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In mathematics, a paraproduct is a non-commutative bilinear operator acting on functions that in some sense is like the product of the two functions it acts on. According to Svante Janson and Jaak Peetre, in an article from 1988, [1] "the name 'paraproduct' denotes an idea rather than a unique definition; several versions exist and can be used for the same purposes."
At equilibrium, the chemical force driving the forward reaction must be equal to the chemical force driving the reverse reaction. Writing the initial active masses of A,B, A' and B' as p, q, p' and q' and the dissociated active mass at equilibrium as ξ {\displaystyle \xi } , this equality is represented by
Consider para-disubstituted benzene p-F-C 6 H 4-Z, where Z is a substituent such as NH 2, NO 2, etc. The fluorine atom is para with respect to the substituent Z in the benzene ring. The image on the right shows four distinguished ring carbon atoms, C1, C2, C3, C4 in p-F-C 6 H 4-Z molecule. The carbon with Z is defined as C1(ipso) and ...
For example, when 2-iodobutane is treated with alcoholic potassium hydroxide (KOH), but-2-ene is the major product and but-1-ene is the minor product. [1] More generally, Zaytsev's rule predicts that in an elimination reaction the most substituted product will be the most stable, and therefore the most favored.
The major product of the addition reaction will be the one formed from the more stable intermediate. Therefore, the major product of the addition of HX (where X is some atom more electronegative than H) to an alkene has the hydrogen atom in the less substituted position and X in the more substituted position.
The methyl group in toluene is small and will lead the ortho product being the major product. On the other hand, the t-butyl group is very bulky (there are 3 methyl groups attached to a single carbon) and will lead the para product as the major one. Even with toluene, the product is not 2:1 but having a slightly less ortho product.
Fractional crystallisation can be used to obtain pure para product, relying on the principle that it is less soluble than the ortho and thus will crystallise first. Care must be taken to avoid cocrystallisation of the ortho isomer. [2] Many nitro compounds' ortho and para isomers have quite different boiling points. These isomers can often be ...
The Curtin–Hammett principle is a principle in chemical kinetics proposed by David Yarrow Curtin and Louis Plack Hammett.It states that, for a reaction that has a pair of reactive intermediates or reactants that interconvert rapidly (as is usually the case for conformational isomers), each going irreversibly to a different product, the product ratio will depend both on the difference in ...