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Draw the most important Lewis structure for [ PF4 ]+ (assuming it exists) and then answer the following questions. The underlined atom is the central atom. All other atoms are bonded directly to the central atom. (a) What is the electron-group geometry, according to VSEPR theory? (b) What is the molecular geometry? (c) Is this species polar or nonpolar? Hints: The electron-group geometry refers to the spatial arrangement of the electron pairs around the central atom. The molecular geometry refers to the spatial arrangement of the bonded atoms around the central atom.
The Correct Answer and Explanation is:
To analyze the [PF₄]⁺ ion, we begin by constructing its Lewis structure.
Step 1: Count the valence electrons
- Phosphorus (P) has 5 valence electrons.
- Each fluorine (F) has 7 valence electrons.
- Total from 4 fluorines: 4 × 7 = 28
- Total before charge: 5 (from P) + 28 (from F) = 33
- Since this is a +1 cation, we subtract one electron: 33 − 1 = 32 valence electrons.
Step 2: Draw the structure
- Place P in the center and connect it to four F atoms with single bonds.
- Each single bond uses 2 electrons × 4 = 8 electrons.
- Distribute the remaining 24 electrons to satisfy the octets on the four F atoms (6 electrons per F atom).
- Phosphorus has 4 bonding pairs and no lone pairs.
Final Lewis Structure:
- P is bonded to 4 F atoms with single bonds.
- Each F has 3 lone pairs.
- The positive charge is associated with the overall ion due to the missing electron.
(a) Electron-group geometry:
Tetrahedral — According to VSEPR theory, four regions of electron density (four bonding pairs) around the central atom result in a tetrahedral electron-group geometry.
(b) Molecular geometry:
Tetrahedral — Since all four electron groups are bonding pairs and there are no lone pairs on the central atom, the molecular geometry matches the electron-group geometry: tetrahedral.
(c) Polarity:
Nonpolar — Although the P–F bonds are polar due to the electronegativity difference, the tetrahedral arrangement results in a symmetrical shape. The bond dipoles cancel out, making the molecule nonpolar overall.
Explanation
The [PF₄]⁺ ion consists of a phosphorus atom centrally bonded to four fluorine atoms. To determine its Lewis structure, we first calculate the total number of valence electrons. Phosphorus contributes five electrons, and each fluorine contributes seven. With four fluorines, the total becomes 33 electrons. Since the ion has a +1 charge, one electron is removed, leaving 32 valence electrons to distribute.
In the Lewis structure, phosphorus forms four single bonds with the fluorine atoms. This uses 8 electrons, leaving 24 electrons which are placed as lone pairs on the fluorine atoms to complete their octets. Phosphorus ends up with four bonded pairs and no lone pairs.
Using VSEPR theory (Valence Shell Electron Pair Repulsion), the electron-group geometry is determined by the number of regions of electron density around the central atom. In this case, there are four bonding pairs and no lone pairs, which gives a tetrahedral geometry. Since all substituents are atoms (not lone pairs), the molecular geometry is also tetrahedral.
Regarding polarity, although each P–F bond is polar due to fluorine’s high electronegativity, the molecule’s geometry causes these dipoles to cancel. A tetrahedral molecule with identical atoms in all positions is symmetric, which results in a nonpolar species. Therefore, [PF₄]⁺, despite having polar bonds, is overall nonpolar due to its symmetrical shape.
This example highlights how molecular shape and electron distribution influence physical properties such as polarity. It demonstrates the usefulness of Lewis structures and VSEPR theory in predicting molecular behavior.
