The shape of a molecule is not merely an interesting detail; it dictates how the substance interacts with others, influencing properties like polarity and reactivity. To determine the three-dimensional arrangement of atoms in a molecule like sulfur tetrafluoride (\(\text{SF}_4\)), chemists use the Valence Shell Electron Pair Repulsion (VSEPR) theory. This theory is built on the principle that electron groups around a central atom will arrange themselves to minimize repulsion, thus leading to the most stable geometry. Applying this process to \(\text{SF}_4\) first requires calculating the valence electrons and creating its Lewis structure.
Calculating Valence Electrons and the Lewis Structure
The first step is to calculate the total number of valence electrons contributed by all atoms in the compound. Sulfur (\(\text{S}\)) provides 6 valence electrons, and the four fluorine (\(\text{F}\)) atoms contribute 7 each. This calculation results in a total of \(6 + (4 \times 7) = 34\) valence electrons available to form the bonds and lone pairs in the \(\text{SF}_4\) molecule.
Sulfur is designated as the central atom because it is the less electronegative element compared to fluorine. Connecting the four fluorine atoms with single covalent bonds uses 8 of the total 34 valence electrons. The remaining 26 electrons are distributed to the fluorine atoms to complete their octets, using 24 electrons total.
Two valence electrons remain after satisfying the fluorine octets. Since sulfur is in the third period of the periodic table, it is capable of expanding its octet, meaning it can accommodate more than eight electrons in its valence shell. These final two electrons form a single lone pair on the central sulfur atom. The resulting Lewis structure shows sulfur with four single bonds and one lone pair, totaling five electron groups.
Defining Electron Domains Using VSEPR Theory
VSEPR theory states that the geometry around a central atom is determined by the number of electron domains, which are regions of high electron density. An electron domain can be a single bond, a multiple bond, or a non-bonding lone pair of electrons; each counts as one domain. The Lewis structure of sulfur tetrafluoride reveals that the central sulfur atom is surrounded by four bonding pairs and one lone pair.
Counting these electron regions gives a total of five electron domains around the central sulfur atom. These five domains will repel each other and spread out in three-dimensional space to achieve the maximum possible separation. The arrangement that minimizes repulsion for five domains is the Trigonal Bipyramidal geometry.
This arrangement has two distinct types of positions: two axial positions (on a linear axis) and three equatorial positions (forming a triangle perpendicular to the axis). The Trigonal Bipyramidal shape describes the arrangement of all five electron domains—both the bonding pairs and the lone pair. This is the electron geometry, which provides the framework for the final molecular shape.
The Final Electron and Molecular Geometries of \(\text{SF}_4\)
The electron geometry of \(\text{SF}_4\) is Trigonal Bipyramidal because the central sulfur atom has five total regions of electron density. This geometric arrangement is the one that minimizes the repulsion between the five electron domains. However, the molecular geometry, defined only by the positions of the atoms themselves, is different.
The lone pair occupies space but is not included when defining the molecular shape. It is placed in one of the three equatorial positions rather than an axial one. This placement minimizes repulsion because lone pairs exert greater repulsive forces than bonding pairs. An equatorial lone pair is only repelled by two bonding pairs at 90 degrees, while an axial lone pair would be repelled by three.
Ignoring the lone pair, the positions of the four fluorine atoms result in the molecular geometry known as Seesaw (or disphenoidal). The lone pair also slightly compresses the bond angles from the ideal Trigonal Bipyramidal angles of \(90^\circ\) and \(120^\circ\). For instance, the F-S-F bond angle between the equatorial fluorines is reduced to approximately \(102^\circ\), and the axial F-S-F angle is reduced to about \(173^\circ\).