Chemical Bonding And Molecular Structure – JEE Main ChemistryPractice Questions & PYQs

Molecular orbital theory assesses the stability of a chemical species by calculating its bond order, which represents half the difference between the number of bonding and antibonding electrons. Both $\mathrm{Li}_2^{+}$ and $\mathrm{Li}^{-}_2$ possess a bond order of 0.5, indicating that each species maintains a net accumulation of electrons in bonding molecular orbitals. Since any positive bond order implies a net attractive force between the constituent atoms, both of these ions are considered stable.

The stability of a molecular anion depends largely on the energy state of the orbital that the additional electron occupies. In the case of $C_2$, the molecule possesses low-energy vacant orbitals that are readily available to host an incoming electron. When an electron enters these vacant spaces, the total energy of the system is reduced, thereby resulting in a more stable molecular configuration compared to the neutral species.

Molecular geometry is governed by VSEPR theory, which positions electron pairs around the central atom to minimize repulsion and dictate the final shape. $ICl_5$ adopts a square pyramidal shape, while $ICl_4^-$ contains four bond pairs and two lone pairs, with the lone pairs occupying opposite corners of an octahedral electron geometry to yield a square planar structure. Consequently, $ICl_5$ is square pyramidal and $ICl_4^-$ is square planar.

The presence of P-H bonds in phosphorus oxoacids is determined by the direct coordination of hydrogen to the central phosphorus atom, which is essential for the characteristic reducing property of these acids. In hypophosphorous acid ($H_3PO_2$), the central phosphorus atom is bonded to two hydrogen atoms directly, while pyrophosphorous acid ($H_4P_2O_5$) is formed by the condensation of two phosphonate units where each phosphorus atom retains one P-H bond, resulting in a total of two P-H bonds per molecule. Both species consequently possess exactly two P-H bonds, fulfilling the structural requirement for the pair.

Sulphur oxoacids are classified by their structural connectivity, specifically whether the sulphur atoms are linked directly or bridged through an oxygen atom. Molecules such as $\mathrm{H}_2\mathrm{S}_2\mathrm{O}_3$, $\mathrm{H}_2\mathrm{S}_4\mathrm{O}_6$, and $\mathrm{H}_2\mathrm{S}_2\mathrm{O}_4$ all feature direct sulphur-sulphur bonds within their frameworks. In contrast, $\mathrm{H}_2\mathrm{S}_2\mathrm{O}_7$ consists of two sulphur centres connected through an oxygen bridge, represented by the structure $\mathrm{HO-SO_2-O-SO_2-OH}$, which ensures that no sulphur-sulphur bond exists in the molecule.

The molecule $HF$ exhibits an unusually high boiling point compared to other hydrogen halides primarily because fluorine is highly electronegative, enabling the formation of strong hydrogen bonds between neighboring molecules. Unlike the weaker van der Waals forces found in other hydrogen halides, this potent electrostatic interaction creates a cohesive network that effectively traps the molecules in the liquid phase. Consequently, breaking these specialized attractions requires a much higher input of thermal energy, which directly elevates the boiling point.

Molecular Orbital Theory provides the necessary framework to evaluate the stability and magnetic behavior of diatomic molecules by analyzing the distribution of electrons within their energy orbitals. In the transformation from $\mathrm{NO}$ to $\mathrm{NO}^{+}$, an electron is removed from an antibonding orbital, which elevates the bond order from 2.5 to 3. This removal effectively pairs the remaining electrons, shifting the species from a paramagnetic state to a diamagnetic one.

The covalent character of metal halides is determined by Fajan's rule, which explains that smaller cations with higher charge density exert greater polarizing power on the surrounding anions. Because the $Be^{2+}$ ion is the smallest in the group, it strongly distorts the electron cloud of the halide, pulling it toward the nucleus and resulting in the formation of $BeX_2$ with significant covalent character. In contrast, larger ions like $Ca^{2+}$ and $Sr^{2+}$ lack the necessary charge density to induce such polarization, making their halides primarily ionic.

To determine the hybridization of the central xenon atom, we first account for its 8 valence electrons and its bonding environment in $XeOF_4$. Four fluorine atoms form single bonds, and 1 oxygen atom forms a double bond, contributing a total of 5 sigma bonds to the structure. This bonding configuration leaves 2 electrons behind as a single lone pair on the xenon atom, resulting in a total steric number of 6. Consequently, the arrangement corresponds to $sp^3d^2$ hybridization.

Determining the hybridization of a central atom involves calculating its steric number, which is the sum of its bonding pairs and lone pairs. For the $[ICl_4]^-$ ion, the central iodine atom is surrounded by 4 bonding pairs and 2 lone pairs, resulting in a total steric number of $4 + 2 = 6$. This specific configuration of electron domains corresponds directly to $sp^3d^2$ hybridization.

Magnetism in diatomic species is determined by the arrangement of electrons within molecular orbitals, where the presence of any unpaired electron results in paramagnetism, while a configuration of fully paired electrons signifies diamagnetism. The molecule $CO$ contains 14 electrons that completely fill all molecular orbitals up to the $\sigma_{2pz}$ level, ensuring that every electron is paired. In contrast, $B_2$, $O_2$, and $NO$ all possess unpaired electrons in their highest occupied molecular orbitals, which makes them paramagnetic.

Molecular Orbital Theory provides the basis for understanding how bonding electrons are distributed between sigma and pi molecular orbitals, which directly determines the nature of the bond order in a diatomic molecule. By calculating the difference between the number of bonding and antibonding electrons and dividing by two, we derive the bond order, which serves as a definitive measure of the strength and composition of the chemical bond in these species.

For $\mathrm{N}_2^{+}$, the bond order is 2.5, which is comprised of 2 pi bonds and 0.5 sigma bonds, fulfilling the specific condition required. By contrast, the $\mathrm{N}_2$ molecule exhibits a bond order of 3.0, consisting of 2 pi bonds and 1 sigma bond. Turning to the oxygen species, $\mathrm{O}_2^{+}$ features a bond order of 2.5 with 1.5 pi bonds and 1 sigma bond, while $\mathrm{O}_2$ has a bond order of 2, formed by 1 pi bond and 1 sigma bond. These distinctions confirm that $\mathrm{N}_2^{+}$ is the specific case possessing two pi bonds and half a sigma bond.

The primary difference between these molecules arises from the ability of the lone pair on the nitrogen atom to participate in $p\pi - d\pi$ back-bonding with the vacant $3d$ orbitals of the silicon atoms in $(\mathrm{SiH}_3)_3 \mathrm{N}$. This interaction imparts partial double-bond character to the Si-N bonds, forcing the molecule to adopt a planar structure rather than the pyramidal geometry found in $(\mathrm{CH}_3)_3 \mathrm{N}$, where such back-bonding cannot occur. Furthermore, because the lone pair on nitrogen is delocalized into the empty $3d$ orbitals of silicon, it is far less available for donation to an external Lewis acid, making $(\mathrm{SiH}_3)_3 \mathrm{N}$ substantially less basic than $(\mathrm{CH}_3)_3 \mathrm{N}$.

According to Molecular Orbital Theory, the electronic configuration of $\mathrm{O}_2$ involves filling molecular orbitals up to the degenerate antibonding levels, resulting in a configuration that ends with $(\pi^* 2p_x)^1 (\pi^* 2p_y)^1$. When an electron is added to form the superoxide ion $\mathrm{O}_2^{-}$, the Aufbau principle dictates that the incoming electron occupies the lowest energy orbital available, which corresponds to one of these partially filled antibonding orbitals. Consequently, the electron enters the $\pi^* 2p_x$ orbital to pair with the electron already present there.

Molecular geometry is determined by the Valence Shell Electron Pair Repulsion (VSEPR) theory, which dictates that the arrangement of atoms and lone pairs around a central atom is governed by the minimization of electron-pair repulsions. In the $NF_3$ molecule, the central nitrogen atom is surrounded by three bonding electron pairs and one lone pair, resulting in a steric number of four and a trigonal pyramidal geometry. Because trigonal planar geometry is only associated with a steric number of three involving three bonding pairs and zero lone pairs, the classification of $NF_3$ as trigonal planar is incorrect.

Covalent bonding relies on the mutual sharing of electrons between non-metal atoms, whereas ionic bonding arises from the electrostatic attraction between oppositely charged ions typically formed by a metal and a non-metal. Examining the provided list, $KCl$ consists of a potassium cation and a chloride anion held together purely by ionic interactions, making it the only compound that contains no covalent bonds. In contrast, $PH_3$, $O_2$, $B_2H_6$, and $H_2SO_4$ are all molecular compounds composed of non-metallic elements that necessarily involve the sharing of electron pairs to form covalent bonds.

Hybridization is determined by the steric number of the central atom, while molecular shape is dictated by the arrangement of bonding pairs and lone pairs around that atom. In the conversion of $\mathrm{BF}_3$ to $\mathrm{BF}_4^{-}$, the boron atom undergoes a change from $\mathrm{sp}^2$ hybridization with a trigonal planar shape to $\mathrm{sp}^3$ hybridization with a tetrahedral shape. The remaining options involve reactions where the hybridization of the central atom remains $\mathrm{sp}^3$ throughout the transformation.

The total number of electrons in the $\mathrm{N}_2^+$ ion is 13, calculated by subtracting one electron from the 14 electrons present in the neutral nitrogen molecule. For homonuclear diatomic molecules with atomic number less than or equal to 7, $s$-$p$ mixing lowers the energy of the $\sigma_{2pz}$ orbital relative to the $\pi$ orbitals, resulting in the energy sequence $\sigma_{1s} < \sigma_{1s}^* < \sigma_{2s} < \sigma_{2s}^* < \pi_{2px} = \pi_{2py} < \sigma_{2pz} < \pi_{2px}^* = \pi_{2py}^* < \sigma_{2pz}^*$. Distributing the 13 electrons according to the aufbau principle yields the configuration $\sigma_{1s}^2 \sigma_{1s}^{*2} \sigma_{2s}^2 \sigma_{2s}^{*2} \pi_{2px}^2 \pi_{2py}^2 \sigma_{2pz}^1$, which places 1 electron in the $\sigma_{2p}$ (or $\sigma_{2pz}$) molecular orbital.

Bond angle is primarily determined by the hybridization of the central atom and the extent of repulsion between lone pairs and bonding pairs, with linear geometries achieving the maximum angle of $180^\circ$. The ion $I_3^-$ adopts a linear geometry with a bond angle of $180^\circ$, followed by $BF_3$, which is $sp^2$ hybridized with a trigonal planar geometry and a bond angle of $120^\circ$. Among the remaining $sp^3$ hybridized molecules, $NH_3$ has a larger bond angle than $PF_3$ because the lower electronegativity of phosphorus compared to nitrogen increases the $p$-character of the $P-F$ bonds, leading to a tighter bond angle in $PF_3$ and resulting in the decreasing order $I_3^{-} > BF_3 > NH_3 > PF_3$.

The stability of diatomic molecular ions is determined by their bond order, calculated as half the difference between the number of bonding and antibonding electrons. While other helium-based species might exhibit electronic configurations that allow for some degree of interaction, the specific orbital filling pattern for $He^{2-}_2$ results in an unstable arrangement that does not support a bonded structure. Because this configuration fails to provide a net attractive force between the nuclei, $He^{2-}_2$ is not a viable molecule according to molecular orbital theory.