LigandIn coordination chemistry, a ligand is an ion or molecule with a functional group that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electron pairs, often through Lewis bases. The nature of metal–ligand bonding can range from covalent to ionic. Furthermore, the metal–ligand bond order can range from one to three. Ligands are viewed as Lewis bases, although rare cases are known to involve Lewis acidic "ligands".
Integration by substitutionIn calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards". Before stating the result rigorously, consider a simple case using indefinite integrals. Compute Set This means or in differential form, Now where is an arbitrary constant of integration.
Nucleophilic substitutionIn chemistry, a nucleophilic substitution is a class of chemical reactions in which an electron-rich chemical species (known as a nucleophile) replaces a functional group within another electron-deficient molecule (known as the electrophile). The molecule that contains the electrophile and the leaving functional group is called the substrate.R. A. Rossi, R. H. de Rossi, Aromatic Substitution by the SRN1 Mechanism, ACS Monograph Series No. 178, American Chemical Society, 1983. .
Catalytic reformingCatalytic reforming is a chemical process used to convert petroleum refinery naphthas distilled from crude oil (typically having low octane ratings) into high-octane liquid products called reformates, which are premium blending stocks for high-octane gasoline. The process converts low-octane linear hydrocarbons (paraffins) into branched alkanes (isoparaffins) and cyclic naphthenes, which are then partially dehydrogenated to produce high-octane aromatic hydrocarbons.
RedoxRedox (ˈrɛdɒks , ˈriːdɒks , reduction–oxidation or oxidation–reduction) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a decrease in the oxidation state. There are two classes of redox reactions: Electron-transfer – Only one (usually) electron flows from the atom being oxidized to the atom that is reduced. This type of redox reaction is often discussed in terms of redox couples and electrode potentials.
Trigonometric substitutionIn mathematics, trigonometric substitution is the replacement of trigonometric functions for other expressions. In calculus, trigonometric substitution is a technique for evaluating integrals. Moreover, one may use the trigonometric identities to simplify certain integrals containing radical expressions. Like other methods of integration by substitution, when evaluating a definite integral, it may be simpler to completely deduce the antiderivative before applying the boundaries of integration.
Hydron (chemistry)In chemistry, the hydron, informally called proton, is the cationic form of atomic hydrogen, represented with the symbol H+. The general term "hydron", endorsed by the IUPAC, encompasses cations of hydrogen regardless of their isotopic composition: thus it refers collectively to protons (1H+) for the protium isotope, deuterons (2H+ or D+) for the deuterium isotope, and tritons (3H+ or T+) for the tritium isotope. Unlike most other ions, the hydron consists only of a bare atomic nucleus.
Determination of equilibrium constantsEquilibrium constants are determined in order to quantify chemical equilibria. When an equilibrium constant K is expressed as a concentration quotient, it is implied that the activity quotient is constant. For this assumption to be valid, equilibrium constants must be determined in a medium of relatively high ionic strength. Where this is not possible, consideration should be given to possible activity variation. The equilibrium expression above is a function of the concentrations [A], [B] etc.
Radical substitutionIn organic chemistry, a radical-substitution reaction is a substitution reaction involving free radicals as a reactive intermediate. The reaction always involves at least two steps, and possibly a third. In the first step called initiation (2,3), a free radical is created by homolysis. Homolysis can be brought about by heat or ultraviolet light, but also by radical initiators such as organic peroxides or azo compounds. UV Light is used to create two free radicals from one diatomic species.
Catalytic cycleIn chemistry, a catalytic cycle is a multistep reaction mechanism that involves a catalyst. The catalytic cycle is the main method for describing the role of catalysts in biochemistry, organometallic chemistry, bioinorganic chemistry, materials science, etc. Since catalysts are regenerated, catalytic cycles are usually written as a sequence of chemical reactions in the form of a loop. In such loops, the initial step entails binding of one or more reactants by the catalyst, and the final step is the release of the product and regeneration of the catalyst.
Post-transition metalThe metallic elements in the periodic table located between the transition metals to their left and the chemically weak nonmetallic metalloids to their right have received many names in the literature, such as post-transition metals, poor metals, other metals, p-block metals and chemically weak metals. The most common name, post-transition metals, is generally used in this article. Physically, these metals are soft (or brittle), have poor mechanical strength, and usually have melting points lower than those of the transition metals.
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
