In this article, we will learn what is Boyle’s law of Gases, definition, formula, graph, equation, examples, etc.

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## What is the Boyle’s Law of Gases?

### Charle’s Law of Gases Basics

The state of matter known as the gaseous state is one in which the substance has no defined shape or volume. It adopts the container’s form and size. The pressure, volume, temperature, and mass of gas are the essential physical attributes of the gas.

Kinetic theory can explain these by considering their chemical composition and mobility. These factors are related to one another, and the values of these qualities determine the condition of the gas, according to careful scientific observation.

- Gas laws are formed by the correlations between pressure, temperature, and volume of a gas.
- The physical properties of gases are fairly straightforward and consistent across the board.
- The fact that all gases generally obey some simple or common gas formula or connection demonstrates these features of diverse gases. These are referred to as gas laws.
- For learning chemistry or physics, Boyle’s law, Charles law, Avogadro law, Gay Lussac law, ideal gas law, and Graham’s law provide the relationship between mass, pressure, volume, temperature, and density of ideal gas molecules.

So without any further ado, for this blog only let’s get into a greater aspect of what Boyle’s Law actually is!

### What is Boyle’s Law?

Robert Boyle, a chemist, and a physicist, was the first to publish the law in 1662. Around the same time in 1679, French Chemist Edme Mariotte found the law, although Boyle was the first to publish it.

- Boyle’s law is regarded as the first scientific law to be represented mathematically as a relationship between two variables.
- Mariotte did establish, however, that the law only applies while the gas’s temperature remains constant.
- Boyle’s Law (also known as the Boyle-Mariotte Law) asserts that if the temperature in a closed system remains constant, the absolute pressure and volume of a given amount of confined gas are inversely proportional.
- The law can be deduced from the kinetic theory of gases under the assumption of an ideal (perfect) gas. Also, this law is derived using a few assumptions about the nature of the gas. A perfect gas is said to be made up of point particles with no intermolecular interactions between them.
- Collisions between ideal gas particles are also considered to be fully elastic, with no energy lost. Gas molecules, in fact, have a non-zero size, exert intermolecular forces on one another, and do not collide perfectly elastically.
- Most gases behave like ideal gases at moderate temperatures and pressures, therefore these differences are usually too tiny to be important for experimentation.
- At sufficiently low pressures, real gases satisfy Boyle’s law, although its product pv tends to decrease slightly at higher pressures when the gas begins to deviate from ideal behavior.

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## Boyle’s Law Statement & Equation

### Boyle’s Law Statement

At constant temperature, Boyle’s law states that the volume of an ideal gas is inversely proportional to its absolute pressure, when mass & temperature is constant.

Boyle’s Law Statement

For a fixed mass of gas at a constant temperature, the volume is inversely proportional to the pressure

### Boyle’s Law Equation

Based on Boyle’s law statement, we can write

**p ∝ 1/V or p ∝ 1/V****p = k1**.**1/V**

Where k1 is the proportionality constant in the above equation. The volume of gas, the temperature of the gas, and the units in which p and V are stated all influence the value of constant k1.

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## Boyle’s Law Equation Derivation & Graph

So, we have got Boyle’s equation from Boyle’s Law as **pV = k1**

At various temperatures, a graph of pressure, p, vs. volume, V, of a gas is shown.

Now, let’s see a graph showing gas pressure, p vs. 1/V

We can deduce from the previous graphs and equations that the product of the pressure and volume of a specific amount of gas is constant at a constant temperature.

So, if a fixed amount of gas at constant temperature (T) occupying volume (V_{1}) at pressure (p_{1}) expands, resulting in volume (V_{2}) and pressure (p_{2}), according to Boyle’s law:

**p _{1} V_{1 }= p_{2} V_{2} = constant**

Where,

- P
_{1}refers to the gas’s initial pressure. - V
_{1}is the gas’s initial volume of occupancy. - P
_{2}refers to the gas’s final pressure. - V
_{2}is the gas’s final volume of occupancy.

**p _{1}V_{1} = k (initial pressure x initial volume)**

**p _{2}V_{2} = k (final pressure x final volume)**

When the volume of a gas’s container is reduced, this equation can be used to anticipate the rise in pressure exerted by the gas on its container’s walls (and its quantity and absolute temperature remain unchanged).

**Some points are as follows:**

- As stated by Boyle’s Law, pressure and volume have an opposite relationship.
- Only if both the number of molecules (n) and the temperature (T) are constant can Boyle’s Law be applied.
- Boyle’s Law is used to forecast the outcome of changing the volume and pressure of a constant quantity of gas only, and only to the starting state.
- P
_{1}V_{1}= P_{2}V_{2}is the Boyle’s Law relationship, where P_{1}and V_{1}are the gas’s initial pressure and volume values, and P_{2}and V_{2}are the gas’s pressure and volume after the change.

## Density & Pressure Relation with Boyles Law

Boyle’s experiments show that gases are very compressible when carried out in a quantitative manner. This is due to the fact that as a gas’s mass is reduced, the same number of molecules occupy a smaller space.

As a result, we may use this Boyle’s law to derive a relationship between density and pressure.

We know that Density = mass per unit volume,** hence d = m/V.**

We get** d = (m/k1) p = k′ p **by plugging the value into the equation.

The above equation shows that pressure is directly proportional to the density of a fixed mass of gas at a constant temperature.

## Solved Exercises on Boyle’s Law

### Boyle’s Law Calculation#1

**A fixed amount of gas takes up 1L of volume and exerts a pressure of 400 kPa on the container’s walls. What would be the pressure exerted by the gas if it were totally moved into a fresh 3 liter container? (assumes that the gas temperature and quantity remain constant)**

**Solution:**

Given,

- V
_{1}(initial volume) = 1L - P
_{1}= 400 kPa initial pressure - V
_{2}(final volume) = 3L

According to Boyle’s law,

And,

** **P_{2} = 133.333 kPa

As a result, the gas exerts a pressure of 133.33 kPa on the 3-liter container’s walls.

### Boyle’s Law Calculation#2

**At 35°C and 1.2 bar pressure, a 120 mL vessel contains a specific amount of gas. At 35°C, the gas is transferred to another 180 mL vessel. What would the pressure be?**

**Solution:**

We’ll apply Boyle’s Law equation here as well.

Given,

- V
_{1}= 120 mL, - P
_{1}= 1.2 bar and - V
_{2}= 180 mL, - P
_{2}=?

Because the temperature remains constant,

- P
_{1}V_{1}= P_{2}V_{2}. - 1.2 x 120 = P
_{2}x 180 - P
_{2}=>0.8 bar

## Boyle’s Law Expectations

- When mass and temperature are held constant, a diagram depicting the relationship between volume and pressure is shown.
- The trapped air behaved like a spring, resisting compression with a force. This effect was dubbed “the spring of the air” by Boyle, who published his findings in a pamphlet of the same name.
- The pressure is derived from the difference in heights of the two mercury columns (76 cm = 1 atm), and the length of the air column and the tubing diameter are used to compute the volume of air.
- Simply considering the properties of gas should reveal the link. Gases are made up of billions of small individual particles that zip around in space at random. As these particles travel around, they collide with the container’s walls, creating a force, or pressure. Now visualize slowly shrinking the container while maintaining the same amount of gas and temperature.
- Because temperature is a measure of kinetic energy (movement) of particles, maintaining a constant temperature ensures that the particles maintain the same speed and momentum. The molecules have less space to move about when the container shrinks.
- Because the gaseous particles have the same speed and momentum, they exert the same amount of force, but it is distributed across a smaller area. As a result, the gas exerts more force per unit area, increasing pressure.
- If the
**temperature changes**during this process, and if the particles’ kinetic energy (movement) changes as well, then Boyle’s law is broken.

## Relation of Boyle’s Law and the Ideal Gas Law

Boyle’s law can be coupled with Charles’ law, Gay Loussac’s law, and Avogadro’s law to form a single formulation known as the **Ideal Gas Law**.

- The ideal gas law is a state equation that describes how gas behaves under a variety of settings.
- The ideal gas law asserts, in a nutshell, that a gas’s pressure and volume are proportionate to its temperature and amount. Mathematically, the ideal gas law is as follows:

**PV = nRT**

Where,

- n= Amount of gas (In moles)
- T= Temperature (K)
- R= Universal Gas Constant

The ideal gas law helps us to forecast how a gas’ behavior will vary when one of its parameters is changed.

## Examples of Boyle’s Law

#### Breathing as Boyle’s Law Examples

The law of Boyle can be used to explain how individuals inhale and exhale air. When the diaphragm extends and contracts, the volume of the lungs expands and contracts, causing the air pressure inside them to change. Inhalation or exhalation is caused by a pressure differential between the interior of the lungs and the outside air.

#### Tire Inflation as Boyle’s Law Examples

We can witness a real-life implementation of Boyle’s Law when we fill your bike tires with air. When we inflate a tire, the gas molecules within compress and pack closer together. As a result, the gas pressure rises and begins to push against the tire’s walls. We may feel the tire getting tighter and more pressured.

#### Soda Bottle as Boyle’s Law Examples

A Coke bottle is another example. The entire bottle is frequently compressed with gas to get carbon dioxide gas into the liquid. The gas is contained in a tiny space and pushes against the bottle’s walls when the bottle is closed, making it difficult to squeeze. However, when the cap is removed, the accessible volume expands, and some of the gas escapes. Its pressure falls at the same moment.

#### A Syringe in Action as Boyle’s Law Examples

A syringe is a piece of medical equipment used to inject or remove fluids. It is made up of a cylinder that holds the fluid and a plunger that controls the pressure. The volume of the fluid decreases as the plunger is pushed down, increasing the pressure. Similarly, when you pull up on the plunger, the volume increases while the pressure decreases. As a result, Boyle’s law governs the operation of a syringe.

#### Balloon Inflation as Boyle’s Law Examples

When you squeeze an inflated balloon, the volume occupied by the air inside the balloon shrinks. As a result of Boyle’s law, this is accompanied by an increase in the pressure imposed by the air on the balloon. As the balloon is squeezed tighter, the pressure builds up until it pops.

#### Scuba Diving as Boyle’s Law Examples

The decrease in pressure caused by a scuba diver rapidly ascending from a deep zone to the surface of the sea can cause the gas molecules in his or her body to expand. These gas bubbles have the potential to harm the diver’s organs and perhaps cause death. Another example of Boyle’s law is the expansion of the gas generated by the scuba diver’s ascent. Another similar example can be found in deep-sea fish that die after reaching the water’s surface (due to the expansion of dissolved gases in their blood).

#### Spray painting as Boyle’s Law Examples

Boyle’s law governs how to spray paint functions. The paint molecules exert a tremendous amount of pressure on the body of the can in which it is enclosed. The volume inside the can is lowered when the top of the can is squeezed, and the paint is thrown out with enormous force. Boyle’s law can be seen in action since pressure has an inverse relationship with volume.

## Applications of Boyle’s Law

- Boyle’s law only applies to perfect gases. Only at high temperatures and low pressures does the law hold true.
- At high pressures, the law breaks down. At high pressures, the merchandise of pressure and volume does not remain constant but exhibits a little increase. This surge is due to a growth in volume, which is generated by repulsive forces between molecules.
- This law holds smart for a perfect gas sample with a relentless mass (closed system solely or no-mass interaction system)

## Conclusion

Despite the fact that Boyle’s law describes the behavior of an ideal gas, it may be applied to real gases at regular temperatures and pressures. Gases begin to depart from any version of the ideal gas law as temperature and pressure rise.

Based on the above equations, theories and formulas, we can be able to find different aspects of various gases and their surrounding area with the help of this Law.

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