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To compute the integral, we set n to its value and use the reduction formula to express it in terms of the (n – 1) or (n – 2) integral. The lower index integral can be used to calculate the higher index ones; the process is continued repeatedly until we reach a point where the function to be integrated can be computed, usually when its index is 0 or 1.
An addition reaction is the reverse of an elimination reaction, in which one molecule divides into two or more molecules. For instance, the hydration of an alkene to an alcohol is reversed by dehydration. There are two main types of polar addition reactions: electrophilic addition and nucleophilic addition.
In chemical kinetics, the overall rate of a reaction is often approximately determined by the slowest step, known as the rate-determining step (RDS or RD-step [1] or r/d step [2] [3]) or rate-limiting step. For a given reaction mechanism, the prediction of the corresponding rate equation (for comparison with the experimental rate law) is often ...
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 } .
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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 ...
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.