formulaeax

chemical formula or molecular formula is a way of expressing information about the atoms that constitute a particular chemical compound.

The chemical formula identifies each constituent element by its chemical symbol and indicates the number of atoms of each element found in each discrete molecule of that compound. If a molecule contains more than one atom of a particular element, this quantity is indicated using a subscript after the chemical symbol (although 18th-century books often used superscripts) and also can be combined by more chemical elements. For example, methane, a small molecule consisting of one carbon atom and four hydrogen atoms, has the chemical formula CH4. The sugar molecule glucose has six carbon atoms, twelve hydrogen atoms and six oxygen atoms, so its chemical formula is C6H12O6.

Chemical formulas may be used in chemical equations to describe chemical reactions. For ionic compounds and other non-molecular substances an empirical formula may be used, in which the subscripts indicate the ratio of the elements.

The 19th-century Swedish chemist Jöns Jakob Berzelius worked out this system for writing chemical formulas.

The connectivity of a molecule often has a strong influence on its physical and chemical properties and behaviour. Two molecules composed of the same numbers of the same types of atoms (i.e. a pair of isomers) might have completely different chemical and/or physical properties if the atoms are connected differently or in different positions. In such cases, a structural formula can be useful, as it illustrates which atoms are bonded to which other ones. From the connectivity, it is often possible to deduce the approximate shape of the molecule.

A chemical formula supplies information about the types and spatial arrangement of bonds in the chemical, though it does not necessarily specify the exact isomer. For example ethane consists of two carbon atoms single-bonded to each other, with each carbon atom having three hydrogen atoms bonded to it. Its chemical formula can be rendered as CH3CH3. In ethylene there is a double bond between the carbon atoms (and thus each carbon only has two hydrogens), therefore the chemical formula may be written: CH2CH2, and the fact that there is a double bond between the carbons is implicit because carbon has a valence of four. However, a more explicit method is to write H2C=CH2 or less commonly H2C::CH2. The two lines (or two pairs of dots) indicate that a double bond connects the atoms on either side of them.

A triple bond may be expressed with three lines or pairs of dots, and if there may be ambiguity, a single line or pair of dots may be used to indicate a single bond.

Molecules with multiple functional groups that are the same may be expressed by enclosing the repeated group in round brackets. For example isobutane may be written (CH3)3CH. This semi-structural formula implies a different connectivity from other molecules that can be formed using the same atoms in the same proportions (isomers). The formula (CH3)3CH implies a central carbon atom attached to one hydrogen atom and three CH3 groups. The same number of atoms of each element (10 hydrogens and 4 carbons, or C4H10) may be used to make a straight chain molecule, butane: CH3CH2CH2CH3.

The alkene but-2-ene has two isomers which the chemical formula CH3CH=CHCH3 does not identify. The relative position of the two methyl groups must be indicated by additional notation denoting whether the methyl groups are on the same side of the double bond (cis or Z) or on the opposite sides from each other (trans or E).

For polymers, parentheses are placed around the repeating unit. For example, a hydrocarbon molecule that is described as CH3(CH2)50CH3, is a molecule with fifty repeating units. If the number of repeating units is unknown or variable, the letter n may be used to indicate this formula: CH3(CH2)nCH3.

For ions, the charge on a particular atom may be denoted with a right-hand superscript. For example Na+, or Cu2+. The total charge on a charged molecule or a polyatomic ion may also be shown in this way. For example: hydronium, H3O+ or sulfate, SO42−.

For more complex ions, brackets are often used to enclose the ionic formula, as in [B12H12]2−, which is found in compounds such as Cs2[B12H12]. Parentheses ( ) can be nested inside brackets to indicate a repeating unit, as in [Co(NH3)6]3+. Here (NH3)6 indicates that the ion contains six NH3 groups, and [ ] encloses the entire formula of the ion with charge +3
Although isotopes are more relevant to nuclear chemistry or stable isotope chemistry than to conventional chemistry, different isotopes may be indicated with a left-hand superscript in a chemical formula. For example, the phosphate ion containing radioactive phosphorus-32 is 32PO43-. Also a study involving stable isotope ratios might include the molecule 18O16O.

A left-hand subscript is sometimes used redundantly to indicate the atomic number. For example, 8O2 for dioxygen, and 168O2 for the most abundant isotopic species of dioxygen. This is convenient when writing equations for nuclear reactions, in order to show the balance of charge more clearly.

In chemistry, the empirical formula of a chemical is a simple expression of the relative number of each type of atom or ratio of the elements in the compound. Empirical formulas are the standard for ionic compounds, such as CaCl2, and for macromolecules, such as SiO2. An empirical formula makes no reference to isomerism, structure, or absolute number of atoms. The term empirical refers to the process of elemental analysis, a technique of analytical chemistry used to determine the relative percent composition of a pure chemical substance by element.

For example hexane has a molecular formula of C6H14, or structurally CH3CH2CH2CH2CH2CH3, implying that it has a chain structure of 6 carbon atoms, and 14 hydrogen atoms. However, the empirical formula for hexane is C3H7. Likewise the empirical formula for hydrogen peroxide, H2O2, is simply HO expressing the 1:1 ratio of component elements. Formaldehyde and acetic acid have the same empirical formula, CH2O. This is the actual chemical formula for formaldehyde, but acetic acid has double the number of atoms.

Chemical formulas most often use integers for each element. However, there is a whole class of compounds, called non-stoichiometric compounds, that cannot be represented by small integers. Such a formula might be written using decimal fractions, as in Fe0.95O, or it might include a variable part represented by a letter, as in Fe1–xO, where x is normally much less than 1. In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles. Now they are known to be composite particles, each made of three quarks bound together by the so-called strong interaction.

The interaction between two or more nucleons is called internucleon interactions or nuclear force, which is also ultimately caused by the strong interaction. (Before the discovery of quarks, the term "strong interaction" referred to just internucleon interactions.)

Nucleons sit at the boundary where particle physics and nuclear physics overlap. Particle physics, particularly quantum chromodynamics, provides the fundamental equations that explain the properties of quarks and of the strong interaction. These equations explain quantitatively how quarks can bind together into protons and neutrons (and all the other hadrons). However, when multiple nucleons are assembled into an atomic nucleus (nuclide), these fundamental equations become too difficult to solve directly (see lattice QCD). Instead, nuclides are studied within nuclear physics, which studies nucleons and their interactions by approximations and models, such as the nuclear shell model. These models can successfully explain nuclide properties, for example, whether or not a certain nuclide undergoes radioactive decay.

The proton and neutron are both baryons and both fermions. In the terminology of particle physics, these two particles make up an isospin doublet (I = 1⁄2). This explains why their masses are so similar, with the neutron just
Protons and neutrons are most important and best known for constituting atomic nuclei, but they can also be found on their own, not part of a larger nucleus. A proton on its own is the nucleus of the hydrogen-1 atom (1H). A neutron on its own is unstable (see below), but they can be found in nuclear reactions (see neutron radiation) and are used in scientific analysis (see neutron scattering).

Both the proton and neutron are made of three quarks. The proton is made of two up quarks and one down quark, while the neutron is one up quark and two down quarks. The quarks are held together by the strong force. It is also said that the quarks are held together by gluons, but this is just a different way to say the same thing (gluons mediate the strong force).

An up quark has electric charge +2⁄3 e, and a down quark has charge −1⁄3 e, so the total electric charge of the proton and neutron are +e and 0, respectively. The word "neutron" comes from the fact that it is electrically "neutral".

The mass of the proton and neutron is quite similar: The proton is 1.6726×10−27 kg or 938.27 MeV/c2, while the neutron is 1.6749×10−27 kg or 939.57 MeV/c2. The neutron is roughly 0.1% heavier. The similarity in mass is explained by the isospin approximate-symmetry in particle physics (also see below).

The spin of both protons and neutrons is 1⁄2. This means they are fermions not bosons, and therefore, like electrons, they are subject to the Pauli exclusion principle. This is a very important fact in nuclear physics: Protons and neutrons in an atomic nucleus cannot all be in the same quantum state, but instead they spread out into nuclear shells analogous to electron shells in chemistry. Another reason that the spin of the proton and neutron is important is because it is the source of nuclear spin in larger nuclei. Nuclear spin is best known for its crucial role in the NMR/MRI technique for chemistry and biochemistry analysis.

The magnetic moment of a proton, denoted μp, is 2.79 nuclear magnetons (μN), while the magnetic moment of a neutron is μn = −1.91 μN. These parameters are also important in NMR/MRI.

neutron by itself is an unstable particle: It undergoes β− decay (a type of radioactive decay) by turning into a proton, electron, and electron antineutrino, with a half-life around ten minutes. (See the Neutron article for further discussion of neutron decay.) A proton by itself is thought to be stable, or at least its lifetime is too long to measure. (This is an important issue in particle physics, see Proton decay.)

Inside a nucleus, on the other hand, both protons and neutrons can be stable or unstable, depending on the nuclide. Inside some nuclides, a neutron can turn into a proton (plus other particles) as described above; inside other nuclides the reverse can happen, where a proton turns into a neutron (plus other particles) through β+ decay or electron capture; and inside still other nuclides, both protons and neutrons are stable and do not change form.

Both of the nucleons have corresponding antiparticles: The antiproton and the antineutron. These antimatter particles have the same mass and opposite charge as the proton and neutron respectively, and they interact in the same way. (This is generally believed to be exactly true, due to CPT symmetry. If there is a difference, it is too small to measure in all experiments to date.) In particular, antinucleons can bind into an "antinucleus". So far, scientists have created antideuterium and antihelium-3 nuclei.

Although it is known that the nucleon is made from three quarks, as of 2006[update], it is not known how to solve the equations of motion for quantum chromodynamics. Thus, the study of the low-energy properties of the nucleon are performed by means of models. The only first-principles approach available is to attempt to solve the equations of QCD numerically, using lattice QCD. This requires complicated algorithms and very powerful supercomputers. However, several analytic models also exist:

The Skyrmion models the nucleon as a topological soliton in a non-linear SU(2) pion field. The topological stability of the Skyrmion is interpreted as the conservation of baryon number, that is, the non-decay of the nucleon. The local topological winding number density is identified with the local baryon number density of the nucleon. With the pion isospin vector field oriented in the shape of a hedgehog, the model is readily solvable, and is thus sometimes called the hedgehog model. The hedgehog model is able to predict low-energy parameters, such as the nucleon mass, radius and axial coupling constant, to approximately 30% of experimental values.

The MIT bag model confines three non-interacting quarks to a spherical cavity, with the boundary condition that the quark vector current vanish on the boundary. The non-interacting treatment of the quarks is justified by appealing to the idea of asymptotic freedom, whereas the hard boundary condition is justified by quark confinement. Mathematically, the model vaguely resembles that of a radar cavity, with solutions to the Dirac equation standing in for solutions to the Maxwell equations and the vanishing vector current boundary condition standing for the conducting metal walls of the radar cavity. If the radius of the bag is set to the radius of the nucleon, the bag model predicts a nucleon mass that is within 30% of the actual mass. An important failure of the basic bag model is its failure to provide a pion-mediated interaction.

The chiral bag model merges the MIT bag model and the Skyrmion model. In this model, a hole is punched out of the middle of the Skyrmion, and replaced with a bag model. The boundary condition is provided by the requirement of continuity of the axial vector current across the bag boundary. Very curiously, the missing part of the topological winding number (the baryon number) of the hole punched into the Skyrmion is exactly made up by the non-zero vacuum expectation value (or spectral asymmetry) of the quark fields inside the bag. As of 2006[update], this remarkable trade-off between topology and the spectrum of an operator does not have any grounding or explanation in the mathematical theory of Hilbert spaces and their relationship to geometry. Several other properties of the chiral bag are notable: it provides a better fit to the low energy nucleon properties, to within 5–10%, and these are almost completely independent of the chiral bag radius (as long as the radius is less than the nucleon radius). This independence of radius is referred to as the Cheshire Cat principle, after the fading to a smile of Lewis Carroll's Cheshire Cat. It is expected that a first-principles solution of the equations of QCD will demonstrate a similar duality of quark-pion descriptions.