BOYLE-MARIOTTE'S LAW: HISTORY, EXPRESSION, EXAMPLES - CHEMISTRY - 2024

The Boyle-Mariotte law is one that expresses the relationship between the pressure exerted by or on a gas, and the volume it occupies; keeping both the temperature of the gas constant, as well as its quantity (number of moles).

This law, together with that of Charles, Gay-Lussac, Charles and Avogadro, describes the behavior of an ideal gas; specifically, in a closed container subjected to volume changes exerted by a mechanical force.

Increase in pressure by reducing the volume of the container. Source: Gabriel Bolívar

The image above briefly summarizes the Boyle-Mariotte law.

The purple dots represent gas molecules or atoms, which collide with the inner walls of the container (left). As the space or volume available in the container occupied by this gas decreases, collisions increase, which translates into an increase in pressure (right).

This shows that the pressure P and volume V of the gas are inversely proportional if the container is hermetically closed; otherwise, a higher pressure would equal a greater expansion of the container.

If a graph V against P were made, with the data of V and P on the Y and X axes, respectively, an asymptotic curve would be observed. The smaller V, the greater the increase in P; that is, the curve will extend towards high values ​​of P on the X axis.

Of course, the temperature remains constant; but, if the same experiment were carried out at different temperatures, the relative positions of these V vs P curves would change on the Cartesian axis. The change would be even more apparent if plotted on a three-dimensional axis, with T constant on the Z axis.

History of Boyle's Law

Background

Since the scientist Galileo Galilei expressed his belief in the existence of a vacuum (1638), scientists began to study the properties of air and partial voids.

Anglo-Irish chemist Robert Boyle began his study of the properties of air in 1638 upon learning that Otto von Guericke, a German engineer and physicist, had built an air pump.

Mercury experiment

To conduct his studies of air pressure, Boyle used a “J” -shaped glass tube, the construction of which was attributed to Robert Hooke, an assistant to Boyle. The end of the short arm was sealed, while the end of the long arm of the tube was open to place the mercury.

From the beginning, Boyle wanted to study the elasticity of air, qualitatively and quantitatively. By pouring mercury through the open end of the “J” tube, Boyle deduced that the air in the short arm of the tube was contracting under the pressure of the mercury.

Results

The greater the amount of mercury added to the tube, the greater the pressure exerted on the air and the smaller its volume. Boyle obtained a negative exponential type plot of air volume as a function of pressure.

Meanwhile, if the volume of air is plotted against the inverse of pressure, we have a straight line with a positive slope.

In 1662, Boyle published the first physical law that was given in the form of an equation, which indicated the functional dependence of two variables. In this case, the pressure and the volume.

Boyle pointed out that there was an inverse relationship between the pressure exerted on a gas and the volume that gas occupied, this relationship being relatively true for real gases. Most gases behave like ideal gases at moderate temperatures and pressures.

As higher pressures and lower temperatures occurred, the deviations in the behavior of real gases from the ideal became more noticeable.

Edme mariotte

The French physicist Edme Mariotte (1620-1684) independently discovered the same law in 1679. But it had the merit of showing that the volume varies with temperature. That is why it is called Mariotte's Law or Boyle and Mariotte's Law.

Strengthening of the law

Daniel Bernoulli (1737) strengthened Boyle's Law by pointing out that the pressure of a gas is produced by the impacts of the gas particles on the walls of the container that contains it.

In 1845, John Waterston published a scientific article, in which he focused on the main principles of the kinetic theory of gases.

Later, Rudolf Clausius, James Maxwell and Ludqwig Boltzmann consolidated the kinetic theory of gases, which relates the pressure exerted by a gas with the speed of the gas particles in motion.

The smaller the volume of the container that contains a gas, the greater the frequency of the impacts of the particles that form it against the walls of the container; and therefore, the greater the pressure exerted by the gas.

What is this law about?

The experiments carried out by Boyle indicate that there is an inverse relationship between the volume occupied by a gas and the pressure exerted on it. However, the indicated relationship is not completely linear, as indicated by a graph of volume variation as a function of pressure attributed to Boyle.

Boyle's Law indicates that the volume occupied by a gas is inversely proportional to the pressure. It is also indicated that the product of the pressure of a gas and its volume is constant.

Mathematic expression

To arrive at the mathematical expression of the Boyle-Mariotte law, we start from:

V ∝ 1 / P

Where indicates that the volume occupied by a gas is inversely proportional to its pressure. However, there is a constant that dictates how inversely proportional this relationship is.

V = k / P

Where k is the constant of proportionality. Solving for k we have:

VP = k

The product of the pressure of a gas and its volume is constant. So:

V ₁ P ₁ = k and V ₂ P ₂ = k

And from this it can be deduced that:

V ₁ P ₁ = V ₂ P ₂

The latter is the final expression or equation for Boyle's law.

What is it for? What problems does Boyle's law solve?

Steam engines

Steam train. Source: Pixabay.

The Boyle-Mariotte Law is applied in the operation of steam engines. It is an external combustion engine that uses the transformation of the thermal energy of a quantity of water into mechanical energy.

The water is heated in a hermetically sealed boiler, and the steam produced exerts a pressure according to the Boyle-Mariote law that produces a volume expansion of a cylinder by pushing a piston.

The linear movement of the piston is transformed into a rotational movement, through the use of a connecting rod and crank system, which can drive the wheels of a locomotive or the rotor of an electric generator.

Currently, the alternative steam engine is a little used engine, since it has been displaced by the electric motor and the internal combustion engine in transport vehicles.

Sip drinks

The action of sucking a soft drink or juice from a bottle through a plastic tube is related to the Boyle-Mariotte law. When air is sucked out of the tube using the mouth, there is a decrease in pressure within the tube.

This pressure drop facilitates the upward movement of the liquid in the tube, allowing its ingestion. This same principle works in drawing blood through the use of a syringe.

Respiratory system

Respiratory system. Source: Pixabay

The Boyle-Mariotte law is closely related to the functioning of the respiratory system. During the inspiration phase, the diaphragm and other muscles contract; for example, the external intercostals that produce an expansion of the rib cage.

This causes a decrease in intrapleural pressure, causing a lung expansion that produces an increase in lung volume. Therefore, intrapulmonary pressure decreases according to the Boyle-Mariotte law.

As intrapulmonary pressure becomes subatmospheric, atmospheric air flows into the lungs, causing an increase in pressure in the lungs; thus equating its pressure to atmospheric pressure, and concluding the inspiration phase.

Subsequently, the inspiratory muscles relax and the expiratory muscles contract. In addition, there is elastic lung retraction, a phenomenon that produces a decrease in lung volume, with a consequent increase in intrapulmonary pressure, explained by the Boyle-Mariotte law.

As intrapulmonary pressure increases, and becomes greater than atmospheric pressure, air flows from the inside of the lungs to the atmosphere. This occurs until the pressures equalize, which concludes the exhalation phase.

Examples (experiments)

Experiment 1

A small hermetically closed balloon is placed, making a knot in its mouth, inside a syringe, from which the plunger has been withdrawn, of approximately 20 ml. The plunger of the syringe is placed towards the middle of the syringe, the needle is withdrawn and the air inlet is blocked.

Observation

By slowly pulling the plunger of the injector, the balloon is observed to inflate.

Explanation

Two pressures are exerted on the wall of the balloon: a pressure on its inner face, a product of the air contained inside the balloon, and another pressure on the outer face of the balloon, exerted by the air contained in the syringe.

By pulling the plunger of the injector, a half-vacuum is created inside. Therefore, the air pressure on the outer face of the pump wall decreases, making the pressure exerted inside the pump relatively higher.

This net pressure, according to the Boyle-Mariote law, will produce a distention of the wall of the balloon and an increase in the volume of the balloon.

Experiment 2

A plastic bottle is cut approximately in half, ensuring that the cut is as horizontal as possible. A tightly fitting balloon is placed in the mouth of the bottle, at the same time a certain amount of water is placed in a deep plate.

Observation

By placing the bottom of the bottle with the balloon over the water in the dish, the balloon inflates moderately.

Explanation

The water displaces a certain amount of air, increasing the air pressure on the wall of the bottle and the inside of the balloon. This causes, according to the Boyle-Mariotte law, an increase in the volume of the balloon, which is visualized by the inflation of the balloon.

References

1. Wikipedia. (2019). Boyle's law. Recovered from: en.wikipedia.org
2. The Editors of Encyclopaedia Britannica. (July 27, 2018). Boyle's law. Encyclopædia Britannica. Recovered from: britannica.com
3. Helmenstine, Todd. (December 05, 2018). The Formula for Boyle's Law. Recovered from: thoughtco.com
4. Young Indian Films. (May 15, 2018). Boyle's Law: Science Experiment For Kids. Recovered from: yifindia.com
5. Cecilia Bembibre. (May 22, 2011). Hot air balloon. Definition ABC. Recovered from: definicionabc.com
6. Ganong, W, F. (2003). Medical Physiology. (19th Edition). Editorial the Modern Manual.