Problem 63 - Chemistry: The Central Science

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 forms are possible that satisfy the octet rule? (c) Using formal charges, select the resonance form from among all the Lewis structures that is most important in describing \(\mathrm{BeCl}_{2}\).

Step-by-Step Solution

Answer

The Lewis structure of BeCl\(_2\) with single bonds (Cl-Be-Cl) does not satisfy the octet rule for the Be atom. However, introducing double bonds between Be and Cl (Cl=Be=Cl) would satisfy the octet rule. Calculating formal charges, the single-bonded structure has a formal charge of 0 for all atoms, while the double-bonded structure has +1 on Cl and -2 on Be. Despite not satisfying the octet rule, the single-bonded structure (Cl-Be-Cl) is the most important resonance form since it has the lowest formal charge on each atom.

Step 1: Draw the Lewis structure using single bonds

To draw the Lewis structure for BeCl\(_2\), we show the valence electrons around each element. Beryllium (Be) has 2 valence electrons, while Chlorine (Cl) has 7 valence electrons. If we use single bonds between Be and Cl atoms, the Lewis structure looks like this: ``` Cl-Be-Cl ``` Here, two electrons are shared between Be and each Cl atom giving a total of 4 electrons around Be. Now, let's check if this Lewis structure satisfies the octet rule. The octet rule states that atoms should have 8 electrons in their valence shell to be stable. Each Cl atom has 8 electrons (6 non-bonding and 2 bonding electrons), but the Be atom has only 4 electrons, which does not satisfy the octet rule.

Step 2: Draw other resonance forms that satisfy the octet rule

As our initial Lewis structure does not satisfy the octet rule, we need to consider other possible resonance forms. To satisfy the octet rule for the Be atom, we need two additional electrons around the Be atom. One way to achieve this is to introduce a double bond between Be and each Cl atom: ``` Cl=Be=Cl ``` Now, each Cl atom still has 8 electrons (4 non-bonding and 4 bonded electrons), and the Be atom has a total of 8 electrons (4 electrons shared with each Cl atom) satisfying the octet rule. This new Lewis structure is another possible resonance form.

Step 3: Use formal charges to determine the most important resonance form

To find the most important resonance form, we will calculate the formal charges for each atom in both possible structures. Formal charge = (Valence electrons) - (Non-bonding electrons) - 1/2(Bonding electrons) ## For the single-bonded structure: ``` Cl-Be-Cl ``` Formal charge of Be = 2 - 0 - 1/2(4) = 0 Formal charge of each Cl = 7 - 6 - 1/2(2) = 0 ## For the double-bonded structure: ``` Cl=Be=Cl ``` Formal charge of Be = 2 - 0 - 1/2(8) = -2 Formal charge of each Cl = 7 - 4 - 1/2(4) = +1 The most important resonance form is the one with the lowest formal charge on each atom. The single-bonded structure has a formal charge of 0 on all atoms, while the double-bonded structure has +1 on Cl and -2 on Be. Therefore, the most important resonance form is the single-bonded structure (Cl-Be-Cl), even though it does not satisfy the octet rule for the Be atom.

Key Concepts

Octet Rule

The octet rule is a fundamental principle in chemistry that guides us in determining how atoms bond together. It states that atoms tend to bond in such a way that they have eight electrons in their valence shell, achieving a stable electron configuration similar to noble gases.

Let's look into why using single bonds for beryllium chloride (\(\mathrm{BeCl}_{2}\)) in its Lewis structure, results in an octet rule check. Beryllium (Be) has two valence electrons, and each chlorine (Cl) atom has seven valence electrons. In the single-bonded structure:

• Each Cl ends up with 8 electrons, which satisfies the octet rule for chlorine.
• Beryllium, however, only ends up with a total of 4 electrons, which does not satisfy the octet rule for beryllium.

In some cases, especially involving certain elements like B, Be, and H, achieving an octet is not always possible or necessary. This shows the limitation of the octet rule when applied to all elements.

Resonance Structures

Resonance structures are different Lewis structures that represent the same compound but differ in the placement of the electrons. They help us understand the possible bonding arrangement in a molecule.

For \(\mathrm{BeCl}_{2}\), the initial single-bonded structure didn't fulfill the octet for beryllium. However, one could hypothesize additional resonance forms by altering the bond configuration:

• Introducing a double bond between Be and each Cl atom could help achieve the octet configuration for Be. This results in a resonance structure of\(\text{Cl=Be=Cl}\).

While this adjusted structure theoretically satisfies the octet rule for all atoms, it isn't always the most stable contribution to the resonance hybrid, as subsequent analysis will show.

Formal Charge Analysis

Formal charge analysis helps determine the most accurate or likely Lewis structure by calculating a charge for each atom using the formula:

• Formal Charge = (Number of valence electrons) - (Number of non-bonding electrons) - \(\frac{1}{2}\)(Number of bonding electrons)

When comparing structures, the goal is to find the arrangement with the least formal charge.

• In the single-bond \(\text{Cl-Be-Cl}\) structure, all atoms have a formal charge of zero.
• The double-bonded \(\text{Cl=Be=Cl}\) structure results in Be having a -2 charge, and each Cl atom a +1 charge.

The structure with the least distribution of formal charges and closest to zero is typically considered the more stable and significant form. In this case, this is the single-bonded structure. Even if it doesn't meet the octet rule for Be, it holds the least charge distribution, making it the preferred resonance structure.