The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body.
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...

The kinetic studies of SN2 reactions suggest an essential feature of its mechanism: it is a single-step process without intermediates. Here, both the nucleophile and the substrate participate in the rate-determining step.
The presence of the more electronegative halogen in the substrate creates a polarized carbon-halide bond. The halide pulls the electron cloud generating an electrophilic center at the carbon atom. Thus, the carbon atom carries a partial positive charge while the halide has a...

Salt stress—which can be triggered by high salt concentrations in a plant’s environment—can significantly affect plant growth and crop production by influencing photosynthesis and the absorption of water and nutrients.

Birch reduction uses solvated electrons as reducing agents. The reaction converts benzene to 1,4-cyclohexadiene. The reaction proceeds by the transfer of a single electron to the ring to form a benzene radical anion. This anion is highly basic—it abstracts a proton from the alcohol to form a cyclohexadienyl radical. Another single electron transfer gives the cyclohexadienyl anion. A proton transfer from the alcohol forms 1,4-cyclohexadiene. Since this reduction occurs via radical anion...

Gravitropism: Plant Responses to Gravity

This lesson deals with the crossed aldol reaction using weak bases. The self-condensation of an aldehyde having α hydrogen is prevented by adding it slowly to a mixture of formaldehyde and weak bases like hydroxide and alkoxide. Upon slow addition of the aldehyde, the base deprotonates the α carbon of the aldehyde to form the corresponding enolate. The enolate subsequently attacks the formaldehyde to form a single crossed product. Figure 1 depicts the aforementioned reaction.