Diazotisation

The nitrosation of primary aromatic amines with nitrous acid (generated in situ from sodium nitrite and a strong acid, such as hydrochloric acid, sulfuric acid, or HBF₄) leads to diazonium salts, which can be isolated if the counterion is non-nucleophilic.
Diazonium salts are important intermediates for the preparation of halides (Sandmeyer Reaction, Schiemann Reaction), and azo compounds. Diazonium salts can react as pseudohalide-type electrophiles, and can therefore be used in specific protocols for the Heck Reaction or Suzuki Coupling.
The intermediates resulting from the diazotization of primary, aliphatic amines are unstable; they are rapidly converted into carbocations after loss of nitrogen, and yield products derived from substitution, elimination or rearrangement processes.

Mechanism

Wolff-Kishner Reduction

The reduction of aldehydes and ketones to alkanes. Condensation of the carbonyl compound with hydrazine forms the hydrazone, and treatment with base induces the reduction of the carbon coupled with oxidation of the hydrazine to gaseous nitrogen, to yield the corresponding alkane.
The Clemmensen Reduction can effect a similar conversion under strongly acidic conditions, and is useful if the starting material is base-labile.

Mechanism

Clemmensen Reduction

The Clemmensen Reduction allows the deoxygenation of aldehydes or ketones, to produce the corresponding hydrocarbon.
The substrate must be stable to strong acid. The Clemmensen Reduction is complementary to the Wolff-Kishner Reduction, which is run under strongly basic conditions. Acid-labile molecules should be reduced by the Wolff-Kishner protocol.

Mechanism

The reduction takes place at the surface of the zinc catalyst. In this reaction, alcohols are not postulated as intermediates, because subjection of the corresponding alcohols to these same reaction conditions does not lead to alkanes. The following proposal employs the intermediacy of zinc carbenoids to rationalize the mechanism of the Clemmensen Reduction:

Aldol Condensation

In some cases, the adducts obtained from the Aldol Addition can easily be converted (in situ) to α,β-unsaturated carbonyl compounds, either thermally or under acidic or basic catalysis. The formation of the conjugated system is the driving force for this spontaneous dehydration. Under a variety of protocols, the condensation product can be obtained directly without isolation of the aldol.
The aldol condensation is the second step of the Robinson Annulation.

Mechanism of the Aldol Condensation

For the addition step see Aldol Addition

Markovnikov's Rule

Markovnikov Rule predicts the regiochemistry of HX addition to unsymmetrically substituted alkenes.
The halide component of HX bonds preferentially at the more highly substituted carbon, whereas the hydrogen prefers the carbon which already contains more hydrogens.
Anti-Markovnikov

Some reactions do not follow Markovnikov's Rule, and anti-Markovnikov products are isolated. This is a feature for example of radical induced additions of HX and of Hydroboration.

Mechanism

The proton adds first to the carbon-carbon double bond. The carbon bearing more substituents forms a more stable carbenium ion; attack of bromide ion follows in a second step:
Markovnikov
Radical reactions require an initiation step. In this example, a bromo radical is formed.

The reversal of the regiochemistry of addition is the result of the reversal of the order in which the two components add to the alkene. Radical addition leads to the formation of the more stable radical, which reacts with HBr to give product and a new bromo radical:
Anti-Markovnikov

Hell-Volhard-Zelinsky Reaction

Treatment with bromine and a catalytic amount of phosphorus leads to the selective α-bromination of carboxylic acids.

Mechanism

Phosphorus reacts with bromine to give phosphorus tribromide, and in the first step this converts the carboxylic acid into an acyl bromide.

An acyl bromide can readily exist in the enol form, and this tautomer is rapidly brominated at the α-carbon. The monobrominated compound is much less nucleophilic, so the reaction stops at this stage. This acyl intermediate compound can undergo bromide exchange with unreacted carboxylic acid via the anhydride, which allows the catalytic cycle to continue until the conversion is complete.

Relativistic Equations ( Dependence of mass and time on velocity)

By Einstein's theory of relativity

                                 m′=m1−v2c2−−−−−√


where:

• v is the magnitude of the velocity of the body;
• c is the speed of light;
• m0 is the rest mass of the body.

The value m is known as the relativistic mass of the body.
The factor 11−v2c2−−−−−√ is known as the Lorentz Factor.




    Δt′=Δt1−v2c2−−−−−√
where:

• Δt′ is the time interval measured from the space ship;
• Δt is the time interval measured in the inertial system containing planet and comet;
• v is the magnitude of the space ship's velocity;
• c is the speed of light in vacuum.