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(a) Draw a set of resonance structures for the hypothetical molecule \(\mathrm{PH}_{5},\) ensuring that \(\mathrm{P}\) obeys the octet rule in each structure. Assume a structure analogous to that of \(\mathrm{PF}_{5}\). (b) To what point group does \(\mathrm{PH}_{5}\) belong? (c) Using \(\mathrm{PH}_{5}\) as a model compound, use a ligand group orbital approach to describe the bonding in \(\mathrm{PH}_{5} .\) Show clearly how you derive the symmetries of both the \(P\) atomic orbitals, and the LGOs of the \(\mathrm{H}_{5}\) fragment.

Short Answer

Expert verified
(a) Hypothetical resonance violates reality here; delocalization not typical. (b) D鈧僪 point group. (c) PH鈧 uses LGOs and symmetry for bonding.

Step by step solution

01

Understand the Requirement for Resonance Structures

Before drawing resonance structures, recognize the need to satisfy the octet rule for phosphorus, despite PH鈧 being a hypervalent molecule typically. Resonance structures may not usually correspond to hypervalent molecules, but for this exercise, we pretend to satisfy the octet rule to explore potential delocalized bonding descriptions.
02

Draw Alternative Resonance Structures

To ensure phosphorus obeys the octet rule, one can envision resonance structures by involving d-orbitals, forming hypothetical structures where double bonds form and break between phosphorus (P) and hydrogen (H). Draw several Lewis structures where phosphorus sacrifices the extra pair of electrons to form various double bonds with hydrogen atoms, maintaining an overall count of 8 electrons around P in each structure, though typically, PH鈧 would have no charge separation and no typical resonance structures.
03

Identify the Point Group

Determine the molecular shape of PH鈧. As it is analogous to PF鈧, PH鈧 would also have a trigonal bipyramidal structure. This structure is symmetric around multiple axes, corresponding to the D鈧僪 point group. Analyze the symmetry elements: a C鈧 rotational axis, 3 vertical mirror planes (蟽v), and a horizontal mirror plane (蟽h).
04

Apply Ligand Group Orbital Approach

Consider the PH鈧 molecule: phosphorus's atomic orbitals need to overlap with the ligand group orbitals formed by the hydrogen atoms. The five hydrogen atoms in a trigonal bipyramidal array will form LGOs. Classify these LGOs into symmetry groups corresponding to the molecular point group D鈧僪. Identify the symmetries of phosphorus's compatible orbitals, which include s, p鈧, p岬, and p饾懅, which can be used to form bonding MOs with these LGOs. Conclude that bonding is achieved through a combination of the p orbitals of phosphorus overlapping with LGOs of the hydrogens.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Resonance Structures
Resonance structures are a way to describe a molecule that can't be represented by a single Lewis structure. In chemistry, it's especially relevant for molecules with delocalized electrons. Although PH鈧 doesn鈥檛 naturally have resonance structures because it tends to break the octet rule with phosphorus forming five bonds, the exercise assumes observing potential resonance structures constrained by the octet rule. To create these hypothetical resonance structures, visualize the phosphorus as forming double bonds with different hydrogen atoms in sequence. This interplay creates distinct Lewis structures while maintaining an overall eight-electron configuration around phosphorus. While typically not realistic for phosphorus in PH鈧, this approach helps conceptualize molecular structure or electron delocalization in theoretical models. Understanding resonance improves the grasp of molecular stability and electron distribution. It's a method to explore potential electronic configurations, even in less conventional scenarios.
Point Group Analysis
Point Group Analysis is used to describe the symmetry aspects of a molecule, which can significantly affect its physical properties and reactions. For PH鈧, the analogous structure to PF鈧 is trigonal bipyramidal, aligning it with the D鈧僪 point group. In molecular symmetry terms, D鈧僪 comprises several symmetry elements:
  • A principal rotational axis (C鈧), which allows for rotation by 120掳
  • Three vertical mirror planes (蟽v) that relate to reflection through the axis planes
  • A horizontal mirror plane (蟽h) at midpoint of the molecule perpendicular to C鈧
Point group analysis provides fundamental insight into symmetry-based predictions, such as spectroscopic properties or how the molecule may respond to external fields, crucial for understanding chemical behavior.
Ligand Group Orbitals
Ligand Group Orbitals (LGOs) are instrumental in understanding the bonding of molecules, especially those with more complex symmetries. For PH鈧, the interactions between phosphorus and hydrogen atoms can be understood by forming LGOs. In a trigonal bipyramidal arrangement, the hydrogens form a specific pattern that can be grouped into symmetries. This grouping follows the point group designation, D鈧僪:
  • The LGOs made from combining the atomic orbitals of the hydrogen atoms are classified into different symmetry types.
  • Each LGO symmetry type will correspond to at least one of the s, p, or d atomic orbitals of the phosphorus.
By matching the symmetry properties of the LGOs with the phosphorus atomic orbitals, you can understand how these orbitals overlap to form molecular orbitals, providing a clearer picture of bonding within the molecule.
Hypervalent Molecules
Hypervalent molecules are those that seemingly exceed the traditional octet rule, involving elements able to possess more than eight electrons in their valence shell. PH鈧 typically falls into this category. Phosphorus in this context utilizes d orbitals to expand its valence shell. This expansion allows phosphorus to make five bonds with hydrogen atoms, fundamentally breaking the octet rule but aligning with the concept of hypervalency. Understanding hypervalency is crucial for explaining how molecules like PH鈧 can exist, including:
  • Phosphorus exceeds the octet by using available d orbitals.
  • Traditionally, these anomalies are more theoretical constructs but aid in the bonding descriptions of such molecules.
Exploring these provides essential insights into the behavior and potential anomalies seen in advanced inorganic chemistry.
Molecular Symmetry
Molecular symmetry is foundational in determining a molecule's physical and chemical characteristics. In PH鈧, its molecular symmetry affects its properties significantly, as seen in its trigonal bipyramidal shape. Analyzing molecular symmetry involves identifying equivalent parts of a molecule and predicting its reaction possibilities and spectroscopic properties. For PH鈧:
  • The symmetrical shape influences vibrational modes observed in spectroscopy, like IR and Raman spectra.
  • Its symmetry also dictates interaction potentials in chemical reactions or with external magnetic and electric fields.
Appreciating molecular symmetry aids in correlating structural features with translational characteristics, vital for both theoretical predictions and practical applications in chemistry.

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Most popular questions from this chapter

(a) Draw the structure of \(\left[\mathrm{CO}_{3}\right]^{2-}\). (b) If all the \(\mathrm{C}-\mathrm{O}\) bond distances are equal, write a set of resonance structures to describe the bonding in \(\left[\mathrm{CO}_{3}\right]^{2-}\) (c) Describe the bonding in \(\left[\mathrm{CO}_{3}\right]^{2-}\) in terms of a hybridization scheme and compare the result with that obtained in part (b).

The I-I bond distance in \(\mathrm{I}_{2}\) (gas phase) is \(267 \mathrm{pm}\), in the \(\left[\mathrm{I}_{3}\right]^{+}\) ion is \(268 \mathrm{pm},\) and in \(\left[\mathrm{I}_{3}\right]^{-}\) is \(290 \mathrm{pm}\) (for the \(\left.\left[\mathrm{AsPh}_{4}\right]^{+} \text {salt }\right)\) (a) Draw Lewis structures for these species. Do these representations account for the variation in bond distance? (b) Use MO theory to describe the bonding and deduce the I-I bond order in each species. Are your results consistent with the structural data?

(a) \(\mathrm{PF}_{5}\) has \(D_{3 \mathrm{h}}\) symmetry. What is its structure? (b) Suggest an appropriate bonding scheme for \(\mathrm{PF}_{5}\) within VB theory, giving appropriate resonance structures.

In \(\left[\mathrm{B}_{2} \mathrm{H}_{7}\right]^{-}(5.11),\) each \(\mathrm{B}\) atom is approximately tetrahedral. (a) How many valence electrons are present in the anion? (b) Assume that each \(\mathrm{B}\) atom is \(s p^{3}\) hybridized. After localization of the three terminal \(\mathrm{B}-\mathrm{H}\) bonds per \(\mathrm{B},\) what \(\mathrm{B}\) -centred orbital remains for use in the bridging interaction? (c) Following from your answer to part (b), construct an approximate orbital diagram to show the formation of \(\left[\mathrm{B}_{2} \mathrm{H}_{7}\right]^{-}\) from two \(\mathrm{BH}_{3}\) units and \(\mathrm{H}^{-}\). What does this approach tell you about the nature of the \(\mathrm{B}-\mathrm{H}-\mathrm{B}\) bridge?

The structures below show (on the left) an octahedral and (on the right) a trigonal prismatic \(\mathrm{XY}_{6}\) molecule. (a) To what point groups do these molecules belong? (b) The bonding MOs in octahedral \(\mathrm{XY}_{6}\) have \(a_{1 g}, e_{g}\) and \(t_{1 u}\) symmetries. Confirm that these symmetries are consistent with the point group that you have assigned. (c) Can there be a triply degenerate set of bonding orbitals for the trigonal prismatic \(\mathrm{XY}_{6}\) molecule? Rationalize your answer.

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