Unlike the easy catalytic hydrogenation of an alkene double bond, hydrogenation of a benzene double bond under similar reaction conditions does not take place easily. For example, in the reduction of stilbene, the benzene ring remains unaffected while the alkene bond gets reduced. Hydrogenation of an alkene double bond is exothermic and a favorable process. In contrast, to hydrogenate the first unsaturated bond of benzene, an energy input is needed; that is, the process is endothermic. This is...

Cyclohexane does not exist in a planar form due to the high angle and torsional strain it would experience in the planar structure. Instead, it adopts non-planar chair and boat conformations.
The chair form is the most stable and derives its name from its resemblance to the “easy chair.” In the chair conformation, two carbon atoms are arranged out-of-plane — one above and one below, minimizing the torsional strain. In the chair form, the bond angle is very close to the ideal...

The chair conformation is the most stable form of cyclohexane due to the absence of angle and torsional strain. The absence of angle strain is a result of cyclohexane’s bond angle being very close to the ideal tetrahedral bond angle of 109.5° in its chair conformer. Similarly, the torsional strain is also absent owing to the perfectly staggered arrangement of bonds.
The hydrogen atoms linked to carbons are arranged in two different axial and equatorial orientations to achieve this...

This lesson discusses the stability of substituted cyclohexanes with a focus on energies of various conformers and the effect of 1,3-diaxial interactions.
The two chair conformations of cyclohexanes undergo rapid interconversion at room temperature. Both forms have identical energies and stabilities, each comprising equal amounts of the equilibrium mixture. Replacing a hydrogen atom with a functional group makes the two conformations energetically non-equivalent.
For example, in...

Aminoacyl-tRNA synthetases are present in both eukaryotes and bacteria. Though eukaryotes have 20 different aminoacyl-tRNA synthetases to couple to 20 amino acids, many bacteria do not have genes for all of these aminoacyl-tRNA synthetases. Despite this, they still use all 20 amino acids to synthesize their proteins. For instance, some bacteria do not have the gene encoding the enzyme that couples glutamine with its partner tRNA. In these organisms, one enzyme adds glutamic acid to all of the...

The Intermediate Value Theorem is a foundational result in calculus that guarantees the existence of solutions within certain intervals for continuous functions. Formally, the Intermediate Value Theorem states that if a function f is continuous on the closed interval [a, b], and if N is any value between f(a) and f(b), then there exists at least one c ∈ (a, b) such that f(c) = N. This theorem is instrumental in proving the existence of roots and in analyzing the behavior of continuous...