Chemical Bonding and Molecular Structure, on the exam screen.

Ethene ($\mathrm{C}_{2}\mathrm{H}_{4}$) has 4 C-H plus 1 C-C sigma bonds (5 sigma) and 1 pi bond (IV). Ethyne ($\mathrm{C}_{2}\mathrm{H}_{2}$) has 2 C-H plus 1 C-C sigma (3 sigma) and 2 pi bonds (I). Methane ($\mathrm{CH}_{4}$) has 4 C-H sigma bonds (III). Ammonia ($\mathrm{NH}_{3}$) has 3 N-H sigma bonds and one lone pair on nitrogen (II). Hence P-IV, Q-I, R-III, S-II.

Formal charge = (valence electrons) $-$ (non-bonding electrons) $-\frac{1}{2}$(bonding electrons). For the doubly bonded terminal O (atom 2): $6-4-\frac{1}{2}(4)=0$; the central O (atom 1): $6-2-\frac{1}{2}(6)=+1$; the singly bonded terminal O (atom 3): $6-6-\frac{1}{2}(2)=-1$. This gives 0, +1, $-1$, matching option (2).

$\mathrm{PCl}_{5}$ has five bond pairs and no lone pair, so it is trigonal bipyramidal (P-III). $\mathrm{BrF}_{5}$ has five bond pairs plus one lone pair; the lone pair occupies one octahedral position and pushes the shape to square pyramidal (Q-IV). $\mathrm{BF}_{4}^-$ is four bond pairs with no lone pair, hence tetrahedral (R-I). $[\mathrm{Ni}(\mathrm{CN})_{4}]^{2-}$ is a $\mathrm{Ni}^{2+}$ $d^8$ complex with the strong-field cyanide ligand, forcing $dsp^2$ hybridisation and a square planar geometry (S-II). NCERT Class 11, Chemical Bonding and Molecular Structure; NCERT Class 12, Coordination Compounds.

$\mathrm{Ne}_{2}$ has 20 electrons, enough to fill every molecular orbital derived from the 1s, 2s and 2p atomic orbitals. Filling in order, $\sigma_{1s}^2\sigma^{*}_{1s}{}^2\sigma_{2s}^2\sigma^{*}_{2s}{}^2\sigma_{2p}^2\pi_{2p}^4\pi^{*}_{2p}{}^4\sigma^{*}_{2p}{}^2$, the last two electrons enter $\sigma^{*}_{2p}$, which is therefore the HOMO. With every bonding orbital matched by its antibonding partner the bond order is zero, which is why $\mathrm{Ne}_{2}$ does not exist as a stable molecule. NCERT Class 11, Chemical Bonding and Molecular Structure.

Boron trifluoride, beryllium difluoride, and carbon dioxide have symmetrical structures leading to zero net dipole moments. 1,4-dichlorobenzene also has a symmetrical structure, making the net dipole moment zero. Chapter: Chemical Bonding and Molecular Structure.

$\mathrm{He}_{2}$ does not exist because helium atoms have a complete outer shell and do not form stable bonds with each other. In contrast, $\mathrm{Li}_{2}$, $\mathrm{C}_{2}$, and $\mathrm{O}_{2}$ can form stable molecules. Chapter: Chemical Bonding and Molecular Structure.