Problem 64 - General Chemistry: Principles and Modern Applications

Question

Fluorine nitrate, \(\mathrm{FONO}_{2}\), is an oxidizing agent used as a rocket propellant. A reference source lists the following data for \(\mathrm{FO}_{\mathrm{a}} \mathrm{NO}_{2}\). (The subscript "a" shows that this O atom is different from the other two.) Bond lengths: \(\mathrm{N}-\mathrm{O}=129 \mathrm{pm}\) $$ \mathrm{N}-\mathrm{O}_{\mathrm{a}}=139 \mathrm{pm} ; \mathrm{O}_{\mathrm{a}}-\mathrm{F}=142 \mathrm{pm} $$ Bond angles: \(\mathrm{O}-\mathrm{N}-\mathrm{O}=125^{\circ}\) $$ \mathrm{F}-\mathrm{O}_{\mathrm{a}}-\mathrm{N}=105^{\circ} $$ \(\mathrm{NO}_{\mathrm{a}} \mathrm{F}\) plane is perpendicular to the \(\mathrm{O}_{2} \mathrm{NO}_{\mathrm{a}}\) plane Use these data to construct a Lewis structure(s), a three-dimensional sketch of the molecule, and a plausible bonding scheme showing hybridization and orbital overlaps.

Step-by-Step Solution

Answer

The Lewis structure for \(\mathrm{FONO}_{2}\) involves nitrogen centrally bonded to three oxygens and one fluorine. Nitrogen is \(sp^2\) hybridized, while the \(O_a\) atom involved in the \(O_a-F\) bond is \(sp^3\) hybridized. The molecule has a trigonal planar geometry around the nitrogen atom and bent/angular geometry around the \(O_a\) atom. This results in a three-dimensional structure with the \(NO_aF\) plane lying perpendicular to the \(O_2 NO_a\) plane.

Step 1: Lewis Structure

The first step is to draw the Lewis structure for \(\mathrm{FONO}_{2}\). Start with considering the valence electrons for each atom - nitrogen (N) has five, oxygen (O) has six, and fluorine (F) has seven. Connect nitrogen to one oxygen (labelled \(O_a\)) and fluorine, and the nitrogen to two other oxygens. Add double bonds to the two oxygen atoms directly connected to the nitrogen, and single bonds for the \(O_a\) to F, and N to \(O_a\). Fill the remaining electrons to complete the octets of each atom, ensuring that each atom follows the octet rule.

Step 2: Molecular Geometry

With the Lewis structure, we can determine the geometry of the molecule. The molecular geometry around the nitrogen atom is trigonal planar, because there three regions of electron density (three bonds). The geometry around the \(O_a\) atom however, is bent/ angular because it has two bonding pairs of electrons and two lone pairs.

Step 3: Bonding Scheme and Hybridization

In the nitrogen atom, the presence of three electron domains suggests an \(sp^2\) hybridization. We have three \(sp^2\) orbitals forming the bonds with the two oxygens and \(O_a\), and one unhybridized p orbital lying perpendicular to the plane of these three bonds. This p orbital is involved in the formation of \(pi\) bonds with the p orbitals of the two oxygen atoms. The oxygen atom attached to Fluorine has two unshared pairs of electrons (in two \(2p\) orbitals) and two shared pairs of electrons (in \(sp^3\)). Therefore, the \(O_a\) atom is \(sp^3\) hybridized.

Step 4: Sketching

Sketch the molecule keeping in mind the bond lengths, bond angles, and the orientation of the molecules in different planes as stated in the problem. Ensure the \(F-O_a-N\) bond angle is 105 degrees, the \(O-N-O\) bond angle is 125 degrees, and the \(NO_aF\) plane is perpendicular to the \(O_2 NO_a\)

Key Concepts

Lewis Structure

Understanding the Lewis structure is crucial for grasping the molecular geometry of molecules like fluorine nitrate (\(\mathrm{FONO}_{2}\)). Start by identifying the number of valence electrons for each atom: nitrogen (5), oxygen (6), and fluorine (7). The total number of valence electrons helps us arrange the atoms logically.

• Draw the skeleton with the central nitrogen atom connected to two oxygen atoms and a third oxygen labeled as \(O_a\), which is further bonded to fluorine.
• Initially, form single bonds between connected atoms (\(\mathrm{N}-\mathrm{O}\), \(\mathrm{N}-\mathrm{O}_a\), and \(\mathrm{O}_a-\mathrm{F}\)).
• Add double bonds where appropriate (between nitrogen and the two oxygens directly bonded to it) to satisfy the octet rule, enhancing bond stability.
• Assign lone pairs to oxygen atoms (including \(O_a\)) to complete their octets. Ensure nitrogen also satisfies the octet rule if possible.

This setup results in a stable configuration reflected in the specified molecular geometry and bond angles.

Bond Angles

Bond angles provide a clear picture of how atoms are spatially arranged around the central atoms. In \(\mathrm{FONO}_{2}\), specific bond angles offer insight into the molecular shape.

• The \(\mathrm{O}-\mathrm{N}-\mathrm{O}\) bond angle is noted as \(125^{\circ}\), typical of a trigonal planar arrangement at the nitrogen center due to the presence of pi-bonding and resonance effects.
• The \(\mathrm{F}-\mathrm{O}_a-\mathrm{N}\) angle measures \(105^{\circ}\), significantly smaller due to the larger space required by lone pairs on \(O_a\), which create a bent or angular geometry at \(O_a\).

Knowing these angles is vital for sketching an accurate 3D structure, important in comprehending the molecule's reactivity, polarity, and interactions.

Hybridization

Hybridization reveals the mixing of atomic orbitals to form new hybrid orbitals that accommodate bonding.

• For the nitrogen atom in \(\mathrm{FONO}_{2}\), it undergoes \(sp^2\) hybridization because it forms three sigma bonds (two with oxygen, one with \(O_a\)). This setup aligns with a trigonal planar geometry.
• At \(O_a\), two lone pairs and two bond pairs lead to \(sp^3\) hybridization, explaining the bent shape through tetrahedral geometry with significant distortion thanks to the electron lone pairs.

These hybridizations facilitate the bond formations we see expressed in the Lewis structure and support both a stable and optimized geometry.

Orbital Overlap

Orbital overlap describes how atomic orbitals combine to form chemical bonds, crucial in understanding stability and directionality.

• In \(\mathrm{FONO}_{2}\), \(\sigma\) bonds form through the effective overlap of \(sp^2\) hybrid orbitals of nitrogen with p orbitals of the oxygen atoms, ensuring strong saturated bonds.
• The unhybridized p orbital remaining on nitrogen participates in \(\pi\) bond formations with the oxygen p orbitals, characteristic of double bonding where electron density is shared above and below the bond axis.
• \(O_a\) forms bonds through \(sp^3\) hybrid orbitals overlapping with fluorine p orbital, securing its role in bond formation and influencing geometry.

The nature of orbital overlaps influences molecular geometry, bond energies, and the molecule's overall chemical behavior, facilitating a comprehensive understanding of \(\mathrm{FONO}_{2}\).