Problem 65 - Chemistry The Central Science In Si Units

Question

In the vapor phase, \(\mathrm{BeCl}_{2}\) exists as a discrete molecule. (a) Draw the Lewis structure of this molecule, using only single bonds. Does this Lewis structure satisfy the octet rule? (b) What other resonance structures are possible that satisfy the octet rule? (c) On the basis of the formal charges, which Lewis structure is expected to be dominant for \(\mathrm{BeCl}_{2} ?\)

Step-by-Step Solution

Answer

The initial Lewis structure, \( \text{Cl} - \text{Be} - \text{Cl} \) with single bonds, is dominant due to minimized formal charges.

Step 1: Draw the Initial Lewis Structure

Begin by drawing the Lewis structure for \( \text{BeCl}_2 \) using single bonds only. Beryllium (Be) is the central atom, and it forms single bonds with two chlorine (Cl) atoms. The Lewis structure looks like this: \[ \text{Cl} - \text{Be} - \text{Cl} \]. Each chlorine atom has three lone pairs of electrons, while beryllium has no lone pairs and only uses the two electrons involved in bonding.

Step 2: Analyze the Octet Rule

Examine whether the initial Lewis structure satisfies the octet rule. The octet rule states that atoms are generally most stable with eight electrons in their valence shell. In \( \text{BeCl}_2 \), beryllium has only four electrons (two bonds), which does not satisfy the octet rule. However, chlorine achieves an octet with its full valence shell.

Step 3: Consider Other Resonance Structures

Consider possible resonance structures for \( \text{BeCl}_2 \) to satisfy the octet rule on the central atom. One option is to form double bonds between beryllium and each chlorine atom. This results in a structure like \[ \text{Cl} = \text{Be} = \text{Cl} \], where beryllium now shares in the full octet. Both chlorine atoms keep their full octet by forming double bonds.

Step 4: Evaluate Formal Charges

Calculate the formal charges for each possible structure to determine which one is more stable. In the initial structure \( \text{Cl} - \text{Be} - \text{Cl} \), beryllium has a formal charge of 0, and each chlorine has a formal charge of 0. In the resonance structure \( \text{Cl} = \text{Be} = \text{Cl} \), the formal charges for beryllium become +1 and -1 for each chlorine, making this structure less likely based on stability.

Step 5: Identify the Dominant Structure

Based on the formal charges calculated, the initial Lewis structure \( \text{Cl} - \text{Be} - \text{Cl} \) with single bonds is expected to be the dominant structure. Even though it does not satisfy the octet rule for beryllium, it minimizes formal charges, adhering to the principle that the most stable structure is one where the formal charges are closest to zero.

Key Concepts

Octet Rule

The octet rule is an important principle in chemistry that helps us to understand how atoms bond in molecules. According to this rule, atoms tend to form bonds in such a way that they have eight electrons in their valence shell. This configuration is considered most stable as it mimics the electron configuration of noble gases.
However, not all atoms strictly follow the octet rule. In the case of beryllium in beryllium chloride (\( \mathrm{BeCl}_{2} \)), the octet rule is not satisfied. Beryllium forms two single bonds with two chlorine atoms, resulting in only four electrons around beryllium rather than eight.

• Chlorine, on the other hand, completes its octet with each atom forming a single bond and retaining three lone pairs of electrons.
• While the octet rule is a good rule of thumb, exceptions like beryllium highlight that some elements can be stable with less than eight electrons.

Resonance Structures

Resonance structures are different ways to represent the same molecule, showing how electrons can be distributed across bonds and atoms in different ways. For many molecules, these structures help illustrate the delocalization of electrons.
For \( \mathrm{BeCl}_{2} \), considering resonance structures might involve forming double bonds between the beryllium and chlorine atoms to satisfy the octet rule for beryllium. This creates a structure: \[ \text{Cl} = \text{Be} = \text{Cl} \].
In this resonance structure:

• Beryllium shares more electrons, reaching a full octet.
• Each chlorine atom retains an octet by forming one double bond and retaining two lone pairs.
• While valid as a resonance form, this structure generates formal charge distribution (as discussed below), impacting its stability.

Formal Charge

Formal charge is a concept that helps chemists determine the distribution of charge within a molecule, aiding in the identification of the most stable molecular structure.
To calculate the formal charge for any atom:

• Subtract the number of non-bonding electrons from the atom’s valence electrons.
• Then, subtract the number of bonds (counted as half the shared electrons) the atom forms in the structure.

In \( \mathrm{BeCl}_{2} \):

• The simple structure \( \text{Cl} - \text{Be} - \text{Cl} \) has a formal charge of 0 for each atom. This means that the electrons are "equally" distributed, making it more stable.
• The resonance structure \( \text{Cl} = \text{Be} = \text{Cl} \) results in formal charges of +1 on beryllium and -1 on each chlorine, suggesting a less stable form due to higher charges.

Minimizing formal charge often determines the dominant Lewis structure, as seen here where the simple bond structure is favored.