Problem 13 - Chemistry and Chemical Reactivity

Question

Draw the Lewis structures of the acid \(\mathrm{HPO}_{2} \mathrm{F}_{2}\) and its anion \(\mathrm{PO}_{2} \mathrm{F}_{2}^{-}\). What is the molecular geometry and hybridization for the phosphorus atom in each species? (H is bonded to an O atom in the acid.)

Step-by-Step Solution

Answer

Both HPO2F2 and PO2F2- have tetrahedral geometries with sp3 hybridization for phosphorus.

Step 1: Count Total Valence Electrons for HPO2F2

For \( \mathrm{HPO}_{2} \mathrm{F}_{2} \), calculate the total number of valence electrons. Hydrogen (H) has 1 electron, phosphorus (P) has 5 electrons, each oxygen (O) has 6 electrons, and each fluorine (F) has 7 electrons. So, \( 1 + 5 + (2 \times 6) + (2 \times 7) = 32 \) valence electrons.

Step 2: Draw Lewis Structure for HPO2F2

Place phosphorus (P) in the center since it is less electronegative, with hydrogen (H) bonded to one oxygen (O). Distribute other oxygen atoms and fluorine atoms around phosphorus. Allocate electrons to satisfy the octet rule, forming \( P-O-H \) and \( P-F \) bonds. Check that each atom, except H, has 8 electrons around it.

Step 3: Determine Molecular Geometry and Hybridization for HPO2F2

In \( \mathrm{HPO}_{2} \mathrm{F}_{2} \), phosphorus is surrounded by four regions of electron density (2 O's, 2 F's), fitting a tetrahedral geometry. The hybridization of phosphorus is \( sp^3 \).

Step 4: Count Total Valence Electrons for PO2F2-

For \( \mathrm{PO}_{2} \mathrm{F}_{2}^{-} \), the total valence electrons add up to 33 (adding one more electron for the negative charge): \( 5 + (2 \times 6) + (2 \times 7) + 1 = 33 \) valence electrons.

Step 5: Draw Lewis Structure for PO2F2-

Start with phosphorus at the center, surrounded by 2 oxygen atoms and 2 fluorine atoms. Add the extra electron to form the anion, making sure each atom (except the central oxygen with double bonds and the single bonded fluorine atoms) satisfies the octet rule. Use one double bond with one oxygen to achieve this.

Step 6: Determine Molecular Geometry and Hybridization for PO2F2-

In \( \mathrm{PO}_{2} \mathrm{F}_{2}^{-} \), the phosphorus atom is still surrounded by four regions of electron density, maintaining a tetrahedral geometry. The hybridization is still \( sp^3 \).

Key Concepts

Phosphorus Hybridization

In the discussion of Lewis structures, an important concept connected to the configuration is hybridization. For the compound in our exercise, namely \( \mathrm{HPO}_{2} \mathrm{F}_{2} \), the phosphorus atom is at the center and forms bonds with oxygen and fluorine atoms. Hybridization describes the mixing of atomic orbitals from the same atom to result in new hybrid orbitals. These are what we observe in covalent bonding.
Phosphorus, with its original 5 valence electrons, undergoes \( sp^3 \) hybridization in \( \mathrm{HPO}_{2} \mathrm{F}_{2} \).\( sp^3 \) hybridization indicates that one \( s \) orbital mixes with three \( p \) orbitals, creating four equivalent \( sp^3 \) hybrid orbitals.
These hybrid orbitals arrange themselves in a way to minimize electron-pair repulsions around phosphorus, thus forming a tetrahedral distribution. This same \( sp^3 \) hybridization is valid for the anion \( \mathrm{PO}_{2} \mathrm{F}_{2}^{-} \), evidenced by similar bonding and geometric configuration.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. For \( \mathrm{HPO}_{2} \mathrm{F}_{2} \), the phosphorus atom is pivotal, surrounded by oxygen and fluorine atoms.
Given phosphorus is bound to four groups, the geometry observed is tetrahedral. A tetrahedral shape occurs when four electron pairs (bonding or non-bonding) organize themselves to be as far apart as possible, minimizing repulsion between them. This geometry is characterized by bond angles of approximately 109.5 degrees.

• This arrangement ensures a symmetry where electrons are evenly distributed.
• In the anion \( \mathrm{PO}_{2} \mathrm{F}_{2}^{-} \), the tetrahedral shape persists with similar reasons explaining the spatial configuration.

By considering electron pairs—both bonding pairs and lone pairs—this geometry explains molecular shape accurately.

Valence Electrons

Valence electrons are pivotal to understanding chemical reactivity and bonding of atoms. Phosphorus has five valence electrons. In \( \mathrm{HPO}_{2} \mathrm{F}_{2} \), considering additional atoms in its molecular structure:

• Hydrogen contributes 1 electron.
• Each of the two oxygens contributes 6 electrons.
• Each of the two fluorines contributes 7 electrons.

This totals up to 32 valence electrons for the molecule.
In the anion \( \mathrm{PO}_{2} \mathrm{F}_{2}^{-} \), the negative charge indicates one additional electron, giving it 33 valence electrons in total. These electrons are distributed among bonds and lone pairs, laying out the base for the Lewis structure. Valence electron count is crucial when predicting a molecule's reactivity, geometry, and bond formation.

Octet Rule

The Octet Rule is a fundamental principle in chemistry, stating that atoms tend to interact in a way that each atom ends up with eight electrons in its valence shell, striving to attain a noble gas electron configuration. However, certain elements like phosphorus can sometimes expand beyond an octet, utilizing d orbitals when necessary.
In \( \mathrm{HPO}_{2} \mathrm{F}_{2} \), ensure that each atom satisfies the octet rule in the Lewis structure, except for hydrogen which follows the duet rule, being stable with two electrons. Each oxygen in this molecule can form double bonds if needed to fulfill its octet.
In the anion \( \mathrm{PO}_{2} \mathrm{F}_{2}^{-} \), the octet is also attained but with an added electron due to the negative charge, which is accounted for by forming a double bond with one of the oxygen atoms. This helps manage the extra electron while maintaining stability in the molecular structure.