Question

Some chemists believe that satisfaction of the octet rule should be the top criterion for choosing the dominant Lewis structure of a molecule or ion. Other chemists believe that achieving the best formal charges should be the top criterion. Consider the dihydrogen phosphate ion, \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) , in which the \(\mathrm{H}\) atoms are bonded to \(\mathrm{O}\) atoms. (a) What is the predicted dominant Lewis structure if satisfying the octet rule is the top criterion? (b) What is the predicted dominant Lewis structure if achieving the best formal charges is the top criterion?

Short answer

In conclusion, the predicted dominant Lewis structure of \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) based on: (a) Satisfying the octet rule is a structure with one double bond between phosphorus and one oxygen atom, and single bonds to the other oxygen atoms. (b) Achieving the best formal charges is a structure with two double bonds between phosphorus and two oxygen atoms, and single bonds to the other two oxygen atoms.

Step-by-step solution

Determine the total number of valence electrons

To draw the Lewis structure of \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\), we first need to count the total number of valence electrons. Hydrogen has 1 valence electron, phosphorus has 5, oxygen has 6, and there is an additional electron due to the negative charge. Total valence electrons = (2 Hydrogens × 1) + (1 Phosphorus × 5) + (4 Oxygens × 6) + 1 = 2 + 5 + 24 + 1 = 32

Draw a skeleton structure of the molecule

Place the least electronegative atom (phosphorus) in the center and surround it with the oxygen atoms. Then, place the hydrogen atoms bonded to two oxygen atoms. Connect them with single bonds. Now, assign the remaining valence electrons as lone pairs on the oxygen atoms.

Predict the dominant Lewis structure based on the octet rule

The octet rule states that an atom in a molecule will be stable when it has 8 electrons in its outer shell (except for hydrogen, which only requires 2). In the skeleton structure, the phosphorus atom has only 4 electrons (from single bonds to each oxygen), so it requires double bonding with one oxygen to satisfy the octet rule. Additionally, hydrogen atoms are already stable with 2 electrons each. The other three oxygen atoms are also stable, having 8 electrons each in their outer shells (2 from the covalent bond and 6 from lone pairs). So, when satisfying the octet rule is the top criterion, the dominant Lewis structure involves a double bond between phosphorus and one of the oxygen atoms, and single bonds to the other oxygen atoms.

Calculate the formal charges

Now, let's calculate the formal charges of each atom in the structure obtained in step 3: Formal charge of Phosphorus = 5 (valence electrons) - 0.5(4 bonding electrons) - 4 (ownership of lone pair electrons) = 0 Formal charge of double-bonded Oxygen = 6 - 0.5(4) - 4 = 0 Formal charge of single-bonded Oxygen with Hydrogen = 6 - 0.5(2) - 6 = -1 Formal charge of single-bonded Oxygen without Hydrogen = 6 - 0.5(2) - 6 = -1 The total formal charge of the ion is (-1)+(-1)= -2 which is not equal to the ion charge (-1).

Predict the dominant Lewis structure based on the best formal charges

For achieving the best formal charges, we need to make sure that the sum of the formal charges is equal to the ion charge (-1). To do this, we can modify the structure obtained in step 3 by converting one of the single-bonded oxygen atoms without hydrogen into a double bond with phosphorus: Formal charge of Phosphorus = 5 - 0.5(6) - 2 = +1 Formal charge of one double-bonded Oxygen = 6 - 0.5(4) - 4 = 0 Formal charge of another double-bonded Oxygen = 6 - 0.5(4) - 4 = 0 Formal charge of single-bonded Oxygen with Hydrogen = 6 - 0.5(2) - 6 = -1 Formal charge of single-bonded Oxygen without Hydrogen = 6 - 0.5(2) - 6 = -1 The total formal charge is now (+1)+(-1)+(-1)= -1, which is equal to the ion charge. So, when achieving the best formal charges is the top criterion, the dominant Lewis structure involves two double bonds between phosphorus and two of the oxygen atoms, and single bonds to the other two oxygen atoms. In conclusion, the predicted dominant Lewis structure of \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) based on: (a) Satisfying the octet rule is a structure with one double bond between phosphorus and one oxygen atom, and single bonds to the other oxygen atoms. (b) Achieving the best formal charges is a structure with two double bonds between phosphorus and two oxygen atoms, and single bonds to the other two oxygen atoms.

Key concepts

Octet Rule

The octet rule is an essential concept in chemistry, providing a fundamental guideline for the formation of stable molecules. It states that atoms tend to form bonds in such a way that they have eight electrons in their outer electron shell. This configuration is particularly stable and is often compared to the electron configuration of noble gases, which are chemically inert.
However, there are exceptions. For example, hydrogen is satisfied with two electrons (a duet) since it only needs to fill its first shell. Similarly, elements like boron and aluminum may not always fulfill the octet rule in every compound.

• The octet rule helps predict how atoms will likely bond. When applied to the Lewis structure of a molecule, it forces atoms to either share electrons through covalent bonds or gain/lose electrons to form ionic bonds.
• For many compounds, especially those of nonmetals, the octet rule gives a clear pathway to predict molecule geometry, stability, and reactivity.

When considering the octet rule for the dihydrogen phosphate ion, \( \mathrm{H}_{2}\mathrm{PO}_{4}^{-} \), phosphorus needs to expand its octet by forming double bonds with oxygen to ensure all atoms in the molecule are stable. In doing so, it achieves a stable configuration with shared electrons, which is necessary for the structure and stability of the ion.

Formal Charge

The concept of formal charge is crucial when evaluating the best Lewis structure for a molecule or ion. It is a bookkeeping tool that helps us keep track of the electron distribution among the atoms and find the most plausible structure. Here's how it works:
Formal charge is calculated using the formula:\[ \text{Formal charge} = \text{(Valence electrons)} - \text{(Non-bonding electrons + 0.5 × Bonding electrons)}\]The goal is to have a formal charge that achieves a zero value or the closest possible to it for each atom, indicating the best electron distribution.

• In the best Lewis structure, the sum of all formal charges should equal the total charge of the molecule or ion.
• Structures that have atoms with minimal formal charges are often preferred.

For the \( \mathrm{H}_{2}\mathrm{PO}_{4}^{-} \) ion, the challenge is to balance the formal charges to reflect its total charge of -1. By adjusting bond formation, such as adding double bonds with oxygen, we can reach an arrangement where the formal charges are consistent with the ion's overall charge.

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial in determining how the atom will bond with others. They are responsible for the chemical properties and reactivity of an element.
To understand Lewis structures, knowing how to count and distribute valence electrons is key.

• Valence electrons for most elements can be deduced from their group number in the periodic table. For example, oxygen has 6 valence electrons (Group 16), phosphorus has 5 (Group 15), and hydrogen has 1 (Group 1).
• In a compound, each element contributes its valence electrons toward the overall electron pool that participates in bonding.

In the \( \mathrm{H}_{2}\mathrm{PO}_{4}^{-} \) ion, we count up to 32 valence electrons among hydrogen, phosphorus, oxygen, and an additional electron from the negative charge. These electrons must be appropriately distributed to form bonds and lone pairs, fulfilling both the octet rule and achieving the best formal charges.