Monatomic gas

Last updated

In physics and chemistry, "monatomic" is a combination of the words "mono" and "atomic", and means "single atom". It is usually applied to gases: a monatomic gas is a gas in which atoms are not bound to each other. Examples at standard conditions of temperature and pressure include all the noble gases (helium, neon, argon, krypton, xenon, and radon), though all chemical elements will be monatomic in the gas phase at sufficiently high temperature (or very low pressure). The thermodynamic behavior of a monatomic gas is much simpler when compared to polyatomic gases because it is free of any rotational or vibrational energy. [1]

Contents

Noble gases

The only chemical elements that are stable single atoms (so they are not molecules) at standard temperature and pressure (STP) are the noble gases. These are helium, neon, argon, krypton, xenon, and radon. Noble gases have a full outer valence shell making them rather non-reactive species. [2] While these elements have been described historically as completely inert, chemical compounds have been synthesized with all but neon and helium. [3]

When grouped together with the homonuclear diatomic gases such as nitrogen (N2), the noble gases are called "elemental gases" to distinguish them from molecules that are also chemical compounds.

Thermodynamic properties

The only possible motion of an atom in a monatomic gas is translation (electronic excitation is not important at room temperature). Thus by the equipartition theorem, the kinetic energy of a single atom of a monatomic gas at thermodynamic temperature T is given by , where kB is the Boltzmann constant. One mole of atoms contains an Avogadro number () of atoms, so that the energy of one mole of atoms of a monatomic gas is , where R is the gas constant.

In an adiabatic process, monatomic gases have an idealised γ-factor (Cp/Cv) of 5/3, as opposed to 7/5 for ideal diatomic gases where rotation (but not vibration at room temperature) also contributes. Also, for ideal monatomic gases: [4] [5] [6]

the molar heat capacity at constant pressure (Cp) is 5/2 R = 20.8 J⋅K−1⋅mol−1 (4.97  cal⋅K−1⋅mol−1).
the molar heat capacity at constant volume (Cv) is 3/2 R = 12.5 J⋅K−1⋅mol−1 (2.98 cal⋅K−1⋅mol−1).

Related Research Articles

<span class="mw-page-title-main">Diatomic molecule</span> Molecule composed of any two atoms

Diatomic molecules are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen or oxygen, then it is said to be homonuclear. Otherwise, if a diatomic molecule consists of two different atoms, such as carbon monoxide or nitric oxide, the molecule is said to be heteronuclear. The bond in a homonuclear diatomic molecule is non-polar.

<span class="mw-page-title-main">Noble gas</span> Group of low-reactive, gaseous chemical elements

The noble gases are the naturally occurring members of group 18 of the periodic table: helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn). Under standard conditions, these elements are odorless, colorless, monatomic gases with very low chemical reactivity and cryogenic boiling points.

<span class="mw-page-title-main">Specific heat capacity</span> Heat required to increase temperature of a given unit of mass of a substance

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.

<span class="mw-page-title-main">Thermodynamic temperature</span> Measure of absolute temperature

Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.

The volumetric heat capacity of a material is the heat capacity of a sample of the substance divided by the volume of the sample. It is the amount of energy that must be added, in the form of heat, to one unit of volume of the material in order to cause an increase of one unit in its temperature. The SI unit of volumetric heat capacity is joule per kelvin per cubic meter, J⋅K−1⋅m−3.

<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 and the gas constant, and 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. It is named after the Austrian scientist Ludwig Boltzmann.

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.

<span class="mw-page-title-main">Ideal gas law</span> Equation of the state of a hypothetical ideal gas

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:

<span class="mw-page-title-main">Ideal gas</span> Mathematical model which approximates the behavior of real gases

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.

In thermodynamics, the Joule–Thomson effect describes the temperature change of a real gas or liquid when it is forced through a valve or porous plug while keeping it insulated so that no heat is exchanged with the environment. This procedure is called a throttling process or Joule–Thomson process. At room temperature, all gases except hydrogen, helium, and neon cool upon expansion by the Joule–Thomson process when being throttled through an orifice; these three gases experience the same effect but only at lower temperatures. Most liquids such as hydraulic oils will be warmed by the Joule–Thomson throttling process.

<span class="mw-page-title-main">Speed of sound</span> Speed of sound wave through elastic medium

The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At 20 °C (68 °F), the speed of sound in air is about 343 m/s, or one km in 2.91 s or one mile in 4.69 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating. At 0 °C (32 °F), the speed of sound in air is about 331 m/s. More simply, the speed of sound is how fast vibrations travel.

<span class="mw-page-title-main">Isobaric process</span> Thermodynamic process in which pressure remains constant

In thermodynamics, an isobaric process is a type of thermodynamic process in which the pressure of the system stays constant: ΔP = 0. The heat transferred to the system does work, but also changes the internal energy (U) of the system. This article uses the physics sign convention for work, where positive work is work done by the system. Using this convention, by the first law of thermodynamics,

In chemistry, noble gas compounds are chemical compounds that include an element from the noble gases, group 18 of the periodic table. Although the noble gases are generally unreactive elements, many such compounds have been observed, particularly involving the element xenon.

<span class="mw-page-title-main">Equipartition theorem</span> Theorem in classical statistical mechanics

In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in translational motion of a molecule should equal that in rotational motion.

The molar heat capacity of a chemical substance is the amount of energy that must be added, in the form of heat, to one mole of the substance in order to cause an increase of one unit in its temperature. Alternatively, it is the heat capacity of a sample of the substance divided by the amount of substance of the sample; or also the specific heat capacity of the substance times its molar mass. The SI unit of molar heat capacity is joule per kelvin per mole, J⋅K−1⋅mol−1.

<span class="mw-page-title-main">Heat capacity ratio</span> Thermodynamic quantity

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.

In chemistry, the term chemically inert is used to describe a substance that is not chemically reactive. From a thermodynamic perspective, a substance is inert, or nonlabile, if it is thermodynamically unstable yet decomposes at a slow, or negligible rate.

<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 physics and chemistry, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all states of a system is known as the system's phase space, and the degrees of freedom of the system are the dimensions of the phase space.

<span class="mw-page-title-main">Properties of nonmetals (and metalloids) by group</span>

Nonmetals show more variability in their properties than do metals. Metalloids are included here since they behave predominately as chemically weak nonmetals.

References

  1. "monatomic gas". Encyclopædia Britannica. Retrieved 6 June 2016.
  2. Laszlo, Pierre; Schrobilgen, Gary J. (1988-04-01). "Ein Pionier oder mehrere Pioniere? Die Entdeckung der Edelgas-Verbindungen". Angewandte Chemie. 100 (4): 495–506. Bibcode:1988AngCh.100..495L. doi:10.1002/ange.19881000406. ISSN   1521-3757.
  3. Christe, Karl O. (2001-04-17). "A Renaissance in Noble Gas Chemistry". Angewandte Chemie International Edition. 40 (8): 1419–1421. doi:10.1002/1521-3773(20010417)40:8<1419::aid-anie1419>3.0.co;2-j. ISSN   1521-3773. PMID   11317290.
  4. Heat Capacity of an Ideal Gas
  5. Heat Capacity of Ideal Gases
  6. Lecture 3: Thermodynamics of Ideal Gases & Calorimetry [ permanent dead link ], p. 2