Question

(a) Predict the \(^{31} \mathrm{P} \mathrm{NMR}\) spectrum of \(\left[\mathrm{HPF}_{5}\right]^{-}\) (assuming a static structure) given that \(J_{\mathrm{PH}}=939 \mathrm{Hz}\) \\[ J_{\mathrm{PF}(\text { axial })}=731 \mathrm{Hz} \text { and } J_{\mathrm{PF}(\text { cquatorial })}=817 \mathrm{Hz} \\] (b) The \(\left[\mathrm{BiF}_{7}\right]^{2-}\) and \(\left[\mathrm{SbF}_{6}\right]^{3-}\) ions have pentagonal bipyramidal and octahedral structures, respectively. Are these observations consistent with VSEPR theory? (c) Consider the following reaction scheme (K.O. Christe \((1995) J . A m .\) Chem. Soc., vol. \(117,\) p. 6136 ): \\[ \mathrm{NF}_{3}+\mathrm{NO}+2 \mathrm{SbF}_{5} \quad \stackrel{420 \mathrm{K}}{\longrightarrow} \quad\left[\mathrm{F}_{2} \mathrm{NO}\right]^{+}\left[\mathrm{Sb}_{2} \mathrm{F}_{11}\right]^{-}+\mathrm{N}_{2} \\] Discuss the reaction scheme in terms of redox and Lewis acid-base chemistry. Comment on the structures of, and bonding in, the nitrogen-containing species in the scheme.

Short answer

The NMR of \([HPF_5]^−\) will show overlapping triplets due to hydrogen and fluorine couplings at three different spacings. The structures are consistent with VSEPR theory. The reaction involves redox and Lewis acid-base chemistry.

Step-by-step solution

Analyzing the NMR Spectrum for (a)

The compound \([HPF_5]^-\) is a fluoro-phosphorus molecule. It contains one phosphorus atom central, bonded to five fluorine atoms. In NMR, the phosphorus nucleus will couple with hydrogen (\(J_{PH}=939\, \text{Hz}\)) and also with the different fluorine atoms (axial and equatorial). For a static structure, three displacements will be visible due to the coupling with different fluorines: axial (\(J_{PF(axial)}=731\, \text{Hz}\)) and equatorial (\(J_{PF(equatorial)}=817\, \text{Hz}\)). The splitting for each coupling must be accounted for individually when predicting the spectrum.

Predicting Effects on NMR Spectrum for (a)

The \(^{31}\text{P}\) NMR spectrum will show a triplet due to coupling with hydrogen (\(J_{PH}\)). Each of these splits further into, overlapped patterns, caused by fluorine couplings: doublets of differing spacing, for axial and equatorial interactions. The triplet's smaller peaks (from fluorine's coupling) reflect subtle inherent nuclear interactions, exemplified by the slight difference in splitting constants. Therefore, the expected spectrum will reflect an organized overlap of these coupling enhancements.

Consistency of Molecular Structures with VSEPR for (b)

\([\text{BiF}_7]^{2-}\) adopts a pentagonal bipyramidal structure, which is consistent with VSEPR theory because of seven electron pairs (5 equatorial, 2 axial) around the central atom. \([\text{SbF}_6]^{3-}\) forms an octahedral structure, in alignment with VSEPR predictions as it accommodates six pairs arranged equidistantly without lone pairs altering the structure. Hence, both structures align with VSEPR predictions based on electron pair repulsion patterns.

Discussing Reaction and Redox Chemistry for (c)

In the reaction, \(\text{NF}_3\) reduces \(\text{SbF}_5\) while \(NO\) is oxidized, which represents a redox process. \(\text{SbF}_5\) is a strong Lewis acid accepting electrons, while \(\text{NF}_3\) acts as a Lewis base donating electrons in the formation of \([F_2NO]^+\). The nitrogen-containing product \([F_2NO]^+\) forms a cation by electron pair donation, showcasing the electron-deficient bonding around nitrogen typical of nitrogen oxides and fluorides.

Key concepts

NMR Spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is an analytical technique utilized to determine the structure of molecules. In

• technique works by analyzing the magnetic properties of nuclei, particularly how they interact with neighboring atoms.
• For a molecule like \[HPF_5\]^-, the \[^{31}\text{P}\] NMR spectrum provides insights into how the phosphorus atom is influenced by atoms it is bonded to, in this case, hydrogen and fluorine.

The process involves examining how the phosphorus nucleus interacts with these atoms.
The coupling constants, like \(J_{PH}=939 \text{Hz}\) and the different \(J_{PF}\) values (axial and equatorial), denote the strength of these interactions.
The \[^{31}\text{P}\] spectrum of \[HPF_5\]^- would reveal a triplet due to the hydrogen-phosphorus interaction. Each signal splits further due to differing interactions with the axial and equatorial fluorine atoms, creating a characteristic complex pattern. Understanding these splitting patterns is crucial for interpreting the structural characteristics of molecules.

VSEPR Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts the shapes of molecules based on electron pair repulsions around their central atoms. It posits that electron pairs arrange themselves to minimize repulsion, determining molecular geometry. VSEPR theory is especially useful for predicting the structures of compounds

• For instance, the \[\text{BiF}_7\]^{2-}\ ion is predicted to form a pentagonal bipyramidal structure. This results from seven electron pairs (five equatorial and two axial), distributing themselves to minimize repulsions.
• Similarly, \[\text{SbF}_6\]^{3-}\, with six pairs, assumes an octahedral arrangement.

These predictions are consistent with the VSEPR model because the central atom’s electron pairs repulse each other equally, ensuring stability and symmetry in the molecular shape.
Considerations like the presence of lone pairs or different repulsion strengths can also slightly alter predicted structures, making VSEPR a vital theoretical tool for chemists.

Lewis Acid-Base Reactions

Lewis acid-base reactions involve the transfer of an electron pair, where a Lewis acid accepts and a Lewis base donates. This broadens the definition beyond traditional acids and bases by focusing on electron pair transactions rather than protons.

• The reaction illustrated in the exercise demonstrates this concept, where \[\text{SbF}_5\] acts as a Lewis acid by accepting electron pairs.
• Conversely, \[\text{NF}_3\] donates electron pairs, serving as a Lewis base in the reaction.

Upon forming the \[\left[\text{F}_2\text{NO}\right]^+\] species, the intense electron pair interactions display the flexibility of Lewis theory in explaining chemical behavior.
The involvement of fluorine in the process highlights its role in stabilizing the electron-deficient species, allowing for diverse reaction strategies based on electron sharing.

Redox Chemistry

Redox chemistry involves electron transfer processes, whereby one substance is oxidized (loses electrons) and another is reduced (gains electrons). Understanding this concept is essential for reactions like those found in the exercise.

• The reaction between \[\text{NF}_3\], \[\text{NO}\], and \[\text{SbF}_5\] underlines redox principles.
• Here, \[\text{NF}_3\] reduces \[\text{SbF}_5\] by donating electrons, while \[\text{NO}\] is oxidized, indicating an electron transfer process.

Such transformations are vital in understanding chemical reactivity, emphasizing balancing oxidation states and the flow of electrons.
Analyzing redox reactions aids in pinpointing electron movement and changes in oxidation states, providing a comprehensive view of chemical transformations and stability. This understanding is pivotal to exploring complex chemistry patterns and predicting reaction outcomes effectively.