and observe the change in pressure. The moving wall converts the effect of molecular collisions into pressure and acts as a pressure gauge. What happens to the pressure when the volume changes?

Example

In an industrial process, a gas confined to a volume of 1 L at a pressure of 20 atm is allowed to flow into a 12-L container by opening the valve that connects the two containers. What is the final pressure of the gas?

Set up the problem by setting up the known and unknown variables. In this case, the initial pressure is 20 atm (P1), the initial volume is 1 L (V1), and the new volume is 1L + 12 L = 13 L (V2), since the two containers are connected. The new pressure (P2) remains unknown.

P1V1 = P2V2

(20 atm)(1 L) = (P2)(13 L).

20 atom = (13) P2.

P2 = 1.54 atm.

The final pressure of the gas is 1.54 atm.

BoyleAn introduction to the relationship between pressure and volume, and an explanation of how to solve gas problems with Boyle’s Law.

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