Question

Consider the following \(\mathrm{XF}_{4}\) ions: \(\mathrm{PF}_{4}^{-}, \mathrm{BrF}_{4}^{-}, \mathrm{ClF}_{4}^{+}\), and \(\mathrm{AlF}_{4}^{-}\). (a) Which of the ions have more than an octet of electrons around the central atom? (b) For which of the ions will the electrondomain and molecular geometries be the same? (c) Which of the ions will have an octahedral electron-domain geometry? (d) Which of the ions will exhibit a see-saw molecular geometry?

Short answer

(a) More than an octet of electrons around the central atom: \(\mathrm{PF}_{4}^{-}\), \(\mathrm{BrF}_{4}^{-}\), and \(\mathrm{ClF}_{4}^{+}\). (b) Same electron-domain and molecular geometries: \(\mathrm{AlF}_{4}^{-}\) (tetrahedral). (c) Octahedral electron-domain geometry: \(\mathrm{BrF}_{4}^{-}\). (d) See-saw molecular geometry: \(\mathrm{PF}_{4}^{-}\) and \(\mathrm{ClF}_{4}^{+}\).

Step-by-step solution

Determining the electron-domain geometries and molecular geometries of the given ions

For each ion, first calculate the total number of valence electrons, and then determine the electron-domain geometry and molecular geometry. Use VSEPR theory to predict the geometries. 1. \(\mathrm{PF}_{4}^{-}\): P has 5 valence electrons, each F atom has 7, and the negative charge adds an additional electron. The total valence electron count is 5 + 4(7) + 1 = 33. P is surrounded by 4 bonding electron pairs and 1 lone pair, resulting in an electron-domain geometry of trigonal bipyramidal and a molecular geometry of see-saw. 2. \(\mathrm{BrF}_{4}^{-}\): Br has 7 valence electrons, each F atom has 7, and the negative charge adds an additional electron. The total valence electron count is 7 + 4(7) + 1 = 36. Br is surrounded by 4 bonding electron pairs and 2 lone pairs, resulting in an electron-domain geometry of octahedral and a molecular geometry of square planar. 3. \(\mathrm{ClF}_{4}^{+}\): Cl has 7 valence electrons, each F atom has 7, and the positive charge reduces an electron. The total valence electron count is 7 + 4(7) - 1 = 34. Cl is surrounded by 4 bonding electron pairs and 1 lone pair, resulting in an electron-domain geometry of trigonal bipyramidal and a molecular geometry of see-saw. 4. \(\mathrm{AlF}_{4}^{-}\): Al has 3 valence electrons, each F atom has 7, and the negative charge adds an additional electron. The total valence electron count is 3 + 4(7) + 1 = 31. Al is surrounded by 4 bonding electron pairs with no lone pairs, resulting in an electron-domain geometry of tetrahedral and a molecular geometry of tetrahedral. Now we can use this information to answer each part of the problem.

Part (a) - Identifying ions with more than an octet of electrons around the central atom

Review the electron-domain geometries of the given ions and determine which ones have more than 8 electrons around the central atom. Remember, the octet rule states that atoms tend to achieve an electron configuration of the nearest noble gas, with 8 electrons. With an odd number of valence electrons (33, 36, and 34 for \(\mathrm{PF}_{4}^{-}\), \(\mathrm{BrF}_{4}^{-}\), and \(\mathrm{ClF}_{4}^{+}\), respectively), these ions naturally exceed the octet rule around the central atom. Therefore, the ions with more than an octet of electrons around the central atom are \(\mathrm{PF}_{4}^{-}\), \(\mathrm{BrF}_{4}^{-}\), and \(\mathrm{ClF}_{4}^{+}\).

Part (b) - Identifying ions with the same electron-domain and molecular geometries

Review the molecular and electron-domain geometries from Step 1 and determine which ions have the same geometries in both cases. The \(\mathrm{AlF}_{4}^{-}\) ion has a tetrahedral electron-domain geometry and molecular geometry, so it is the only ion with the same geometries in both cases.

Part (c) - Identifying ions with an octahedral electron-domain geometry

Review the electron-domain geometries from Step 1 and determine which ions have an octahedral electron-domain geometry. The \(\mathrm{BrF}_{4}^{-}\) ion has an octahedral electron-domain geometry.

Part (d) - Identifying ions with a see-saw molecular geometry

Review the molecular geometries from Step 1 and determine which ions exhibit a see-saw molecular geometry. Both the \(\mathrm{PF}_{4}^{-}\) and \(\mathrm{ClF}_{4}^{+}\) ions have a see-saw molecular geometry.

Key concepts

Electron-Domain Geometry

Understanding the electron-domain geometry is pivotal for predicting the shapes of molecules. This concept refers to the arrangement around a central atom of all regions of electron density (bonding pairs and lone pairs of electrons). According to the Valence Shell Electron Pair Repulsion (VSEPR) theory, electron clouds around the central atom will repulse each other, and this repulsion leads to the arrangement that minimizes the energy of the molecule.

The electron-domain geometries are based on the number of electron pairs surrounding a central atom. For example, with two electron domains, the geometry will be linear; with three, it'll be trigonal planar; with four, the geometry can be tetrahedral, and so forth. The presence of lone pairs influences the overall shape since they occupy more space than bonding pairs, resulting in different molecular geometries even if the electron-domain geometries are the same.

Molecular Geometry

Differing slightly from electron-domain geometry, molecular geometry refers to the spatial arrangement of only the bonding pairs of electrons, or how a molecule’s atoms are positioned. Even though VSEPR theory starts with the electron-domain geometry, for determining molecular geometry we consider only the position of the atoms and ignore the lone pairs of electrons.

Visualizing Shapes in 3D Space

When there are no lone pairs on the central atom, the electron-domain geometry and molecular geometry will be the same. In cases where lone pairs are present, the molecular geometry will adjust. For instance, while a tetrahedral electron-domain geometry might lead one to expect a molecular shape that matches, the presence of one lone pair will alter that molecular geometry to become trigonal pyramidal.

Octet Rule

The octet rule is a chemical rule of thumb that reflects the observation that atoms of main-group elements tend to bond in such a way that each atom ends up with eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. This rule helps explain the ratios in which atoms combine to form compounds and why certain atoms follow or do not follow this rule.

There are exceptions to the rule, typically involving molecules with an odd number of electrons, molecules in which one or more atoms possess more or fewer than eight electrons, and molecules with central atoms in period three or below on the periodic table which can have more than eight valence electrons. Elements capable of having more than eight valence electrons are often referred to as having an 'expanded octet'.

Valence Electrons

Valence electrons are the electrons present in the outermost shell of an atom. They are of utmost importance as they play a key role in chemical reactions and bonding. The number of valence electrons determines an element's chemical properties and how it behaves in a chemical reaction.

Understanding via Periodic Table Groupings

The periodic table arrangement aligns with the number of valence electrons in each group (vertical columns). For instance, all the elements in group 1 have one valence electron, while group 2 elements have two valence electrons. Transition metals are more complex, but generally, the main-group elements adhere to this rule. Valence electrons are used to predict the types of chemical bonds an atom might form and are crucial in determining the geometry of a molecule as described by VSEPR theory.