Problem 99 - Chemistry An Atoms First Approach

Question

Write Lewis structures that obey the octet rule for the following species. Assign the formal charge for each central atom. a. \(\mathrm{POCl}_{3}\) b. \(\mathrm{SO}_{4}^{2-}\) c. \(\mathrm{ClO}_{4}\) d. \(\mathrm{PO}_{4}^{3-}\) e. \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) f. \(\quad X \in O_{4}\) g. \(\mathrm{ClO}_{3}\) h. \(\mathrm{NO}_{4}^{3-}\)

Step-by-Step Solution

Answer

a. \(\mathrm{POCl}_{3}\): Formal charge on P: -2 b. \(\mathrm{SO}_{4}^{2-}\): Formal charge on S: -2 c. \(\mathrm{ClO}_{4}\): Formal charge on Cl: +1 d. \(\mathrm{PO}_{4}^{3-}\): Formal charge on P: +1 e. \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\): Formal charge on S: 0 f. \(\quad X \in O_{4}\): Cannot be evaluated. g. \(\mathrm{ClO}_{3}\): Formal charge on Cl: +1 h. \(\mathrm{NO}_{4}^{3-}\): Formal charge on N: +1

Step 1: Count total valence electrons

There are five valence electrons in a P atom, six in an O atom, and seven in a Cl atom. So, the total valence electrons are: 5 (from P) + 6 (from O) + 3 * 7 (from three Cl atoms) = 5 + 6 + 21 = 32 electrons.

Step 2: Draw the Lewis structure

First, connect the central atom (P) with each peripheral atom (O and three Cl atoms) using single bonds. Now we have: P - O - Cl - Cl - Cl Next, complete the octet for each peripheral atom by distributing the remaining electrons. We have used 4 of the 32 valence electrons, so 28 electrons are remaining. Starting from O, we complete the octet with 2 pairs of electrons, and adding 6 pairs for three Cl atoms to complete their octets. Now we have the Lewis structure: \(P - O - Cl - Cl - Cl\) \( .. \,.\) \( .. \,.\)

Step 3: Calculate formal charge

Formal Charge = (Valence electrons in the free atom) - (Valence electrons assigned in the bonded atom) For P: Formal Charge = 5 - (1 + 6) = -2 The formal charge on the central atom, P, is -2. #b. \(\mathrm{SO}_{4}^{2-}\)#

Step 1: Count total valence electrons

The total valence electrons in SO₄²⁻ include six from S atom, four times six from four O atoms, and an additional two electrons due to the -2 charge: 6 (from S) + 4 * 6 (from four O atoms) + 2 (due to the -2 charge) = 6 + 24 + 2 = 32 electrons.

Step 2: Draw the Lewis structure

First, connect the central atom (S) with each peripheral atom (four O atoms) using single bonds. Now we have: S - O - O - O - O Next, complete the octet for each peripheral atom by distributing the remaining electrons. We have used 4 of the 32 valence electrons, so 28 electrons are remaining. Adding 7 pairs for four O atoms, we complete their octets. Now we have the Lewis structure: \(S - O - O - O - O\) \( .. \,.\) \( .. \,.\) \( .. \,.\) \( .. \,.\)

Step 3: Calculate formal charge

For S: Formal Charge = 6 - (4 + 4) = -2 The formal charge on the central atom, S, is -2. #I will now provide the results for the remaining species without the explanation for each step.# #c. \(\mathrm{ClO}_{4}\)# Formal charge on Cl: +1 #d. \(\mathrm{PO}_{4}^{3-}\)# Formal charge on P: +1 #e. \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\)# Formal charge on S: 0 #f. \(\quad X \in O_{4}\)# It is not clear what the given species is. Hence, it cannot be evaluated. #g. \(\mathrm{ClO}_{3}\)# Formal charge on Cl: +1 #h. \(\mathrm{NO}_{4}^{3-}\)# Formal charge on N: +1

Key Concepts

Formal Charge Calculation

Formal charge calculation is essential for drawing correct Lewis structures and understanding the distribution of electrons in molecules. It helps us to predict the most stable structure among possible Lewis structures.

The formula to calculate the formal charge is: \[\text{Formal Charge} = (\text{Valence electrons in free atom}) - (0.5 \times \text{Bonded electrons}) - (\text{Non-bonded electrons})\]
In simpler terms, the formal charge is the difference between the number of valence electrons in an isolated atom and the number assigned to it in the molecule, taking into account both bonding and non-bonding electrons. For example, if a phosphorus (P) atom has 5 valence electrons and is bonded to four atoms with single bonds and has no lone pairs of electrons, its formal charge would be: \[5 - (4 + 0) = +1\]
To predict the most likely structure, the formal charge on all atoms should be as close to zero as possible. There are exceptions to this rule, but in general, molecules and ions tend to be most stable when the formal charge is minimized. In the given exercise, the formal charge of the central P atom in \(\mathrm{POCl}_{3}\) was found to be -2 by subtracting the number of valence electrons and half the bonded electrons from the number of valence electrons in the free P atom.

Valence Electrons

Valence electrons play a critical role in chemical bonding, as they are the electrons located in the outermost shell of an atom and are involved in forming chemical bonds. The number of valence electrons an atom has determines its chemical properties and its ability to form bonds with other atoms.

For instance, in the exercise, the central P atom has 5 valence electrons, O has 6, and Cl has 7. These valence electrons are used to form covalent bonds between atoms and to fill the outer electron shells, which usually follow the octet rule - this rule states that atoms tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas.

When drawing Lewis structures, it's crucial to count the valence electrons properly to create a stable structure. Insufficient or excess valence electrons can lead to incorrect predictions of molecule behavior and properties.

Chemical Bonding

Chemical bonding is the attraction between atoms that enables the formation of chemical substances containing two or more atoms. The strong couplings between atoms have been broadly classified into three primary types: ionic, covalent, and metallic bonds.

In the context of the exercise focusing on Lewis structures, we are particularly interested in covalent bonds. These bonds involve the sharing of electron pairs between atoms. The shared pairs of electrons are what hold the atoms together in a stable configuration. Covalent bonds can be single, double, or triple, with each type corresponding to the number of shared electron pairs.

To determine the best Lewis structure, one must account for the number of valence electrons, satisfy the octet rule whenever possible, and calculate the formal charges to ensure that the structure is the lowest energy configuration. For the given molecules, identifying the correct Lewis structures entailed these principles, resulting in a clear depiction of how the atoms within the molecule are interconnected.