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The laws describing the behaviour of gases under fixed pressure, volume 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. These macroscopic gas laws were found to be consistent with atomic and kinetic theory.
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In 1643, the Italian physicist and mathematician, Evangelista Torricelli, who for a few months had acted as 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.
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.
Boyle's law states that:
The concept can be represented with these formulae:
where P is the pressure, 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).
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).
Charles' law states that:
Therefore,
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, Amontons' law or the pressure law was founded by Joseph Louis Gay-Lussac in 1808.
Gay-Lussac's law states that:
Therefore,
,
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]
Avogadro's law states that:
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:
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:
This can also be written as:
With the addition of Avogadro's law, the combined gas law develops into the ideal gas law:
An equivalent formulation of this law is:
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:
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.
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
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.
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:
The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. It treats a gas as composed of numerous particles, too small to see with a microscope, which are constantly in random motion. Their collisions with each other and with the walls of their container are used to explain physical properties of the gas—for example the relationship between its temperature, pressure and volume. The particles are now known to be the atoms or molecules of the gas.
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' law is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles' 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.
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. Under these conditions, essentially all molecules which arrive at the hole continue and pass through the hole, since collisions between molecules in the region of the hole are negligible. Conversely, when the diameter is larger than the mean free path of the gas, flow obeys the Sampson flow law.
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.
The bulk modulus of a substance is a measure of the resistance of a substance to bulk compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume. It is sometimes also known as the isentropic expansion factor and is denoted by γ (gamma) for an ideal gas or κ (kappa), the isentropic exponent for a real gas. The symbol γ is used by aerospace and chemical engineers.
A gas thermometer is a thermometer that measures temperature by the variation in volume or pressure of a gas.
In statistical mechanics, the translational partition function, is that part of the partition function resulting from the movement (translation) of the center of mass. For a single atom or molecule in a low pressure gas, neglecting the interactions of molecules, the canonical ensemble can be approximated by:
Gas is one of the four fundamental states of matter. The others are solid, liquid, and plasma.