For a monatomic ideal gas,, and for a diatomic gas ( such as nitrogen and oxygen, the main components of air ).

For simple diatomic molecules, the obtained wavefunctions are represented mathematically by the equations

For example, in the homonuclear diatomic molecules of the first ten elements, the molecular orbitals derived from the p < sub > x </ sub > and the p < sub > y </ sub > atomic orbitals result in two degenerate bonding orbitals ( of low energy ) and two degenerate antibonding orbitals ( of high energy ).

For example, the two diatomic gases, hydrogen and oxygen, can combine to form a liquid, water, in an exothermic reaction, as described by the following equation:

For moderate temperatures, the constant for a monoatomic gas is while for a diatomic gas it is.

For example, molecular nitrogen is inert under ordinary conditions, existing as diatomic molecules,.

For gaseous systems, the factor f, the number of degrees of freedom, commonly has the value 3 in the case of the monatomic gas, 5 for many diatomic gases, and 7 for larger molecules at ambient temperatures.

For diatomic molecules, this process is trivial, and can be made from a single measurement of the rotational spectrum.

For homonuclear diatomic molecules, bonding π molecular orbitals have no nodal planes that pass between the bonded atoms.

For example, in diatomic nitrogen N ≡ N the bond order is 3, while in acetylene H − C ≡ C − H the bond order between the two carbon atoms is also 3, and the C − H bond order is 1.

For heteronuclear diatomic molecules, the u / g symbol does not correspond to any exact symmetry of the electronic molecular Hamiltonian.

2. For a body consisting of 2 particles ( ex. diatomic molecule ) in 3-D plane with constant distance between them ( let's say d ) we can show it's degree of freedom to be 5.

For diatomic molecules there is only one ( single or multiple ) bond so the bond dipole moment is the molecular dipole moment, with typical values in the range of 0 to 11 D. At one extreme, a symmetrical molecule such as chlorine,, has zero dipole moment, while near the other extreme, gas phase potassium bromide, KBr, which is highly ionic, has a dipole moment of 10. 5 D.

For example, if a colloid consists of a solid phase dispersed in a liquid, the solid particles will not diffuse through a membrane, whereas with a true solution the dissolved ions or molecules will diffuse through a membrane.

For alkenes and similar double bonded molecules, the same prioritizing process is followed for the substituents.

For example, at room temperature, only 0. 4 % of all acetic acid molecules are dissociated.

For bimolecular reactions, two molecules collide and react with each other.

For example up to 200, 000 different small molecules might be made in plants, although not all these will be present in the same species, or in a single cell.

For each acetyl group that enters the citric acid cycle, three molecules of NADH are produced.

For example, in the 1919 book Chemistry of Human Life physician George W. Carey states that, " Health depends on a proper amount of iron phosphate Fe < sub > 3 </ sub >( PO < sub > 4 </ sub >)< sub > 2 </ sub > in the blood, for the molecules of this salt have chemical affinity for oxygen and carry it to all parts of the organism.

For this reason, infrared, microwaves, and radio waves are thought to damage molecules and biological tissue only by bulk heating, not excitation from single photons of the radiation ( however, there does remain controversy about possible non-thermal biological damage from low frequency EM radiation, see below ).

For molecules of a liquid to evaporate, they must be located near the surface, be moving in the proper direction, and have sufficient kinetic energy to overcome liquid-phase intermolecular forces.

For biological molecules the diffusion coefficients normally range from 10 < sup >− 11 </ sup > to 10 < sup >− 10 </ sup > m < sup > 2 </ sup >/ s.

For the circulatory system and bone marrow in which cells can occur in a liquid suspension and not bound up in solid tissue, it makes sense for them to communicate by soluble, circulating protein molecules.

For a biological organism to survive, these myriad components must interact with each other and with their environment in a way that processes food, removes waste, moves components to the correct location, and is responsive to signalling molecules, other organisms, light, sound, temperature and many other factors.

For molecules with N atoms in them, linear molecules have 3N – 5 degrees of vibrational modes, whereas nonlinear molecules have 3N – 6 degrees of vibrational modes ( also called vibrational degrees of freedom ).

For example, the covalent bond present within HCl molecules is much stronger than the forces present between the neighbouring molecules, which exist when the molecules are sufficiently close to each other.

For example, single La atoms have been isolated by implanting them into fullerene molecules.

For instance, an LC may flow like a liquid, but its molecules may be oriented in a crystal-like way.

For example, injection of a flux of a liquid crystal between two close parallel plates ( viscous fingering ), causes orientation of the molecules to couple with the flow, with the resulting emergence of dendritic patterns.

For example, when a thin polymer coating ( usually a polyimide ) is spread on a glass substrate and rubbed in a single direction with a cloth, it is observed that liquid crystal molecules in contact with that surface align with the rubbing direction.

For molecules that possess a center of inversion ( centrosymmetric molecules ) there are additional labels of symmetry that can be applied to molecular orbitals.

For all of these usages of ' latent heat ', a more systematic terminology uses ' latent heat capacity '.

For example, the strongest evidence for therapeutic interventions is provided by systematic review of randomized, triple-blind, placebo-controlled trials with allocation concealment and complete follow-up involving a homogeneous patient population and medical condition.

For American anarchist historian Eunice Minette Schuster " It is apparent ... that Proudhonian Anarchism was to be found in the United States at least as early as 1848 and that it was not conscious of its affinity to the Individualist Anarchism of Josiah Warren and Stephen Pearl Andrews ... William B. Greene presented this Proudhonian Mutualism in its purest and most systematic form .".

For American anarchist historian Eunice Minette Schuster " It is apparent ... that Proudhonian Anarchism was to be found in the United States at least as early as 1848 and that it was not conscious of its affinity to the Individualist Anarchism of Josiah Warren and Stephen Pearl Andrews ... William B. Greene presented this Proudhonian Mutualism in its purest and most systematic form .".

For the Neoplatonist they also formed a raw material for the writing of more systematic treatises in which were given arguments and means by which to struggle against some defect ( such as anger, envy, gossip, flattery ) or to overcome some difficult circumstance ( such as a mourning, an exile, downfall, disgrace ).

For example, if an experiment contains a systematic error, then increasing the sample size generally increases precision but does not improve accuracy.

: For the purpose of this Declaration, torture is defined as the deliberate, systematic or wanton infliction of physical or mental suffering by one or more persons acting alone or on the orders of any authority, to force another person to yield information, to make a confession, or for any other reason.

For much of the movement's history, Conservative Judaism deliberately avoided publishing systematic explications of theology and belief ; this was a conscious attempt to hold together a wide coalition.

For example, the issue of systematic underinvestment in research is addressed by the patent system that creates artificial monopolies for successful inventions.

For unambiguity, this article follows the systematic naming scheme throughout.

For many decades, some scholars of the Ancient Near East argued that it was impossible to define there as being a singular Mesopotamian religion, with Leo Oppenheim ( 1964 ) stating that " a systematic presentation of Mesopotamian religion cannot and should not be written.

< li > For the purpose of this Statute, ' crime against humanity ' means any of the following acts when committed as part of a widespread or systematic attack directed against any civilian population, with knowledge of the attack:

For the psychology of totemism, Thurnwald later ( 1917 – 18 ) put forth a detailed, systematic presentation ; by means of concrete examples, he also raised questions about the connections of totemism with ancestor worship, notions of souls, and beliefs in power, magic, offerings, and oracles.

For example, one might refer to the systemic, systematic, or institutional bias of a particular institution in devaluing contributions by women, men or ethnic minorities.

For Kierkegaard, at least, Jaspers felt that Kierkegaard's whole method of indirect communication precludes any attempts to properly expound his thought into any sort of systematic teaching.

For example, qualitative data analysis often involves a fairly structured approach to coding the raw data into systematic information, and quantifying intercoder reliability.

For this reason, today he is considered the founder, or co-founder ( with Quincy Wright and Pitirim Sorokin as well as others such as Kenneth Boulding, Anatol Rapaport and Adam Curle ), of the scientific analysis of conflict ; an interdisciplinary field of quantitative and mathematical social science dedicated to systematic investigation of the causes of war and conditions of peace.

For many years he was uncertain whether he discovered a true physical phenomenon or whether his measurements suffered from a systematic bias ( indeed, the first measurements did have a positive temperature bias as the instruments were liable to radiative heating by solar radiation ).

For five years, the Dreyfus brothers studied and experimented in a logical, systematic manner in Switzerland and France.

For example, while Edmund Burke's " Reflections on the Revolution in France " ( 1790 ) contains no systematic account of the connection between the Enlightenment and the Revolution, it is heavily spiced with hostile references to the French Revolutionaries as merely politicised philosophes.

For the enthusiastic driver the differences are truly staggering, genuine and systematic improvements were achieved to the setup and feel of the whole car.

For the long-run, there has been stronger support for ( 1 ) and ( 2 ) and no systematic association of and.

For example, " tartaric acid ", a compound found in wine, has a systematic name of 2, 3-dihydroxybutanedioic acid.

For six years, Kuwa war machines ( six battalions ) were directed to systematic torturing of Baggara tribes, completely destroying their infrastructures and eliminating their educated youth ; leaders ; and the elite.