HydrogenHydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, and highly combustible. Hydrogen is the most abundant chemical substance in the universe, constituting roughly 75% of all normal matter. Stars such as the Sun are mainly composed of hydrogen in the plasma state. Most of the hydrogen on Earth exists in molecular forms such as water and organic compounds.
Hydrogen vehicleA hydrogen vehicle is a vehicle that uses hydrogen fuel for motive power. Hydrogen vehicles include hydrogen-fueled space rockets, as well as ships and aircraft. Power is generated by converting the chemical energy of hydrogen to mechanical energy, either by reacting hydrogen with oxygen in a fuel cell to power electric motors or, less commonly, by burning hydrogen in an internal combustion engine. there are two models of hydrogen cars publicly available in select markets: the Toyota Mirai (2014–), which is the world's first mass-produced dedicated fuel cell electric vehicle (FCEV), and the Hyundai Nexo (2018–).
Hydrogen infrastructureA hydrogen infrastructure is the infrastructure of hydrogen pipeline transport, points of hydrogen production and hydrogen stations (sometimes clustered as a hydrogen highway) for distribution as well as the sale of hydrogen fuel, and thus a crucial prerequisite before a successful commercialization of automotive fuel cell technology. A hydrogen highway is a chain of hydrogen-equipped filling stations and other infrastructure along a road or highway which allow hydrogen vehicles to travel.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
Group actionIn mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group acts on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it.
PhenolsIn organic chemistry, phenols, sometimes called phenolics, are a class of chemical compounds consisting of one or more hydroxyl groups (−OH) bonded directly to an aromatic hydrocarbon group. The simplest is phenol, C6H5OH. Phenolic compounds are classified as simple phenols or polyphenols based on the number of phenol units in the molecule. Phenols are both synthesized industrially and produced by plants and microorganisms. Phenols are more acidic than typical alcohols.
Hydrogen economyThe hydrogen economy uses hydrogen to decarbonize economic sectors which are hard to electrify, essentially, the "hard-to-abate" sectors such as cement, steel, long-haul transport, etc. In order to phase out fossil fuels and limit climate change, hydrogen can be created from water using renewable sources such as wind and solar, and its combustion only releases water vapor into the atmosphere. Although with a very low volumetric energy density hydrogen is an energetic fuel, frequently used as rocket fuel, but numerous technical challenges prevent the creation of a large-scale hydrogen economy.
Chemical formulaIn chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, such as parentheses, dashes, brackets, commas and plus (+) and minus (−) signs. These are limited to a single typographic line of symbols, which may include subscripts and superscripts. A chemical formula is not a chemical name since it does not contain any words.
Hydrogen productionHydrogen production is the family of industrial methods for generating hydrogen gas. As of 2020, the majority of hydrogen (~95%) is produced from fossil fuels by steam reforming of natural gas and other light hydrocarbons, partial oxidation of heavier hydrocarbons, and coal gasification. Other methods of hydrogen production include biomass gasification, methane pyrolysis, and electrolysis of water. Methane pyrolysis and water electrolysis can use any source of electricity including solar power.
Hydrogen bondIn chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a lone pair of electrons—the hydrogen bond acceptor (Ac). Such an interacting system is generally denoted , where the solid line denotes a polar covalent bond, and the dotted or dashed line indicates the hydrogen bond.
Diazonium compoundDiazonium compounds or diazonium salts are a group of organic compounds sharing a common functional group where R can be any organic group, such as an alkyl or an aryl, and X is an inorganic or organic anion, such as a halide. According to X-ray crystallography the linkage is linear in typical diazonium salts. The bond distance in benzenediazonium tetrafluoroborate is 1.083(3) Å, which is almost identical to that for dinitrogen molecule (N≡N). The linear free energy constants σm and σp indicate that the diazonium group is strongly electron-withdrawing.
Hydrogen storageSeveral methods exist for storing hydrogen. These include mechanical approaches such as using high pressures and low temperatures, or employing chemical compounds that release H2 upon demand. While large amounts of hydrogen are produced by various industries, it is mostly consumed at the site of production, notably for the synthesis of ammonia. For many years hydrogen has been stored as compressed gas or cryogenic liquid, and transported as such in cylinders, tubes, and cryogenic tanks for use in industry or as propellant in space programs.
Unitary groupIn mathematics, the unitary group of degree n, denoted U(n), is the group of n × n unitary matrices, with the group operation of matrix multiplication. The unitary group is a subgroup of the general linear group GL(n, C). Hyperorthogonal group is an archaic name for the unitary group, especially over finite fields. For the group of unitary matrices with determinant 1, see Special unitary group. In the simple case n = 1, the group U(1) corresponds to the circle group, consisting of all complex numbers with absolute value 1, under multiplication.
Automorphism groupIn mathematics, the automorphism group of an object X is the group consisting of automorphisms of X under composition of morphisms. For example, if X is a finite-dimensional vector space, then the automorphism group of X is the group of invertible linear transformations from X to itself (the general linear group of X). If instead X is a group, then its automorphism group is the group consisting of all group automorphisms of X. Especially in geometric contexts, an automorphism group is also called a symmetry group.
R33-class airshipThe R.33 class of British rigid airships were built for the Royal Naval Air Service during the First World War, but were not completed until after the end of hostilities, by which time the RNAS had become part of the Royal Air Force. The lead ship, R.33, served successfully for ten years and survived one of the most alarming and heroic incidents in airship history when she was torn from her mooring mast in a gale. She was called a "Pulham Pig" by the locals, as the blimps based there had been, and is immortalised in the village sign for Pulham St Mary.
Organolithium reagentIn organometallic chemistry, organolithium reagents are chemical compounds that contain carbon–lithium (C–Li) bonds. These reagents are important in organic synthesis, and are frequently used to transfer the organic group or the lithium atom to the substrates in synthetic steps, through nucleophilic addition or simple deprotonation. Organolithium reagents are used in industry as an initiator for anionic polymerization, which leads to the production of various elastomers.
Alkyl groupIn organic chemistry, an alkyl group is an alkane missing one hydrogen. The term alkyl is intentionally unspecific to include many possible substitutions. An acyclic alkyl has the general formula of . A cycloalkyl group is derived from a cycloalkane by removal of a hydrogen atom from a ring and has the general formula . Typically an alkyl is a part of a larger molecule. In structural formulae, the symbol R is used to designate a generic (unspecified) alkyl group. The smallest alkyl group is methyl, with the formula .
Quadratic formIn mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, is a quadratic form in the variables x and y. The coefficients usually belong to a fixed field K, such as the real or complex numbers, and one speaks of a quadratic form over K. If , and the quadratic form equals zero only when all variables are simultaneously zero, then it is a definite quadratic form; otherwise it is an isotropic quadratic form.
Group (mathematics)In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties. For example, the integers with the addition operation is an infinite group, which is generated by a single element called 1 (these properties characterize the integers in a unique way).
Linear independenceIn the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.
