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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."
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 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.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
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
The concepts of syn and anti addition are used to characterize the different reactions of organic chemistry by reflecting the stereochemistry of the products in a reaction. The type of addition that occurs depends on multiple different factors of a reaction, and is defined by the final orientation of the substituents on the parent molecule .
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.
An element–reaction–product table is used to find coefficients while balancing an equation representing a chemical reaction. Coefficients represent moles of a substance so that the number of atoms produced is equal to the number of atoms being reacted with. [1] This is the common setup: Element: all the elements that are in the reaction ...