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The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and ...
,
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The de ...
and
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
of a sample of gas could be obtained which would hold to approximation for all gases.

# Boyle's law

In 1662
Robert Boyle Robert Boyle (; 25 January 1627 – 31 December 1691) was an Anglo-Irish natural philosopher, chemist, physicist, alchemist and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the founders of m ...
studied the relationship between volume and pressure of a gas of fixed amount at constant temperature. He observed that 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 constant temperature, the product of the pressure and volume of a given mass of an
ideal gas 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 ...
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. A statement of Boyle's law is as follows: The concept can be represented with these formulae: *$V \propto \frac$, meaning "Volume is inversely proportional to Pressure", or *$P \propto \frac$, meaning "Pressure is inversely proportional to Volume", or *$P V = k_1$, or $P_1 V_1 = P_2 V_2$ where is the pressure, and is the volume of a gas, and is the constant in this equation (and is not the same as the proportionality constants in the other equations in this article).

# Charles's law

Charles's law, or the law of volumes, was found in 1787 by
Jacques Charles Jacques Alexandre César Charles (November 12, 1746 – April 7, 1823) was a French inventor, scientist, mathematician, and balloonist. Charles wrote almost nothing about mathematics, and most of what has been credited to him was due to mistakin ...
. It states that, for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wo ...
, assuming in a closed system. The statement of Charles's 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). As a mathematical equation, Charles's law is written as either: :$V \propto T\,$, or :$V/T=k_2$, or :$V_1/T_1=V_2/T_2$, where ''"V"'' is the volume of a gas, ''"T"'' is the absolute temperature and ''k''2 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 found by
Joseph Louis Gay-Lussac Joseph Louis Gay-Lussac (, , ; 6 December 1778 – 9 May 1850) was a French chemist and physicist. He is known mostly for his discovery that water is made of two parts hydrogen and one part oxygen (with Alexander von Humboldt), for two laws ...
in 1808. It states that, for a given mass and constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wo ...
. As a mathematical equation, Gay-Lussac's law is written as either: :$P \propto T\,$, or :$P/T=k$, or :$P_1/T_1=P_2/T_2$, :where ''P'' is the pressure, ''T'' is the absolute temperature, and ''k'' is another proportionality constant.

Avogadro's law (hypothesized in 1811) states that at a constant temperature and pressure, the volume occupied by an ideal gas is directly proportional to the number of molecules of the gas present in the container. This gives rise to the molar volume of a gas, which at
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(273.15 K, 1 atm) is about 22.4 L. The relation is given by :$V \propto n\,$, or :$\frac=\frac \,$ :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 (quantity) of gas: :$PV = k_5 T$ This can also be written as: :$\frac = \frac$ With the addition of
Avogadro's law Avogadro's law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) 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 ca ...
, the combined gas law develops into the
ideal gas law 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 st ...
: :$PV = nRT$ :where :*''P'' is pressure :*''V'' is volume :*''n'' is the number of moles :*''R'' is the universal gas constant :*''T'' is temperature (K) :The proportionality constant, now named R, is the
universal gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment pe ...
with a value of 8.3144598 (kPa∙L)/(mol∙K). An equivalent formulation of this law is: :$PV = Nk_\textT$ :where :*''P'' is the pressure :*''V'' is the volume :*''N'' is the number of gas molecules :*''k''B is the
Boltzmann constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...
(1.381×10−23J·K−1 in SI units) :*''T'' is the temperature (K) These equations are exact only for an
ideal gas 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 ...
, which neglects various intermolecular effects (see
real gas Real gases are nonideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behaviour of real gases, the following must be taken into account: *compressibility effects ...
). 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 Graham's law of effusion (also called Graham's law of diffusion) was formulated by Scottish physical chemist Thomas Graham in 1848. Keith J. Laidler and John M. Meiser, ''Physical Chemistry'' (Benjamin/Cummings 1982), pp. 18–19 Graham foun ...
: states that the rate at which gas molecules diffuse is inversely proportional to the square root of the gas density at constant temperature. Combined with Avogadro's law (i.e. since equal volumes have equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight. ; Dalton's law of
partial pressure 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 g ...
s: 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: : :$P_\textrm = P_1 + P_2 + P_3 + \cdots + P_n \equiv \sum_^n P_i ,$ : :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 Amagat's law or the Law of Partial Volumes describes the behaviour and properties of mixtures of ideal (as well as some cases of non-ideal) gases. It is of use in chemistry and thermodynamics. It is named after Emile Amagat. Overview Amagat's ...
of partial volumes: 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: : :$V_\textrm = V_1 + V_2 + V_3 + \cdots + V_n \equiv \sum_^n V_i ,$ : :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 In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. It was formulat ...
: 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 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 g ...
of that gas in equilibrium with that liquid.'' : :$p = k_\, c$ : ;
Real gas law Real may refer to: Currencies * Brazilian real (R\$) * Central American Republic real * Mexican real * Portuguese real * Spanish real * Spanish colonial real Music Albums * ''Real'' (L'Arc-en-Ciel album) (2000) * ''Real'' (Bright album) (2010) ...
: formulated by
Johannes Diderik van der Waals Johannes Diderik van der Waals (; 23 November 1837 – 8 March 1923) was a Dutch theoretical physicist and thermodynamicist famous for his pioneering work on the equation of state for gases and liquids. Van der Waals started his career as a s ...
(1873).

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