(a) Predict the electron-domain geometry around the central Xe atom in \(\mathrm{XeF}_{2}, \mathrm{XeF}_{4}\) , and \(\mathrm{XeF}_{6}\) . (b) The molecule IF has a pentagonal bipyramid structure: five fluorines are equatorial, forming a flat pentagon around the central iodine atom, and the other two fluorines are axial. Predict the molecular geometry of IF \(_{6}^{-}\)

To predict the electron-domain geometry around a central atom, start by counting the number of electron domains. To do this, count the number of bonded atoms and lone pairs of electrons on the central atom. (a) For XeF2, XeF4, and XeF6: - In XeF2, Xe is bonded to two F atoms. We know that Xe has 8 valence electrons, so after forming two single bonds with F atoms, it will have 3 lone pairs remaining. Therefore, there are a total of 5 electron domains around the central Xe atom. - In XeF4, Xe is bonded to four F atoms. After forming these 4 single bonds, Xe has 2 lone pairs remaining. Thus, there are a total of 6 electron domains around the central Xe atom. - In XeF6, Xe is bonded to six F atoms. As Xe has used all of its 8 valence electrons for bonding, it has no lone pairs left. Hence, there are a total of 6 electron domains around the central Xe atom. (b) For IF6-: - In IF6-, I is bonded to six F atoms. The iodine atom has one additional electron due to the negative charge. Hence, after forming six single bonds with F atoms, I has one lone pair remaining. Thus, there are a total of 7 electron domains around the central I atom.

Now that we know the number of electron domains around the central atom in each molecule, we can use VSEPR theory to predict their electron-domain geometries. Electron domains will arrange themselves in such a way that they minimize repulsion and maximize their distances from one another. (a) For XeF2, XeF4, and XeF6: - XeF2: With 5 electron domains around the central Xe atom, this molecule has a trigonal bipyramidal electron-domain geometry. - XeF4: With 6 electron domains around the central Xe atom, this molecule has an octahedral electron-domain geometry. - XeF6: With 6 electron domains around the central Xe atom, this molecule also has an octahedral electron-domain geometry. (b) For IF6-: With 7 electron domains around the central I atom, this molecule has a pentagonal bipyramidal electron-domain geometry.

Since we now know the electron-domain geometry of IF6-, we can predict its molecular geometry by considering the positions of the bonded atoms. In this molecule, 5 F atoms are in the equatorial plane, forming a flat pentagon around the central iodine atom, and the remaining 2 F atoms are above and below the iodine in an axial arrangement. As a result, the overall molecular geometry of the IF6- ion is pentagonal bipyramidal.