Roots, often written as radicals, identify the quantity that must be raised to a specific exponent to produce a given value. A radical expression consists of two main components: the radicand, which is the value placed inside the root symbol, and the index, which indicates the degree of the root being taken. The notation n√a indicates the principal nth root of a. If n equals 2, the operation is the square root, while n = 3 defines the cube root. When n is even, a negative radicand does not...

In the presence of heat or light, alkanes react with molecular halogens to form alkyl halides by a substitution reaction called radical halogenation. This reaction has three steps: initiation, propagation, and termination, as seen in the radical chlorination of methane to produce methyl chloride.
In the initiation step of the reaction, the chlorine molecule undergoes homolytic cleavage in the presence of light or heat, forming two highly reactive chlorine radicals. Propagation occurs in two...

In organic synthesis, the formation of products can be altered by changing the reaction conditions. For example, a dibromo addition product is formed when propene is treated with bromine at room temperature. In contrast, propene undergoes allylic substitution in non-polar solvents at high temperatures to give 3-bromopropene. In order to avoid the addition reaction, the bromine concentration must be kept as low as possible throughout the reaction. This can be achieved using N-bromosuccinimide...

Radical substitution reactions can be used to remove functional groups from molecules. The hydrogenolysis of alkyl halides is one such reaction, where the weak Sn–H bond in tributyltin hydride reacts with alkyl halides to form alkanes. Here, the reagent Bu3SnH yields tributyltin halide as a byproduct.
The bonds formed in this reaction are stronger than the bonds broken, making it energetically favorable. The reaction follows a radical chain mechanism similar to radical halogenation reactions,...

Activated manganese(IV) oxide can selectively oxidize allylic and benzylic alcohols via a radical intermediate mechanism. Primary allylic alcohols are oxidized to aldehydes, while secondary allylic alcohols yield ketones. The redox reaction of potassium permanganate with an Mn(II) salt such as manganese sulfate (under either alkaline or acidic conditions), followed by thorough drying, yields the oxidizing agent: activated MnO2. While MnO2 is insoluble in the solvents used for the reaction, the...