Gas laws

Last updated October 17, 2024

The laws describing the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions are called gas laws. The basic gas laws were discovered by the end of the 18th century when scientists found out that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases. The combination of several empirical gas laws led to the development of the ideal gas law.

History

In 1643, the Italian physicist and mathematician, Evangelista Torricelli, who for a few months had acted as Galileo Galileo's secretary, conducted a celebrated experiment in Florence.^[1] He demonstrated that a column of mercury in an inverted tube can be supported by the pressure of air outside of the tube, with the creation of a small section of vacuum above the mercury.^[2] This experiment essentially paved the way towards the invention of the barometer, as well as drawing the attention of Robert Boyle, then a "skeptical" scientist working in England. Boyle was inspired by Torricelli's experiment to investigate how the elasticity of air responds to varying pressure, and he did this through a series of experiments with a setup reminiscent of that used by Torricelli.^[3] Boyle published his results in 1662.

Later on, in 1676, the French physicist Edme Mariotte, independently arrived at the same conclusions of Boyle, while also noting some dependency of air volume on temperature.^[4] However it took another century and a half for the development of thermometry and recognition of the absolute zero temperature scale, which eventually allowed the discovery of temperature-dependent gas laws.

Boyle's law

In 1662, Robert Boyle systematically studied the relationship between the volume and pressure of a fixed amount of gas at a constant temperature. He observed that the volume of a given mass of a gas is inversely proportional to its pressure at a constant temperature. Boyle's law, published in 1662, states that, at a 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.

Statement

Boyle's law states that:

The volume of a given mass of a gas is inversely related to its pressure when its temperature is kept constant.

The concept can be represented with these formulae:

$V\propto {\frac {1}{P}}$ , meaning "Volume is inversely proportional to Pressure", or
$P\propto {\frac {1}{V}}$ , meaning "Pressure is inversely proportional to Volume", or
$PV=k_{1}$ , or

$P_{1}V_{1}=P_{2}V_{2}$ where $P$ is the pressure, $V$ is the volume of a gas, and $k 1$ is the constant in this equation (and is not the same as the proportionality constants in the other equations).

Charles' law

Charles' law, or the law of volumes, was founded in 1787 by Jacques Charles. It states that, for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature, assuming in a closed system. The statement of Charles' law is as follows: the volume (V) of a given mass of a gas, at constant pressure (P), is directly proportional to its temperature (T).

Statement

Charles' law states that:

The volume of a given fixed mass of a dry gas is directly proportional to its absolute temperature at a constant pressure.

Therefore,

$V\propto T\,$ , or
${V \over T}=k_{2}$ , or

{V_{1} \over T_{1}}={V_{2} \over T_{2}}

,

where "V" is the volume of a gas, "T" is the absolute temperature and k₂ is a proportionality constant (which is not the same as the proportionality constants in the other equations in this article).

Gay-Lussac's law

Gay-Lussac's law, Amontons' law or the pressure law was founded by Joseph Louis Gay-Lussac in 1808.

Statement

Gay-Lussac's law states that:

The pressure exerted by a given mass and constant volume of an ideal gas on the sides of its container is directly proportional to its absolute temperature.

Therefore,

$P\propto T\,$ , or
${P \over T}=k$ , or

${P_{1} \over T_{1}}={P_{2} \over T_{2}}$ ,

where P is the pressure, T is the absolute temperature, and k is another proportionality constant.

Avogadro's law

Avogadro's law, Avogadro's hypothesis, Avogadro's principle or Avogadro-Ampère's hypothesis is an experimental gas law which was hypothesized by Amedeo Avogadro in 1811. It related the volume of a gas to the amount of substance of gas present.^[5]

Statement

Avogadro's law states that:

The volume occupied by an ideal gas at a constant temperature is directly proportional to the number of molecules of the gas present in the container.

This statement gives rise to the molar volume of a gas, which at STP (273.15 K, 1 atm) is about 22.4 L. The relation is given by:

V\propto n\,

, or

{\frac {V_{1}}{n_{1}}}={\frac {V_{2}}{n_{2}}}\,

where n is equal to the number of molecules of gas (or the number of moles of gas).

Combined and ideal gas laws

The combined gas law or general gas equation is obtained by combining Boyle's law, Charles's law, and Gay-Lussac's law. It shows the relationship between the pressure, volume, and temperature for a fixed mass of gas:

PV=k_{5}T

This can also be written as:

{\frac {P_{1}V_{1}}{T_{1}}}={\frac {P_{2}V_{2}}{T_{2}}}

With the addition of Avogadro's law, the combined gas law develops into the ideal gas law:

PV=nRT

where P is the pressure, V is volume, n is the number of moles, R is the universal gas constant and T is the absolute temperature.

The proportionality constant, now named R, is the universal gas constant with a value of 8.3144598 (kPa∙L)/(mol∙K).

An equivalent formulation of this law is:

PV=Nk_{\text{B}}T

where P is the pressure, V is the volume, N is the number of gas molecules, k_B is the Boltzmann constant (1.381×10⁻²³J·K⁻¹ in SI units) and T is the absolute temperature.

These equations are exact only for an ideal gas, which neglects various intermolecular effects (see real gas). However, the ideal gas law is a good approximation for most gases under moderate pressure and temperature.

This law has the following important consequences:

If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas.
If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present.
If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume.
If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature.

Other gas laws

Graham's law: This law states that the rate at which gas molecules diffuse is inversely proportional to the square root of the gas density at a constant temperature. Combined with Avogadro's law (i.e. since equal volumes have an equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight.
Dalton's law of partial pressures: This law states that the pressure of a mixture of gases simply is the sum of the partial pressures of the individual components. Dalton's law is as follows:; $P_{\textrm {total}}=P_{1}+P_{2}+P_{3}+\cdots +P_{n}\equiv \sum _{i=1}^{n}P_{i},$; and all component gases and the mixture are at the same temperature and volume; where P_total is the total pressure of the gas mixture; P_i is the partial pressure or pressure of the component gas at the given volume and temperature.
Amagat's law of partial volumes: This law states that the volume of a mixture of gases (or the volume of the container) simply is the sum of the partial volumes of the individual components. Amagat's law is as follows:; $V_{\textrm {total}}=V_{1}+V_{2}+V_{3}+\cdots +V_{n}\equiv \sum _{i=1}^{n}V_{i},$; and all component gases and the mixture are at the same temperature and pressure; where V_total is the total volume of the gas mixture or the volume of the container,; V_i is the partial volume, or volume of the component gas at the given pressure and temperature.
Henry's law: This states that at constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid. The equation is as follows:; $p=k_{\rm {H}}\,c$
Real gas law: This was formulated by Johannes Diderik van der Waals in 1873.

Related Research Articles

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure.

In thermodynamics, the specific heat capacity of a substance is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. It is also referred to as massic heat capacity or as the specific heat. More formally it is the heat capacity of a sample of the substance divided by the mass of the sample. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg⁻¹⋅K⁻¹. For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg⁻¹⋅K⁻¹.

In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas as if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture.

<span class="mw-page-title-main">Boltzmann constant</span> Physical constant relating particle kinetic energy with temperature

The Boltzmann constant is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the gas constant, in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy and heat capacity. It is named after the Austrian scientist Ludwig Boltzmann.

<span class="mw-page-title-main">Gas constant</span> Physical constant equivalent to the Boltzmann constant, but in different units

The molar gas constant is denoted by the symbol $R$ or $R$ . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, rather than energy per temperature increment per particle. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.

The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of the empirical Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. The ideal gas law is often written in an empirical form:

Boyle's law, also referred to as the Boyle–Mariotte law or Mariotte's law, is an empirical gas law that describes the relationship between pressure and volume of a confined gas. Boyle's law has been stated as:

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.

An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions.

Dalton's law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. This empirical law was observed by John Dalton in 1801 and published in 1802. Dalton's law is related to the ideal gas laws.

Graham's law of effusion was formulated by Scottish physical chemist Thomas Graham in 1848. Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the molar mass of its particles. This formula is stated as:

Charles's law 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.

<span class="mw-page-title-main">Effusion</span> Process of a gas escaping through a small hole

In physics and chemistry, effusion is the process in which a gas escapes from a container through a hole of diameter considerably smaller than the mean free path of the molecules. Such a hole is often described as a pinhole and the escape of the gas is due to the pressure difference between the container and the exterior.

Avogadro's law or Avogadro-Ampère's hypothesis is an experimental gas law relating the volume of a gas to the amount of substance of gas present. The law is a specific case of the ideal gas law. A modern statement is:

Avogadro's law states that "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules."
For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

In chemistry, colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent particles in a solution, and not on the nature of the chemical species present. The number ratio can be related to the various units for concentration of a solution such as molarity, molality, normality (chemistry), etc. The assumption that solution properties are independent of nature of solute particles is exact only for ideal solutions, which are solutions that exhibit thermodynamic properties analogous to those of an ideal gas, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be reasonably approximated by the assumption that the solution is ideal.

Gay-Lussac's law usually refers to Joseph-Louis Gay-Lussac's law of combining volumes of gases, discovered in 1808 and published in 1809. However, it sometimes refers to the proportionality of the volume of a gas to its absolute temperature at constant pressure. The latter law was published by Gay-Lussac in 1802, but in the article in which he described his work, he cited earlier unpublished work from the 1780s by Jacques Charles. Consequently, the volume-temperature proportionality is usually known as Charles's Law.

In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. It is simply defined as the ratio of the molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure. It is a useful thermodynamic property for modifying the ideal gas law to account for the real gas behaviour. In general, deviation from ideal behaviour becomes more significant the closer a gas is to a phase change, the lower the temperature or the larger the pressure. Compressibility factor values are usually obtained by calculation from equations of state (EOS), such as the virial equation which take compound-specific empirical constants as input. For a gas that is a mixture of two or more pure gases, the gas composition must be known before compressibility can be calculated.
Alternatively, the compressibility factor for specific gases can be read from generalized compressibility charts that plot $as a function of pressure at constant temperature.$

An amagat is a practical unit of volumetric number density. Although it can be applied to any substance at any conditions, it is defined as the number of ideal gas molecules per unit volume at 1 atm (101.325 kPa) and 0 °C (273.15 K). It is named after Émile Amagat, who also has Amagat's law named after him.

<span class="mw-page-title-main">Gas thermometer</span>

A gas thermometer is a thermometer that measures temperature by the variation in volume or pressure of a gas.

<span class="mw-page-title-main">Gas</span> State of matter

Gas is one of the four fundamental states of matter. The others are solid, liquid, and plasma. A pure gas may be made up of individual atoms, elemental molecules made from one type of atom, or compound molecules made from a variety of atoms. A gas mixture, such as air, contains a variety of pure gases. What distinguishes gases from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer.

In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law. The physical region covered by a system may or may not coincide with a control volume used to analyze the system.

References

↑ Lagouge, Michel. "History of Gas Laws" (PDF).
↑ "Torricelli's barometric experiment". brunelleschi.imss.fi.it. 2008-01-23. Retrieved 2024-03-21.
↑ Purdue University. "Gas Laws".
↑ "Edme Mariotte | Experimental Physics, Pressure Law & Hydrostatics | Britannica". www.britannica.com. Retrieved 2024-03-21.
↑ "Avogadro's law". Encyclopædia Britannica . Retrieved 3 February 2016.

Castka, Joseph F.; Metcalfe, H. Clark; Davis, Raymond E.; Williams, John E. (2002). Modern Chemistry. Holt, Rinehart and Winston. ISBN 0-03-056537-5.
Guch, Ian (2003). The Complete Idiot's Guide to Chemistry. Alpha, Penguin Group Inc. ISBN 1-59257-101-8.
Zumdahl, Steven S (1998). Chemical Principles. Houghton Mifflin Company. ISBN 0-395-83995-5.

External links

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[1] Lagouge, Michel. "History of Gas Laws" (PDF).

[2] "Torricelli's barometric experiment". brunelleschi.imss.fi.it. 2008-01-23. Retrieved 2024-03-21.

[3] Purdue University. "Gas Laws".

[4] "Edme Mariotte | Experimental Physics, Pressure Law & Hydrostatics | Britannica". www.britannica.com. Retrieved 2024-03-21.

[Britannica-5] "Avogadro's law". Encyclopædia Britannica . Retrieved 3 February 2016.

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Gas laws

Contents

History

Boyle's law

Statement

Charles' law

Statement

Gay-Lussac's law

Statement

Avogadro's law

Statement

Combined and ideal gas laws

Other gas laws

Related Research Articles

References

External links