Which among the following molecules is
(a) involved in mathrmsp^3d$\mathrm{sp^3d}$ hybridization,
(b) has different bond lengths and
(c) has lone pair of electrons on the central atom?
A.mathrmPF_5$\mathrm{PF}_5$
B.mathrmXeF_4$\mathrm{XeF}_4$
C.mathrmSF_4$\mathrm{SF}_4$
D.mathrmXeF_2$\mathrm{XeF}_2$
Solution & Explanation
### Related Formula
textSteric Number = frac12 left( V + M - C + A right)$$\text{Steric Number} = \frac{1}{2} \left( V + M - C + A \right)$$
where,
V$V$ = valence electrons of central atom
M$M$ = number of monovalent surrounding atoms
C$C$ = cationic charge, A$A$ = anionic charge
### Core Logic
Let's calculate the hybridization, shape, and lone pairs for each option:
1. mathrmPF_5$\mathrm{PF}_5$:VSEPR Theory and Hybridization
- Central atom: Phosphorus (V=5$V=5$).
- Steric Number = frac12(5 + 5) = 5 implies mathrmsp^3d$= \frac{1}{2}(5 + 5) = 5 \implies \mathrm{sp^3d}$ hybridization.
- Lone pairs = 5 - 5 = 0$= 5 - 5 = 0$.
- Geometry: Trigonal bipyramidal. It has different axial and equatorial bond lengths, but no lone pair on the central atom.
2. mathrmXeF_4$\mathrm{XeF}_4$:
- Central atom: Xenon (V=8$V=8$).
- Steric Number = frac12(8 + 4) = 6 implies mathrmsp^3d^2$= \frac{1}{2}(8 + 4) = 6 \implies \mathrm{sp^3d^2}$ hybridization (fails condition a).
3. mathrmSF_4$\mathrm{SF}_4$:VSEPR Theory and Hybridization
- Central atom: Sulfur (V=6$V=6$).
- Steric Number = frac12(6 + 4) = 5 implies mathrmsp^3d$= \frac{1}{2}(6 + 4) = 5 \implies \mathrm{sp^3d}$ hybridization.
- Lone pairs = 5 - 4 = 1$= 5 - 4 = 1$ lone pair on sulfur.
- Shape: See-saw. It contains axial and equatorial bonds which have distinct lengths (1.64~mathrmmathringA$1.64~\mathrm{\mathring{A}}$ vs 1.54~mathrmmathringA$1.54~\mathrm{\mathring{A}}$ due to lone pair-bond pair repulsion). This satisfies all three conditions.
4. mathrmXeF_2$\mathrm{XeF}_2$:
- Central atom: Xenon (V=8$V=8$).
- Steric Number = frac12(8 + 2) = 5 implies mathrmsp^3d$= \frac{1}{2}(8 + 2) = 5 \implies \mathrm{sp^3d}$ hybridization.
- Lone pairs = 5 - 2 = 3$= 5 - 2 = 3$ lone pairs on Xe.
- Shape: Linear. Both Xe-F bonds are identical in length (fails condition b).
VSEPR Theory and Hybridization
### Step 1: Conclusion
Hence, only mathrmSF_4$\mathrm{SF}_4$ satisfies all the given parameters.
### Pattern Recognition
For any trigonal bipyramidal molecular geometry (steric number 5), the axial bonds suffer more repulsion (from 3 equatorial bonds at 90^circ$90^\circ$) than the equatorial bonds (which have only 2 axial neighbors at 90^circ$90^\circ$). Consequently, the axial bonds are always longer and weaker than equatorial bonds.
### Evaluation Rubric / Model Answer
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### Chapter Mix
Class 11 Chemistry: Chemical Bonding and Molecular Structure
More Chemical Bonding and Molecular Structure Previous-Year Questions — Page 7
Q85jee_main_2024_31_jan_morningHybridization
The number of species from the following in which the central atom uses sp^3$sp^3$ hybrid orbitals in its bonding is
NH_3, SO_2, SiO_2, BeCl_2, CO_2, H_2O, CH_4, BF_3$NH_3, SO_2, SiO_2, BeCl_2, CO_2, H_2O, CH_4, BF_3$
Numerical Answer.Answer: 4 to 4
Solution
### Core Logic
Analyzing the hybridization of the central atom in each species:
- NH_3$NH_3$: 3 bp + 1 lp = 4 electron domains rightarrow sp^3$\rightarrow sp^3$
- SO_2$SO_2$: 2 bp + 1 lp = 3 electron domains rightarrow sp^2$\rightarrow sp^2$
- SiO_2$SiO_2$: A giant covalent network where each Si is bonded to 4 oxygens tetrahedrally rightarrow sp^3$\rightarrow sp^3$
- BeCl_2$BeCl_2$: 2 bp + 0 lp = 2 electron domains rightarrow sp$\rightarrow sp$
- CO_2$CO_2$: 2 bp + 0 lp = 2 electron domains rightarrow sp$\rightarrow sp$
- H_2O$H_2O$: 2 bp + 2 lp = 4 electron domains rightarrow sp^3$\rightarrow sp^3$
- CH_4$CH_4$: 4 bp + 0 lp = 4 electron domains rightarrow sp^3$\rightarrow sp^3$
- BF_3$BF_3$: 3 bp + 0 lp = 3 electron domains rightarrow sp^2$\rightarrow sp^2$
Total species with sp^3$sp^3$ hybridization: NH_3, SiO_2, H_2O, CH_4$NH_3, SiO_2, H_2O, CH_4$. Total count = 4.
### Evaluation Rubric / Model Answer
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### Chapter Mix
Class 11 Chemistry: Chemical Bonding and Molecular Structure
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