Problem 69 - Chemistry The Science in Context

Question

The trifluorosulfate anion was isolated in 1999 as the tetramethylammonium salt \(\left[\left(\mathrm{CH}_{3}\right)_{4} \mathrm{N}\right]^{+}\left[\mathrm{SO}_{2} \mathrm{F}_{3}\right]^{-}.\) a. Determine the geometry around the nitrogen atom in the cation and describe the \(C-N\) bonding according to valence bond theory. b. The \(S-O\) bond lengths in the anion are both \(143 \mathrm{pm}\). Draw the Lewis structure that is consistent with this bond length. c. What is the molecular geometry of the anion?

Step-by-Step Solution

Answer

b) Draw the Lewis structure for the trifluorosulfate anion using the given S-O bond lengths. c) What is the molecular geometry of the trifluorosulfate anion?

Step 1: a. Geometry around Nitrogen atom and CN bonding description

First, let's analyze the tetramethylammonium cation $\left(\left(\mathrm{CH}_{3}\right)_{4} \mathrm{N}\right)^{+}$. To identify the geometry around the nitrogen atom, we need to determine the number of electron domains surrounding it. An electron domain can be either a bonding pair of electrons (bond to another atom) or a lone pair of electrons. The nitrogen atom is bonded to four carbon atoms, so it has four bonding electron pairs with no lone pairs. According to the Valence Shell Electron Pair Repulsion Theory (VSEPR), four electron domains will give a tetrahedral geometry around the N atom. So, the nitrogen atom has a tetrahedral geometry. Using valence bond theory, we see that the \(C-N\) bonds are formed by overlapping of sp³-hybrid orbitals on the nitrogen atom with the s-orbitals of the hydrogens on the carbon atoms.

Step 2: b. Drawing the Lewis structure of the anion

Now let's analyze the trifluorosulfate anion, \(\mathrm{SO}_{2} \mathrm{F}_{3}^{-}\). First, we need to sum the total number of valence electrons; sulfur has 6, each oxygen has 6, each fluorine has 7, and there is an additional electron because of the negative charge. Adding these gives us a total of 32 valence electrons. A possible Lewis structure consistent with the SO bond length of 143 pm is to consider sulfur as the central atom double bonded to each of the two oxygen atoms and single bonded to each of the three fluorine atoms. This structure will fulfill the octet rule for all atoms: O=S=F | | F F Each double bond to oxygen uses 4 electrons, and each single bond to fluorine uses 2 electrons, resulting in the usage of all 32 available electrons.

Step 3: c. Molecular geometry of the anion

To determine the molecular geometry of \(\mathrm{SO}_{2} \mathrm{F}_{3}^{-}\), we need to count the number of electron domains surrounding the central sulfur atom. In the Lewis structure created in step b, sulfur is double bonded to two oxygen atoms and singly bonded to three fluorine atoms. This results in five electron domains around the sulfur atom. Since there are no lone pairs on sulfur, these five electron domains result in a trigonal bipyramidal geometry for the trigonal bipyramidal geometry.

Key Concepts

VSEPR Theory in Practice

Understanding the shape of molecules is crucial in chemistry, and Valence Shell Electron Pair Repulsion (VSEPR) theory offers a handy tool for predicting molecular geometry. It's based on the principle that electron pairs around a central atom will repel each other and, as a result, will arrange themselves as far apart as possible in three dimensions. This naturally leads to specific geometric arrangements.

For example, when a central atom is surrounded by four pairs of bonding electrons—such as with the nitrogen atom in a tetramethylammonium cation—the electrons will repel each other equally in all directions and settle at the corners of an imaginary tetrahedron, creating what's known as a tetrahedral molecular geometry.

Crafting the Lewis Structure

The Lewis structure is a two-dimensional diagram that shows how the atoms in a molecule are connected and where the electrons are distributed. To draw a correct Lewis structure, start by counting all the valence electrons available (from each atom and any charge on the molecule).

Then, arrange the atoms with the least electronegative atom typically in the center (except hydrogen, which is almost always on the outside), and distribute the electrons to form bonds while satisfying the octet rule—where applicable. For the trifluorosulfate anion, we place sulfur in the center, form bonds with oxygen and fluorine, and use double bonds between sulfur and oxygen to represent the shared electron pairs, all while ensuring all the 32 valence electrons are accounted for.

Determining Molecular Geometry

Once we know how atoms are bound together from the Lewis structure, we can use VSEPR theory to predict the molecular geometry. This is done by recognizing the shapes associated with different counts of electron domains (regions of electron density like bonds or lone pairs). A molecule like \(\mathrm{SO}_{2} \mathrm{F}_{3}^{-}\), which has a central atom with five regions of electron density but no lone pairs, will adopt a trigonal bipyramidal shape. This geometry features a triangle in one plane with two additional atoms above and below the central atom, resembling two pyramids attached at the base.

Becoming familiar with these concepts enables us to visualize and predict the structure of complex molecules, which is essential for understanding chemical reactions and properties.