Boyle's Law

Boyle's Law

Boyle's Law, published in 1662, states that, at constant temperature, the product of the pressure and volume of a given mass of an ideal gas in a closed system is always constant. It can be verified experimentally using a pressure gauge and a variable volume container. It can also be derived from the kinetic theory of gases: if a container, with a fixed number of molecules inside, is reduced in volume, more molecules will strike a given area of the sides of the container per unit time, causing a greater pressure.

where P is the pressure, and V is the volume of a gas, and k₁ is the constant in this equation (and is not the same as the proportionality constants in the other equations below). The statement of Boyle 's law is as follows:

The volume of a given mass of a gas is inversely related to the pressure exerted on it at a given temperature and given number of moles.

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

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).

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.