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To predict the molecular structures, first, we need to determine the total number of valence electrons for each molecule using the periodic table. a. In \(\mathrm{PCl}_{3}\), P has 5 valence electrons and Cl has 7. So we have (1x5) + (3x7) = 26 valence electrons. b. In \(\mathrm{SCl}_{2}\), S has 6 valence electrons and Cl has 7. So we have (1x6) + (2x7) = 20 valence electrons. c. In \(\mathrm{SiF}_{4}\), Si has 4 valence electrons and F has 7. So we have (1x4) + (4x7) = 32 valence electrons.

Next, we will arrange the atoms and connect them with single bonds using the valence electrons. a. In \(\mathrm{PCl}_{3}\), P is the central atom, and it is surrounded by three Cl atoms. After creating the single bonds, we are left with 20 valence electrons. b. In \(\mathrm{SCl}_{2}\), S is the central atom, and it is surrounded by two Cl atoms. After creating the single bonds, we are left with 16 valence electrons. c. In \(\mathrm{SiF}_{4}\), Si is the central atom, and it is surrounded by four F atoms. After creating the single bonds, we are left with 24 valence electrons.

We will now distribute the remaining valence electrons to each atom as lone pairs to satisfy the octet rule (8 electrons in each element's outer shell). a. In \(\mathrm{PCl}_{3}\), after distributing the remaining 20 valence electrons, each Cl atom has 3 lone pairs, and P has one lone pair. b. In \(\mathrm{SCl}_{2}\), after distributing the remaining 16 valence electrons, each Cl atom has 3 lone pairs, and S has two lone pairs. c. In \(\mathrm{SiF}_{4}\), after distributing the remaining 24 valence electrons, each F atom has 3 lone pairs, and Si has no lone pairs because it is already in an octet configuration with its four single bonds.

Now, we will identify the molecular geometry and bond angles using the VSEPR theory. a. \(\mathrm{PCl}_{3}\): P has a total of 4 electron groups (3 single bonds and 1 lone pair), so its electronic geometry is tetrahedral. Since one of the electron regions is a lone pair, the molecular geometry is trigonal pyramidal. The bond angle in a tetrahedral is \(109.5^{\circ}\), but, in a trigonal pyramidal, the bond angle will be slightly less due to lone pair repulsion. b. \(\mathrm{SCl}_{2}\): S has a total of 4 electron groups (2 single bonds and 2 lone pairs), so its electronic geometry is tetrahedral. Since two of the electron regions are lone pairs, the molecular geometry is bent or V-shaped. The bond angle in a tetrahedral is \(109.5^{\circ}\), but, in a bent molecule with two lone pairs, the bond angle will be even further reduced due to greater lone pair repulsion. c. \(\mathrm{SiF}_{4}\): Si has a total of 4 electron groups (4 single bonds and no lone pairs), so its electronic geometry is tetrahedral. Since there are no lone pairs, the molecular geometry is also tetrahedral, and the bond angle is \(109.5^{\circ}\). In summary, the molecular structures and bond angles are: a. \(\mathrm{PCl}_{3}\): trigonal pyramidal, bond angle slightly less than \(109.5^{\circ}\) b. \(\mathrm{SCl}_{2}\): bent (or V-shaped), bond angle significantly less than \(109.5^{\circ}\) c. \(\mathrm{SiF}_{4}\): tetrahedral, bond angle of \(109.5^{\circ}\)