Question

(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 \(_{6}^{-}\)

Short answer

(a) The electron-domain geometries around the central Xe atom in XeF2, XeF4, and XeF6 are trigonal bipyramidal, octahedral, and octahedral, respectively. (b) The molecular geometry of IF6- is pentagonal bipyramidal.

Step-by-step solution

(1) Determine the number of electron domains around the central atom in each molecule.

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.

(2) Predict the electron-domain geometries around the central atom in each molecule.

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.

(3) Predict the molecular geometry of IF6-.

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.

Key concepts

Electron-Domain Geometry

To understand electron-domain geometry, it's essential to know that this concept involves the arrangement of electron pairs around a central atom in a molecule. Each electron pair, whether it's a bonding pair or a lone pair, is considered an electron domain. Count both the bonded atoms and lone pairs to find the number of electron domains.
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Using VSEPR (Valence Shell Electron Pair Repulsion) theory, electron domains arrange themselves to minimize repulsion, determining the overall shape. For example, in \( ext{XeF}_2\), there are 5 electron domains around the central Xenon (Xe) atom, including two bonded pairs (from fluorine atoms) and three lone pairs, resulting in a trigonal bipyramidal arrangement at the electron-domain level.
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Similarly, in \( ext{XeF}_4\) and \( ext{XeF}_6\), the total electron domains are 6, leading to octahedral electron-domain geometries. Remember, it's all about minimizing repulsion between these domains, which influences the spatial arrangement around the central atom.

Trigonal Bipyramidal

The trigonal bipyramidal geometry is a specific arrangement occurring when there are 5 electron domains around a central atom. This geometry is characterized by three atoms in a plane, equidistant around the central atom, forming a triangle, with two more atoms positioned above and below the plane.
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As seen in the molecule \( ext{XeF}_2\), although there are only two fluorine atoms bonded to Xenon, the three lone pairs take the equatorial positions. Lone pairs spread out more than bonding pairs, which is why they occupy equatorial positions, reducing repulsion effectively. The result is that the molecular shape we identify as linear, but under VSEPR-oriented electron-domain geometry, it's trigonal bipyramidal.
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It's fascinating how lone pairs influence geometry so greatly, often leading to non-intuitive shapes in the molecule that reflect fundamental principles of molecular interactions.

Octahedral Geometry

Octahedral geometry arises when there are 6 electron domains around a central atom. This is a symmetrical shape where each of the six domains forms a vertex of an octahedron, often leading to a very balanced distribution of electron pairs.
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For both \( ext{XeF}_4\) and \( ext{XeF}_6\), the central Xenon atom exhibits an octahedral electron-domain geometry with these 6 domains. In \( ext{XeF}_4\), two lone pairs sit opposite one another on the octahedron, influencing the molecule's square planar shape. Conversely, \( ext{XeF}_6\) has used all eight valence electrons in bonding, achieving a regular octahedral shape devoid of lone pairs. Thus, no extra lone pair manipulates the symmetric distribution.
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The octahedral shape reflects an efficient and low-energy configuration, ideal for accommodating multiple electron domains with minimal repulsion.

Pentagonal Bipyramidal Geometry

The pentagonal bipyramidal geometry occurs when a central atom accommodates 7 electron domains. This configuration sees five domains forming a planar pentagon around the central atom, and the remaining two positioned axially, one above and one below the plane.
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In the case of \(\text{IF}_6^-\), the iodine atom at the center forms bonds with six fluorine atoms and has one lone pair. This lone pair is vital in defining geometry as the electron domains fight for space in a configuration that minimizes their repulsion. It's impressive how such specific geometric arrangements can dictate molecular function and reactivity.
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Complex molecules like \(\text{IF}_6^-\) showcase the beauty of VSEPR theory in predicting and explaining molecular structures through electron-domain geometry. Organic and inorganic chemists rely heavily on these principles to infer the potential behaviors and reactions of molecules in experimental and theoretical scenarios.