Identify the correct statements among the following (I) Removal of a proton from \(\left(\mathrm{H}_{3} \mathrm{C}\right)_{2} \mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{3}\) leads to a more stable carbocation. (II) The hydrogen bonding is strong in \(\mathrm{S}-\mathrm{H}-\mathrm{-} \mathrm{S}\). (III) The central carbon atom in a \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}^{\bullet}\) free radical possesses 5 electrons. (IV) The number of \(\sigma\) bonds in but-1-en-3-yne is 7 . (a) all are correct (b) (IV) only' (c) (I) and (IV) only (d) (I), (III) and (IV)

Understanding carbocation stability is essential in IIT JEE Organic Chemistry. A carbocation is an ion with a positively charged carbon atom. The stability of carbocations is influenced by several factors, including the inductive effect, hyperconjugation, and resonance.

Inductive effect refers to the electron-donating or withdrawing properties of substituents attached to the carbocation. In the example from our exercise, the carbocation formed by removing a proton from \(\left(\mathrm{H}_{3} \mathrm{C}\right)_{2}\mathrm{CH}-\mathrm{CH}-\mathrm{CH}_{3}\) is stablized by the electron-donating effect of the adjacent methyl groups. This effect helps to spread the positive charge over a larger area, making the carbocation more stable.

Another stabilizing factor is hyperconjugation, which involves the interaction of the σ bonds of the neighboring methyl groups with the empty p-orbital of the carbocation, further dispersing the charge. The more hyperconjugation, the more stable the carbocation. Additionally, carbocations can be stabilized by resonance, where the positive charge is delocalized over several atoms. However, in the given example, resonance does not play a role in the stability of the carbocation.

It's important for students to recognize these stabilizing factors when evaluating the stability of carbocations in organic reactions.

Hydrogen bonding is a fundamental concept in chemistry, which is especially vital in the study of Organic Chemistry for IIT JEE. It is a particular type of intermolecular force that occurs between a hydrogen atom bonded to a highly electronegative atom (like nitrogen, oxygen, or fluorine) and another electronegative atom.

The strength of hydrogen bonds has significant implications on the physical properties of molecules, such as boiling points, melting points, and solubility. For example, water's unique properties, including its high boiling point and surface tension, are attributed to strong hydrogen bonds between water molecules.

In the given exercise, Statement II mentions hydrogen bonding in \(\mathrm{S}-\mathrm{H}-\mathrm{-}\mathrm{S}\), which is incorrect as sulfur does not usually form strong hydrogen bonds, unlike the aforementioned electronegative elements, due to its lower electronegativity and larger size. This misunderstanding could lead students astray, so it's crucial to note that not all molecules with hydrogen are capable of forming strong hydrogen bonds.

Free radicals are highly reactive species in organic chemistry, characterized by the presence of an unpaired electron. In the context of IIT JEE Organic Chemistry, students must become adept at identifying and understanding the behavior of free radicals.

A free radical is usually formed by the homolytic cleavage of a covalent bond, which leads to the formation of two radicals, each with one unpaired electron. These species are reactive due to their tendency to gain an additional electron to achieve a stable electronic configuration.

For instance, Statement III in our exercise describes the free radical \(\left(\mathrm{CH}_{3}\right)_{3}\mathrm{C}^{\bullet}\). This structure shows the central carbon atom with three methyl groups and possesses an unpaired electron, totaling four valence electrons, which contradicts the student’s claim of five valence electrons. It is vital to correctly count electrons to predict the behavior of free radicals in reactions such as chain propagation steps in polymerizations or halogenations.

Sigma (σ) bonds form the backbone of organic structures and understanding them is crucial in IIT JEE Organic Chemistry. A σ bond is a single covalent bond formed by the head-on overlap of atomic orbitals. They are stronger and more stable than pi (π) bonds, which result from the sideways overlap of p-orbitals.

In organic molecules, each single bond is a σ bond, and in multiple bonds (like double or triple bonds), there is always one σ bond along with one or two π bonds. In our exercise, students are required to count the number of σ bonds in but-1-en-3-yne. By recognizing that this molecule has a double bond (containing one σ and one π bond) and a triple bond (containing one σ and two π bonds), the student can correctly count three single σ bonds, two σ bonds associated with the double bond, and two σ bonds associated with the triple bond, confirming that there are a total of seven σ bonds.

Through practice, students can master the skill of counting σ bonds in various organic molecules, aiding in the prediction of molecular geometry and reactivity.