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P1V1 = P2V2
The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system

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Boyle's law, also referred to as the Boyle-Mariotte law, or Mariotte's law (especially in France), is an experimental gas law that describes how the pressure of a gas tends to decrease as the volume of the container increases. A modern statement of Boyle's law is:

The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system.

Mathematically, Boyle's law can be stated as:

Pressure is inversely proportional to the volume

or

where P is the pressure of the gas, V is the volume of the gas, and k is a constant.

The equation states that the product of pressure and volume is a constant for a given mass of confined gas and this holds as long as the temperature is constant. For comparing the same substance under two different sets of conditions, the law can be usefully expressed as:

This equation shows that, as volume increases, the pressure of the gas decreases in proportion. Similarly, as volume decreases, the pressure of the gas increases. The law was named after chemist and physicist Robert Boyle, who published the original law in 1662.

This relationship between pressure and volume was first noted by Richard Towneley and Henry Power in the 17th century. Robert Boyle confirmed their discovery through experiments and published the results. According to Robert Gunther and other authorities, it was Boyle's assistant, Robert Hooke, who built the experimental apparatus. Boyle's law is based on experiments with air, which he considered to be a fluid of particles at rest in between small invisible springs. At that time, air was still seen as one of the four elements, but Boyle disagreed. Boyle's interest was probably to understand air as an essential element of life; for example, he published works on the growth of plants without air. Boyle used a closed J-shaped tube and after pouring mercury from one side he forced the air on the other side to contract under the pressure of mercury. After repeating the experiment several times and using different amounts of mercury he found that under controlled conditions, the pressure of a gas is inversely proportional to the volume occupied by it. The French physicist Edme Mariotte (1620-1684) discovered the same law independently of Boyle in 1679, but Boyle had already published it in 1662. Mariotte did, however, discover that air volume changes with temperature. Thus this law is sometimes referred to as Mariotte's law or the Boyle-Mariotte law. Later, in 1687 in the Philosophiæ Naturalis Principia Mathematica, Newton showed mathematically that in an elastic fluid consisting of particles at rest, between which are repulsive forces inversely proportional to their distance, the density would be directly proportional to the pressure, but this mathematical treatise is not the physical explanation for the observed relationship. Instead of a static theory, a kinetic theory is needed, which was provided two centuries later by Maxwell and Boltzmann.

This law was the first physical law to be expressed in the form of an equation describing the dependence of two variable quantities.

The law itself can be stated as follows:

For a fixed mass of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional.

Or Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship. If volume increases, then pressure decreases and vice versa, when the temperature is held constant.

Therefore, when the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved.

Relation with kinetic theory and ideal gases

Boyle's law states that at constant temperature the volume of a given mass of a dry gas is inversely proportional to its pressure.

Most gases behave like ideal gases at moderate pressures and temperatures. The technology of the 17th century could not produce very high pressures or very low temperatures. Hence, the law was not likely to have deviations at the time of publication. As improvements in technology permitted higher pressures and lower temperatures, deviations from the ideal gas behavior became noticeable, and the relationship between pressure and volume can only be accurately described employing real gas theory. The deviation is expressed as the compressibility factor.

Boyle (and Mariotte) derived the law solely by experiment. The law can also be derived theoretically based on the presumed existence of atoms and molecules and assumptions about motion and perfectly elastic collisions (see kinetic theory of gases). These assumptions were met with enormous resistance in the positivist scientific community at the time, however, as they were seen as purely theoretical constructs for which there was not the slightest observational evidence.

Daniel Bernoulli (in 1737-1738) derived Boyle's law by applying Newton's laws of motion at the molecular level. It remained ignored until around 1845, when John Waterston published a paper building the main precepts of kinetic theory; this was rejected by the Royal Society of England. Later works of James Prescott Joule, Rudolf Clausius and in particular Ludwig Boltzmann firmly established the kinetic theory of gases and brought attention to both the theories of Bernoulli and Waterston.

The debate between proponents of energetics and atomism led Boltzmann to write a book in 1898, which endured criticism until his suicide in 1906. Albert Einstein in 1905 showed how kinetic theory applies to the Brownian motion of a fluid-suspended particle, which was confirmed in 1908 by Jean Perrin.

The mathematical equation for Boyle's law is:

where P denotes the pressure of the system, V denotes the volume of the gas, k is a constant value representative of the temperature and volume of the system.

So long as temperature remains constant the same amount of energy given to the system persists throughout its operation and therefore, theoretically, the value of k will remain constant. However, due to the derivation of pressure as perpendicular applied force and the probabilistic likelihood of collisions with other particles through collision theory, the application of force to a surface may not be infinitely constant for such values of V, but will have a limit when differentiating such values over a given time. Forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure P must decrease proportionally. Conversely, reducing the volume of the gas increases the pressure. Boyle's law is used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas.

The initial and final volumes and pressures of the fixed amount of gas, where the initial and final temperatures are the same (heating or cooling will be required to meet this condition), are related by the equation:

Boyle's law, Charles's law, and Gay-Lussac's law form the combined gas law. The three gas laws in combination with Avogadro's law can be generalized by the ideal gas law.

Boyle's law is often used as part of an explanation on how the breathing system works in the human body. This commonly involves explaining how the lung volume may be increased or decreased and thereby cause a relatively lower or higher air pressure within them (in keeping with Boyle's law). This forms a pressure difference between the air inside the lungs and the environmental air pressure, which in turn precipitates either inhalation or exhalation as air moves from high to low pressure.

Related phenomena:

Other gas laws:

Dalton's law - Gas law describing pressure contributions of component gases in a mixture

Charles's law - Relationship between volume and temperature of a gas at constant pressure

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Boyle's law, also referred to as the Boyle-Mariotte law, or Mariotte's law (especially in France), is an experimental gas law that describes how the pressure of a gas tends to decrease as the volume of the container increases.

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North Carolina School of Science and Mathematics

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V1/T1 = V2/T2
When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion.

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Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is:

When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion.

This relationship of direct proportion can be written as:

So this means:

where:

This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as:

The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion.

The law was named after scientist Jacques Charles, who formulated the original law in his unpublished work from the 1780s.

In two of a series of four essays presented between 2 and 30 October 1801, John Dalton demonstrated by experiment that all the gases and vapours that he studied expanded by the same amount between two fixed points of temperature. The French natural philosopher Joseph Louis Gay-Lussac confirmed the discovery in a presentation to the French National Institute on 31 Jan 1802, although he credited the discovery to unpublished work from the 1780s by Jacques Charles. The basic principles had already been described by Guillaume Amontons and Francis Hauksbee a century earlier.

Dalton was the first to demonstrate that the law applied generally to all gases, and to the vapours of volatile liquids if the temperature was well above the boiling point. Gay-Lussac concurred. With measurements only at the two thermometric fixed points of water, Gay-Lussac was unable to show that the equation relating volume to temperature was a linear function. On mathematical grounds alone, Gay-Lussac's paper does not permit the assignment of any law stating the linear relation. Both Dalton's and Gay-Lussac's main conclusions can be expressed mathematically as:

where V ₁₀₀ is the volume occupied by a given sample of gas at 100 °C; V ₀ is the volume occupied by the same sample of gas at 0 °C; and k is a constant which is the same for all gases at constant pressure. This equation does not contain the temperature and so is not what became known as Charles's Law. Gay-Lussac's value for k (), was identical to Dalton's earlier value for vapours and remarkably close to the present-day value of . Gay-Lussac gave credit for this equation to unpublished statements by his fellow Republican citizen J. Charles in 1787. In the absence of a firm record, the gas law relating volume to temperature cannot be attributed to Charles. Dalton's measurements had much more scope regarding temperature than Gay-Lussac, not only measuring the volume at the fixed points of water but also at two intermediate points. Unaware of the inaccuracies of mercury thermometers at the time, which were divided into equal portions between the fixed points, Dalton, after concluding in Essay II that in the case of vapours, "any elastic fluid expands nearly in a uniform manner into 1370 or 1380 parts by 180 degrees (Fahrenheit) of heat", was unable to confirm it for gases.

Charles's law appears to imply that the volume of a gas will descend to zero at a certain temperature (−266.66 °C according to Gay-Lussac's figures) or −273.15 °C. Gay-Lussac was clear in his description that the law was not applicable at low temperatures:

but I may mention that this last conclusion cannot be true except so long as the compressed vapours remain entirely in the elastic state; and this requires that their temperature shall be sufficiently elevated to enable them to resist the pressure which tends to make them assume the liquid state.

At absolute zero temperature, the gas possesses zero energy and hence the molecules restrict motion. Gay-Lussac had no experience of liquid air (first prepared in 1877), although he appears to have believed (as did Dalton) that the "permanent gases" such as air and hydrogen could be liquified. Gay-Lussac had also worked with the vapours of volatile liquids in demonstrating Charles's law, and was aware that the law does not apply just above the boiling point of the liquid:

I may, however, remark that when the temperature of the ether is only a little above its boiling point, its condensation is a little more rapid than that of atmospheric air. This fact is related to a phenomenon which is exhibited by a great many bodies when passing from the liquid to the solid-state, but which is no longer sensible at temperatures a few degrees above that at which the transition occurs.

The first mention of a temperature at which the volume of a gas might descend to zero was by William Thomson (later known as Lord Kelvin) in 1848:

This is what we might anticipate when we reflect that infinite cold must correspond to a finite number of degrees of the air-thermometer below zero; since if we push the strict principle of graduation, stated above, sufficiently far, we should arrive at a point corresponding to the volume of air being reduced to nothing, which would be marked as −273° of the scale (−100/.366, if .366 be the coefficient of expansion); and therefore −273° of the air-thermometer is a point which cannot be reached at any finite temperature, however low.

However, the "absolute zero" on the Kelvin temperature scale was originally defined in terms of the second law of thermodynamics, which Thomson himself described in 1852. Thomson did not assume that this was equal to the "zero-volume point" of Charles's law, merely that Charles's law provided the minimum temperature which could be attained. The two can be shown to be equivalent by Ludwig Boltzmann's statistical view of entropy (1870).

However, Charles also stated:

The volume of a fixed mass of dry gas increases or decreases by 1⁄273 times the volume at 0 °C for every 1 °C rise or fall in temperature. Thus:

where VVT is the volume of gas at temperature T, ₀ is the volume at 0 °C.

The kinetic theory of gases relates the macroscopic properties of gases, such as pressure and volume, to the microscopic properties of the molecules which make up the gas, particularly the mass and speed of the molecules. To derive Charles's law from kinetic theory, it is necessary to have a microscopic definition of temperature: this can be conveniently taken as the temperature being proportional to the average kinetic energy of the gas molecules, E k:

Under this definition, the demonstration of Charles's law is almost trivial. The kinetic theory equivalent of the ideal gas law relates PV to the average kinetic energy:

Boyle's law - Relationship between pressure and volume in a gas at constant temperature

Combined gas law - Combination of Charles', Boyle's and Gay-Lussac's gas laws

Gay-Lussac's law - Relationship between pressure and temperature of a gas at constant volume.

Avogadro's law - Relationship between volume and number of moles of a gas at constant temperature and pressure.

Ideal gas law - Equation of the state of a hypothetical ideal gas

Hand boiler

Thermal expansion - Tendency of matter to change volume in response to a change in temperature

Krönig, A. (1856), "Grundzüge einer Theorie der Gase", Annalen der Physik, 99 (10): 315-22, Bibcode:1856AnP...175..315K, doi:10.1002/andp.18561751008. Facsimile at the Bibliothèque nationale de France (pp. 315-22).

Clausius, R. (1857), "Ueber die Art der Bewegung, welche wir Wärme nennen", Annalen der Physik und Chemie, 176 (3): 353-79, Bibcode:1857AnP...176..353C, doi:10.1002/andp.18571760302. Facsimile at the Bibliothèque nationale de France (pp. 353-79).

Joseph Louis Gay-Lussac - Liste de ses communications, archived from the original on October 23, 2005 . (in French)

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Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is: When the pressure on a sample of a dry gas is held constant, the Kelvin temperature and the volume will be in direct proportion.

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Charles's law on balloons  | Liquid nitrogen

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P1/T1 = P2/T2
The pressure of a gas of fixed mass is directly proportional to the gas's absolute temperature, PROVIDED THE VOLUME REMAINS CONSTANT

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Chemistry: Gay-Lussac's Law (Gas Laws) with 2 examples | Homework Tutor on Make a GIF

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Browse MakeaGif's great section of animated GIFs, or make your very own. Upload, customize and create the best GIFs with our free GIF animator! See it. GIF it. Share it.

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The Sci Guys: Science at Home - SE2 - EP11: Gay-Lussac's Law of Ideal Gases

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Find high-quality images, photos, and animated GIFS with Bing Images

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Gay-Lussac and Jean-Baptiste Biot made a hydrogen balloon ascent to a height of 7,016 metres (23,018 ft) in an early investigation of the Earth's atmosphere. He wanted to collect samples of the air at different heights to record differences in temperature and moisture.

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Ideal gas equation: PV = nRT | Chemistry | Khan Academy

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7.3.1: Practice Problems- Applications of the Ideal Gas Law

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PROBLEM \(\PageIndex{1}\) What is the density of laughing gas, dinitrogen monoxide, N 2 O, at a temperature of 325 K and a pressure of 113.0 kPa? PROBLEM \(\PageIndex{2}\) Calculate the density of Freon 12, CF 2Cl 2, at 30.0 °C and 0.954 atm.

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The Ideal and Combined Gas
Use your knowledge of the ideal and combined gas laws to solve the following
problems.
1)
If four moles of a gas at a pressure of 5.4 atmospheres have a volume of
120 liters, what is the temperature?
1973 K
2)
If I initially have a gas with a pressure of 84 kPa and a temperature of 35 0
C and I heat it an additional 230 degrees, what will the new pressure be?
Assume the volume of the container is constant.
146.7 kPa
3)
My car has an internal volume of 2600 liters. If the sun heats my car from
a temperature of 200 C to a temperature of 550 C, what will the pressure
inside my car be? Assume the pressure was initially 760 mm Hg.
850.8 or 851 mm Hg
4)
How many moles of gas are in my car in problem #3?
108 mol
5)
A toy balloon filled with air has an internal pressure of 1.25 atm and a
volume of 2.50 L. If I take the balloon to the bottom of the ocean where
the pressure is 95 atmospheres, what will the new volume of the balloon
be? How many moles of gas does the balloon hold? (Assume T = 285 K)
.0329 L
.13 mol
For chemistry help, visit www.chemfiesta.com
&copy; 2000 Cavalcade Publishing - All Rights Reserved
MIXED GAS LAWS WORKSHEET (modified by Mr. Jasmann)
Created by Tara L. Moore at www.learning.mgccc.cc.ms.us/pk/sciencedocs/gaslawwksheet.htm
Directions: Answer each question below. Then write the name of the gas law used to solve each question
in the left margin next to each question.
1.
A gas occupies 3.5L at 2.5 mm Hg pressure. What is the volume at 10 mm Hg at the same temperature?
.875 L
2.
A constant volume of oxygen is heated from 100C to 185C. The initial pressure is 4.1 atm. What is the final
pressure?
5.03 atm
3.
A sample of 25L of NH3 gas at 10C is heated at constant pressure until it fills a volume of 50L. What is the
new temperature in C?
293 C
4.
A certain quantity of argon gas is under 16 torr pressure at 253K in a 12L vessel. How many moles of argon
are present?
.012 mol
5.
An unknown gas weighs 34g and occupies 6.7L at 2 atm and 245K. What is its molecular weight?
51.1 g/mol
6.
An ideal gas occupies 400ml at 270 mm Hg and 65C. If the pressure is changed to 1.4 atm and the
temperature is increased to 100C, what is the new volume?
110.4 mL or .110 L
7.
What is the volume of 23g of neon gas at 1C and a pressure of 2 atm?
12.8 L
8.
If 11 moles of HCl gas occupies 15L at 300C, what is the pressure in torr?
26,220 torr
9.
The pressure is 6.5 atm, 2.3 mole of Br2 gas occupies 9.3 L . What is the temperature in C?
47 C
For chemistry help, visit www.chemfiesta.com
&copy; 2000 Cavalcade Publishing - All Rights Reserved
10. A 600mL balloon is filled with helium at 700mm Hg barometric pressure. The balloon is released and climbs
to an altitude where the barometric pressure is 400mm Hg. What will the volume of the balloon be if, during
the ascent, the temperature drops from 24 to 5C?
983 mL or .983 L
11. An unknown gas has a volume of 200L at 5 atm and -140C. What is its volume at STP?
2052.6 or 2053 L
12. In an autoclave, a constant amount of steam is generated at a constant volume. Under 1.00 atm pressure the
steam temperature is 100C. What pressure setting should be used to obtain a 165C steam temperature for
the sterilization of surgical instruments?
21.22 kPa
13. Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure
of oxygen (PO2) at 101.3kPa of total pressure if it's known that the partial pressures of nitrogen, carbon
dioxide, and other gases are 79.1kPa, 0.040kPa, and 0.94kPa, respectively? What is the name of the gas law
used for this?
21.22 kPa
14. Explain why the rates of diffusion of nitrogen gas and carbon monoxide gas are almost identical at the same
temperature?
Since their molar masses are the same, their rates of diffusion
should be the same according the Graham's law
15. What distinguishes effusion from diffusion? How are these processes similar?
Diffusion is gas moving spontaneously from areas of high concentration to low
concentration
Effusion is diffusion of a gas escaping from a tiny opening
16. Which of the gases effuses faster at the same temperature: molecular chlorine, nitrogen dioxide, ammonia or
molecular nitrogen gas? And why?
Fastest
Slowest
NH3 &gt; N2 &gt; NO2 &gt; Cl2
since lower masses effuse faster
17. Explain what each of the following changes would do to the pressure in a closed container (increase or
decrease pressure). A) Part of the gas is removed, B) The container size (volume) is decreased, and
C)Temperature is increased.
A. gas removed  decrease in pressure
B. Volume decrease  increase in pressure
C. Temperature increase  increase in pressure
18. Determine the total pressure of a gas mixture that contains oxygen, nitrogen and helium in the following
partial pressures of 2.0atm for oxygen, 4.7atm for nitrogen and 253.25kPa for helium.
9.2 atm or 931.96 kPa
For chemistry help, visit www.chemfiesta.com
&copy; 2000 Cavalcade Publishing - All Rights Reserved

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