Question

The molecules \(\mathrm{SiF}_{4}, \mathrm{SF}_{4}\), and \(\mathrm{XeF}_{4}\) have molecular formulas of the type \(\mathrm{AF}_{4}\), but the molecules have different molecular geometries. Predict the shape of each molecule, and explain why the shapes differ.

Short answer

The molecular geometries of \(\mathrm{SiF}_{4}\), \(\mathrm{SF}_{4}\), and \(\mathrm{XeF}_{4}\) are tetrahedral, see-saw shaped, and square planar, respectively. These shapes differ due to the number of valence electrons, electron domain geometries, and the influence of lone pairs on the geometry of the molecules. The Si in \(\mathrm{SiF}_{4}\) has a tetrahedral geometry with all bonding pairs, while S in \(\mathrm{SF}_{4}\) has a trigonal bipyramidal geometry with one lone pair, forming a see-saw shape. In \(\mathrm{XeF}_{4}\), Xe has an octahedral geometry with two lone pairs, resulting in a square-planar molecular geometry.

Step-by-step solution

Determine the number of valence electrons

First, we need to find the number of valence electrons for each atom in the given molecules. For silicon (Si) in \(\mathrm{SiF}_{4}\): Si has 4 valence electrons. For sulfur (S) in \(\mathrm{SF}_{4}\): S has 6 valence electrons. For xenon (Xe) in \(\mathrm{XeF}_{4}\): Xe has 8 valence electrons. For fluorine (F): F has 7 valence electrons. (present in each molecule)

Determine the electron domain geometry (EDG)

Next, we determine the electron-domain geometry (EDG) for each central atom by adding up the valence electrons and dividing by 2 (since each bond requires two electrons). The EDG is determined by counting both bond electron pairs and lone (non-bond electron) pairs around the central atom. For \(\mathrm{SiF}_{4}\): Si has 4 valence electrons (from Step 1) and forms 4 single bonds with 4 F atoms. Thus, the total electron pairs = 4/2 = 2. The EDG is tetrahedral. For \(\mathrm{SF}_{4}\): S has 6 valence electrons (from Step 1) and forms 4 single bonds with 4 F atoms. Thus, the total electron pairs = (6 + 2)/2 = 4. The EDG is trigonal bipyramidal. For \(\mathrm{XeF}_{4}\): Xe has 8 valence electrons (from Step 1) and forms 4 single bonds with 4 F atoms. Thus, the total electron pairs = (8 + 4)/2 = 6. The EDG is octahedral.

Determine molecular geometry (MG)

Now we can predict the molecular geometry (MG) using the EDGs obtained in the previous step. For \(\mathrm{SiF}_{4}\): With tetrahedral electron domain geometry and no lone pairs, the molecular geometry is also tetrahedral. For \(\mathrm{SF}_{4}\): With trigonal bipyramidal electron domain geometry and one lone pair, the molecular geometry is see-saw shaped. For \(\mathrm{XeF}_{4}\): With octahedral electron domain geometry and two lone pairs, the molecular geometry is square planar.

Explain the differences in molecular geometries

Finally, we can explain the differences in molecular geometries by analyzing the electron domain geometries and how the lone pairs affect the geometries of the molecules. For \(\mathrm{SiF}_{4}\), a tetrahedral geometry where all electron pairs are bonding pairs results in a tetrahedral molecular geometry. For \(\mathrm{SF}_{4}\), the trigonal bipyramidal geometry has one lone pair, which repels the other electron domains, distorting the geometry and resulting in a see-saw shaped molecular geometry. For \(\mathrm{XeF}_{4}\), the octahedral geometry has two lone pairs, which repel the other electron domains, resulting in a square-planar molecular geometry. In conclusion, the different molecular geometries of \(\mathrm{SiF}_{4}\), \(\mathrm{SF}_{4}\), and \(\mathrm{XeF}_{4}\) are due to the number of valence electrons, electron domain geometries, and how lone pairs influence the geometry of the molecules.