Reaction rateThe reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit time. Reaction rates can vary dramatically. For example, the oxidative rusting of iron under Earth's atmosphere is a slow reaction that can take many years, but the combustion of cellulose in a fire is a reaction that takes place in fractions of a second.
Spectrum of a ringIn commutative algebra, the prime spectrum (or simply the spectrum) of a ring R is the set of all prime ideals of R, and is usually denoted by ; in algebraic geometry it is simultaneously a topological space equipped with the sheaf of rings . For any ideal I of R, define to be the set of prime ideals containing I. We can put a topology on by defining the to be This topology is called the Zariski topology. A basis for the Zariski topology can be constructed as follows. For f ∈ R, define Df to be the set of prime ideals of R not containing f.
Local ringIn mathematics, more specifically in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on varieties or manifolds, or of algebraic number fields examined at a particular place, or prime. Local algebra is the branch of commutative algebra that studies commutative local rings and their modules. In practice, a commutative local ring often arises as the result of the localization of a ring at a prime ideal.
Peptide synthesisIn organic chemistry, peptide synthesis is the production of peptides, compounds where multiple amino acids are linked via amide bonds, also known as peptide bonds. Peptides are chemically synthesized by the condensation reaction of the carboxyl group of one amino acid to the amino group of another. Protecting group strategies are usually necessary to prevent undesirable side reactions with the various amino acid side chains. Chemical peptide synthesis most commonly starts at the carboxyl end of the peptide (C-terminus), and proceeds toward the amino-terminus (N-terminus).
Wilkinson's catalystWilkinson's catalyst is the common name for chloridotris(triphenylphosphine)rhodium(I), a coordination complex of rhodium with the formula [RhCl(PPh3)3], where 'Ph' denotes a phenyl group). It is a red-brown colored solid that is soluble in hydrocarbon solvents such as benzene, and more so in tetrahydrofuran or chlorinated solvents such as dichloromethane. The compound is widely used as a catalyst for hydrogenation of alkenes. It is named after chemist and Nobel laureate Sir Geoffrey Wilkinson, who first popularized its use.
I-adic topologyIn commutative algebra, the mathematical study of commutative rings, adic topologies are a family of topologies on the underlying set of a module, generalizing the p-adic topologies on the integers. Let R be a commutative ring and M an R-module. Then each ideal a of R determines a topology on M called the a-adic topology, characterized by the pseudometric The family is a basis for this topology. With respect to the topology, the module operations of addition and scalar multiplication are continuous, so that M becomes a topological module.
Carboxylic acidIn organic chemistry, a carboxylic acid is an organic acid that contains a carboxyl group () attached to an R-group. The general formula of a carboxylic acid is or , with R referring to the alkyl, alkenyl, aryl, or other group. Carboxylic acids occur widely. Important examples include the amino acids and fatty acids. Deprotonation of a carboxylic acid gives a carboxylate anion. Carboxylic acids are commonly identified by their trivial names. They often have the suffix -ic acid.
StereoisomerismIn stereochemistry, stereoisomerism, or spatial isomerism, is a form of isomerism in which molecules have the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in space. This contrasts with structural isomers, which share the same molecular formula, but the bond connections or their order differs. By definition, molecules that are stereoisomers of each other represent the same structural isomer.
Absolute configurationAbsolute configuration refers to the spatial arrangement of atoms within a chiral molecular entity (or group) and its resultant stereochemical description. Absolute configuration is typically relevant in organic molecules where carbon is bonded to four different substituents. This type of construction creates two possible enantiomers. Absolute configuration uses a set of rules to describe the relative positions of each bond around the chiral center atom.
Mannich reactionIn organic chemistry, the Mannich reaction is a three-component organic reaction that involves the amino alkylation of an acidic proton next to a carbonyl () functional group by formaldehyde () and a primary or secondary amine () or ammonia (). The final product is a β-amino-carbonyl compound also known as a Mannich base. Reactions between aldimines and α-methylene carbonyls are also considered Mannich reactions because these imines form between amines and aldehydes. The reaction is named after Carl Mannich.
