Give the electron-domain and molecular geometries for the following molecules and ions: (a) \(\mathrm{HCN},(\mathbf{b}) \mathrm{SO}_{3}^{2-},(\mathbf{c}) \mathrm{SF}_{4}\) \((\mathbf{d}) \mathrm{PF}_{6},(\mathbf{e}) \mathrm{NH}_{3} \mathrm{Cl}^{+},(\mathbf{f}) \mathrm{N}_{3}^{-}\)

First, we identify the central atom in each molecule or ion. Then, we will count the number of bonding and non-bonding electron pairs (domains) surrounding the central atom. (a) HCN - Central atom: C C has 3 electron domains (1 single bond with H, 1 triple bond with N) (b) \(\mathrm{SO}_{3}^{2-}\) - Central atom: S S has 4 electron domains (3 double bonds with O, 1 lone pair) (c) \(\mathrm{SF}_{4}\) - Central atom: S S has 5 electron domains (4 single bonds with F, 1 lone pair) (d) \(\mathrm{PF}_{6}\) - Central atom: P P has 6 electron domains (6 single bonds with F) (e) \(\mathrm{NH}_{3}\mathrm{Cl}^{+}\) - Central atom: N N has 4 electron domains (3 single bonds with H, 1 coordinate covalent bond with Cl) (f) \(\mathrm{N}_{3}^{-}\) - Central atom: N (middle nitrogen, index 2) N has 3 electron domains (1 single bond with \(N_{1}\), 1 triple bond with \(N_{3}\))

Using the number of electron domains found in step 1, we can determine the electron-domain geometry of each molecule or ion. (a) HCN: 3 domains - Trigonal planar (b) \(\mathrm{SO}_{3}^{2-}\): 4 domains - Tetrahedral (c) \(\mathrm{SF}_{4}\): 5 domains - Trigonal bipyramidal (d) \(\mathrm{PF}_{6}\): 6 domains - Octahedral (e) \(\mathrm{NH}_{3}\mathrm{Cl}^{+}\): 4 domains - Tetrahedral (f) \(\mathrm{N}_{3}^{-}\): 3 domains - Trigonal planar

Now we can determine the molecular geometries of each molecule or ion, considering the positions of bonded atoms and lone pairs: (a) HCN: 3 domains, 0 lone pairs - Linear (b) \(\mathrm{SO}_{3}^{2-}\): 4 domains, 1 lone pair - Trigonal pyramidal (c) \(\mathrm{SF}_{4}\): 5 domains, 1 lone pair - See-saw (d) \(\mathrm{PF}_{6}\): 6 domains, 0 lone pairs - Octahedral (e) \(\mathrm{NH}_{3}\mathrm{Cl}^{+}\): 4 domains, 0 lone pairs - Tetrahedral (f) \(\mathrm{N}_{3}^{-}\): 3 domains, 0 lone pairs - Linear So, the electron-domain and molecular geometries for the given molecules and ions are as follows: (a) HCN: Electron-Domain Geometry - Trigonal planar, Molecular Geometry - Linear (b) \(\mathrm{SO}_{3}^{2-}\): Electron-Domain Geometry - Tetrahedral, Molecular Geometry - Trigonal pyramidal (c) \(\mathrm{SF}_{4}\): Electron-Domain Geometry - Trigonal bipyramidal, Molecular Geometry - See-saw (d) \(\mathrm{PF}_{6}\): Electron-Domain Geometry - Octahedral, Molecular Geometry - Octahedral (e) \(\mathrm{NH}_{3}\mathrm{Cl}^{+}\): Electron-Domain Geometry - Tetrahedral, Molecular Geometry - Tetrahedral (f) \(\mathrm{N}_{3}^{-}\): Electron-Domain Geometry - Trigonal planar, Molecular Geometry - Linear