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The main idea is to express an integral involving an integer parameter (e.g. power) of a function, represented by I n, in terms of an integral that involves a lower value of the parameter (lower power) of that function, for example I n-1 or I n-2. This makes the reduction formula a type of recurrence relation. In other words, the reduction ...
This reaction produced the 1,6-addition product 2 in 0% yield, the 1,6-addition product 3 in approximately 99% yield, and the 1,4-addition product 4 in less than 2% yield. This particular catalyst and set of reaction conditions led to the mostly regioselective and enantioselective 1,6-Michael addition of ethyl sorbate 1 to product 3 .
Reductive elimination is an elementary step in organometallic chemistry in which the oxidation state of the metal center decreases while forming a new covalent bond between two ligands. It is the microscopic reverse of oxidative addition, and is often the product-forming step in many catalytic processes. Since oxidative addition and reductive ...
Depending on the product structure, it could promptly react further to eject a leaving group to give the addition–elimination reaction sequence. Addition reactions are useful in analytic chemistry, as they can identify the existence and number of double bonds in a molecule. For example, bromine addition will consume a bromine solution ...
Cosine power-reduction formula: an illustrative diagram. The red, orange and blue triangles are all similar, and the red and orange triangles are congruent. The hypotenuse A D ¯ {\displaystyle {\overline {AD}}} of the blue triangle has length 2 cos θ {\displaystyle 2\cos \theta } .
As an example, consider the gas-phase reaction NO 2 + CO → NO + CO 2.If this reaction occurred in a single step, its reaction rate (r) would be proportional to the rate of collisions between NO 2 and CO molecules: r = k[NO 2][CO], where k is the reaction rate constant, and square brackets indicate a molar concentration.
Polyaddition (or addition polymerisation [2] [3]) is a polymerization reaction that forms polymers via individual independent addition reactions.Polyaddition occurs as a reaction between functional groups on molecules with low degrees of polymerization, such as dimers, trimers and oligomers, to form species of higher molar mass.
Free-radical reactions depend on one or more relatively weak bonds in a reagent. Under reaction conditions (typically heat or light), some weak bonds homolyse into radicals, which then induce further decomposition in their compatriots before recombination. Different mechanisms typically apply to reagents without such a weak bond.