Question

Write a Lewis structure for (a) \(\mathrm{XeF}_{3}{ }^{+}\) (b) \(\mathrm{PCl}_{4}^{+}\) (c) \(\mathrm{BrF}_{5}\) (d) \(\mathrm{HPO}_{4}^{2-}(\) no \(\mathrm{P}-\mathrm{H}\) or \(\mathrm{O}-\mathrm{O}\) bonds \()\)

Short answer

Answer: The Lewis structures for each ion species are: (a) \(\text{XeF}_{3}^{+}\): [Xe(F)(F)(F)]\(^{+}\) (b) \(\text{PCl}_{4}^{+}\): [\(\text{P}(\text{Cl})_{4}\)]\(^{+}\) (c) \(\text{BrF}_{5}\): Br(F)\(_{5}\) (d) \(\text{HPO}_{4}^{2-}\): [H - O = P(=O)(-O)^{-}(-O)^{-}]\(^{2-}\) (with resonance structures formed by moving the double bond between the \(\text{P}\) and any of the other three \(\text{O}\) atoms.)

Step-by-step solution

Determine Total Number of Valence Electrons

To find the Lewis structure, first count the total number of valence electrons for each species: (a) \(\text{XeF}_{3}^{+}\) : Xe (8) + 3F (3x7) - 1(charge) = 28 electrons (b) \(\text{PCl}_{4}^{+}\) : P (5) + 4Cl (4x7) - 1(charge) = 34 electrons (c) \(\text{BrF}_{5}\) : Br (7) + 5F (5x7) = 42 electrons (d) \(\text{HPO}_{4}^{2-}\) : H (1) + P (5) + 4O (4x6) + 2(charge) = 32 electrons

Draw Skeletal Structure and Assign Electrons

Place the central atom (least electronegative element) in the center, and surround it with the other atoms. Distribute bonding electrons to form bonds between atoms, then assign the remaining electrons as lone pairs on surrounding atoms. (a) \(\text{XeF}_{3}^{+}\): \(\text{Xe}\) is at the center with 3 bonds to \(\text{F}\), remaining 10 valence electrons as 5 lone pairs on \(\text{Xe}\). (b) \(\text{PCl}_{4}^{+}\): \(\text{P}\) is at the center with 4 bonds to \(\text{Cl}\), remaining 2 valence electrons as 1 lone pair on \(\text{P}\). (c) \(\text{BrF}_{5}\): \(\text{Br}\) is at the center with 5 bonds to \(\text{F}\), remaining 2 valence electrons as 1 lone pair on \(\text{Br}\). (d) \(\text{HPO}_{4}^{2-}\): \(\text{P}\) is at the center with 4 bonds to \(\text{O}\), remaining 6 valence electrons as 3 lone pairs on 3 \(\text{O}\) atoms.

Complete Octet and Arrange Resonance Structures

Make sure that each atom, except hydrogen, has an octet of electrons. In case there are resonance structures, draw molecules accordingly: Only \(\text{HPO}_{4}^{2-}\) displays resonance structures, including double bonds between the central \(\text{P}\) and three \(\text{O}\) atoms in alternating positions.

Add Formal Charges and Write Final Lewis Structures

Indicate the correct charge for each species, and write the complete Lewis structure: (a) \(\text{XeF}_{3}^{+}\): [Xe(F)(F)(F)]\(^{+}\) (b) \(\text{PCl}_{4}^{+}\): [\(\text{P}(\text{Cl})_{4}\)]\(^{+}\) (c) \(\text{BrF}_{5}\): Br(F)\(_{5}\) (d) \(\text{HPO}_{4}^{2-}\): [H - O = P(=O)(-O)^{-}(-O)^{-}]\(^{2-}\) (Resonance structures can be formed by moving the double bond between the \(\text{P}\) and any of the other three \(\text{O}\) atoms.)

Key concepts

Valence Electrons

Valence electrons are the electrons located in the outermost shell of an atom. They play a critical role in how atoms bond and interact with each other.
When drawing Lewis structures, the first step is to determine the total number of valence electrons available. Let's look at

• For each atom, identify how many valence electrons it contributes to the molecule. Elements in different groups of the periodic table have varying numbers of valence electrons. For instance, group 1 elements have 1 valence electron, while group 17 elements have 7.
• After identifying the number of valence electrons for each atom, sum them up. Remember to account for any charges on ions, adding electrons for negative charges and subtracting for positive charges.

For example, let's consider XeF d_{3}^{+} : Xenon (Xe), being a noble gas, contributes 8 valence electrons. Each Fluorine (F) atom contributes 7 electrons, totaling 21 for three Fluorine atoms. Since the ion has a positive charge ( +1 ), subtract one electron, resulting in a total of 28 valence electrons. Understanding how these electrons arrange within molecules helps predict molecule bonding and shapes.

Resonance Structures

Resonance structures are multiple Lewis structures that collectively describe the bonding in a molecule. They capture the idea that sometimes electrons can be delocalized within a molecule.
Resonance often occurs in ions or molecules with double bonds or more complex Lewis structures.

• In drawing resonance structures, certain atoms can share electrons in different ways, without changing the actual arrangement of atoms.
• It is important to remember that the actual structure is not one single resonance form but an average of them, often called a resonance hybrid.
• Resonance structures can contribute differently to the resonance hybrid depending on their stability, determined by factors like formal charge distributions and octet completion.

Consider HPO _{4}^{2-} , an example with resonance: Phosphorus can form double bonds with different Oxygen atoms in the molecule, hence resulting in multiple equivalent structures showing different placements of these double bonds. Understanding these distributions can help explain the behavior and reactivity of such molecules.

Formal Charge

Formal charges help us understand the distribution of electrons in a molecule, which is vital in determining the most plausible Lewis structure.
Calculating formal charge allows us to find out which atoms are most "comfortable," in terms of electrons.

• To determine the formal charge, use the formula: Formal Charge = (Valence Electrons) - (Non-bonding Electrons + 1/2 Bonding Electrons) . It provides insight into the electron distribution.
• Lower formal charges are usually preferred. They indicate the optimum electron sharing within the molecule.
• In cases where molecules have multiple Lewis structures, the one with the smallest formal charges, considering absolute values, is generally the most stable.

For HPO_{4}^{2-} , consider the different resonance structures: Phosphorus can exhibit different formal charges when bonded to Oxygen atoms in various ways. The most stable form will have the smallest and well-distributed formal charges across the molecule. Understanding and calculating formal charges help in choosing the best Lewis structure representation.