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

Short answer

The Lewis structure of BeCl2 with single bonds gives all atoms a formal charge of zero, making it the most important resonance structure in describing the molecule, even though it does not satisfy the octet rule. Two other resonance forms are possible, both with a double bond to one Cl atom, but these have nonzero charges on Be and Cl, making them less likely.

Step-by-step solution

Drawing the Lewis structure with single bonds

To draw the Lewis structure of BeCl2, we first need to determine the total number of valence electrons. Beryllium (Be) has 2 valence electrons (group 2) and each Chlorine (Cl) atom has 7 valence electrons (group 17). Therefore, the total number of valence electrons for BeCl2 is \(2 + 2 \times 7 = 16\). Now, we will connect Be with each Cl atom with a single bond, which will use 4 valence electrons, leaving 12. These remaining 12 electrons will be distributed on the Cl atoms, so each Cl atom will have 6 non-bonding electrons. After completing the Lewis structure with single bonds, we can see that Cl atoms satisfy the octet rule with 8 electrons around them, but Be has only 4 electrons instead of 8 required by the octet rule. So, the given Lewis structure does not satisfy the octet rule.

Possible resonance forms

Since the Lewis structure with single bonds does not satisfy the octet rule, we have to consider other possible resonance forms. A resonance form that satisfies the octet rule involves having Be with a double bond to one Cl atom and a single bond to the other. There are two possible resonance structures like this, one with a double bond to the first Cl atom and the other with a double bond to the second Cl atom.

Formal charges

To determine the most important resonance structure, we need to calculate formal charges for each structure. The formula for formal charge is: Formal Charge = (Number of valence electrons in the free atom) - (Number of non-bonding electrons) - (Number of bonding electrons/2) For the structure with single bonds: - Formal charge on Be: \(2 - 0 - (4/2) = 0\) - Formal charge on each Cl: \(7 - 6 - (2/2) = 0\) For the two resonance structures with the double bond to one Cl atom: - Formal charge on Be: \(2 - 0 - (6/2) = -1\) - Formal charge on the Cl with double bond: \(7 - 4 - (4/2) = +1\) - Formal charge on the Cl with single bond: \(7 - 6 - (2/2) = 0\) According to the principle of formal charges, the best resonance structure is the one with the lowest formal charges on the atoms. The structure with single bonds has zero charges on all atoms, while the resonance structures with double bonds have nonzero charges on Be and Cl atoms. Thus, the Lewis structure of BeCl2 with single bonds is the most important in describing the molecule, even though it does not satisfy the octet rule.

Key concepts

Resonance Forms

To truly understand the nature of certain molecules, it's essential to grasp the concept of resonance forms. Resonance forms are alternative Lewis structures for a molecule where the atoms are in the same positions, but the electron arrangements are different. It is important to note that these are not isomers, which would involve different connectivity of atoms, but rather different possible distributions of electrons in the same molecular framework.

Resonance is a way to delocalize electron density across a molecule to provide a better representation of the true electronic structure. In the real world, the molecule doesn't flip-flop between these forms; the true structure is actually an average of all the possible resonance forms, known as the resonance hybrid. This understanding helps clarify why some molecules don't always conform strictly to simple rules such as the octet rule.

Formal Charge Calculation

The concept of formal charge is essential in predicting the most stable form of a molecule among its various Lewis structures, especially when dealing with resonance forms. The formal charge is a hypothetical charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electronegativity.

To calculate the formal charge on an atom, use the formula:
Formal Charge = (Number of valence electrons in the free atom) - (Number of non-bonding electrons) - (Number of bonding electrons/2).

By comparing the formal charges of different resonance forms, you can often determine which form is more prevalent in nature. The rule of thumb is that the more stable resonance form has the smallest absolute values of formal charges and is often the one where negative formal charges reside on more electronegative atoms.

Octet Rule

The octet rule is a chemical tenet which posits that atoms tend to bond in such a way that each atom has eight electrons in its valence shell, thus gaining the electron configuration of a noble gas and the associated stability. This rule applies well to many molecules, especially when predicting the arrangement of electrons in atoms like carbon, nitrogen, oxygen, and the halogens.

However, there are exceptions that one must be cautious of. Elements in the third period and beyond on the periodic table can have more than eight electrons due to available d-orbitals, and some elements like hydrogen, boron, and beryllium often have less than an eight-electron arrangement. In the case of BeCl₂, beryllium does not follow the octet rule as it is stable with only four valence electrons in its shell, providing a pertinent reminder to always consider exceptions when applying this rule.