CatalysisCatalysis (kəˈtæləsɪs) is the process of change in rate of a chemical reaction by adding a substance known as a catalyst (ˈkætəlɪst). Catalysts are not consumed by the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recycles quickly, very small amounts of catalyst often suffice; mixing, surface area, and temperature are important factors in reaction rate. Catalysts generally react with one or more reactants to form intermediates that subsequently give the final reaction product, in the process of regenerating the catalyst.
Raney nickelRaney nickel ˈreɪniː_ˈnɪkəl, also called spongy nickel, is a fine-grained solid composed mostly of nickel derived from a nickel–aluminium alloy. Several grades are known, of which most are gray solids. Some are pyrophoric, but most are used as air-stable slurries. Raney nickel is used as a reagent and as a catalyst in organic chemistry. It was developed in 1926 by American engineer Murray Raney for the hydrogenation of vegetable oils. Raney is a registered trademark of W. R. Grace and Company.
Integration by substitutionIn calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards". Before stating the result rigorously, consider a simple case using indefinite integrals. Compute Set This means or in differential form, Now where is an arbitrary constant of integration.
Trigonometric substitutionIn mathematics, trigonometric substitution is the replacement of trigonometric functions for other expressions. In calculus, trigonometric substitution is a technique for evaluating integrals. Moreover, one may use the trigonometric identities to simplify certain integrals containing radical expressions. Like other methods of integration by substitution, when evaluating a definite integral, it may be simpler to completely deduce the antiderivative before applying the boundaries of integration.
