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

We'll start by drawing the Lewis structure of \(\mathrm{BeCl}_{2}\) with single bonds only. To do this, first count the total number of valence electrons for each atom in the molecule. Beryllium (Be) is in group 2, so it has 2 valence electrons, and chlorine (Cl) is in group 7, and it has 7 valence electrons. Since there are two chlorine atoms, the total number of valence electrons in the molecule is: \[(2) + (2 \times 7) = 16\] Now, using these valence electrons, draw the Lewis structure with single bonds: Be is the central atom, making a single bond to each Cl atom: Cl | Be | Cl Next, add the lone pairs to the chlorine atoms so that they follow the octet rule (8 electrons for each atom): Cl : : Be | Cl : :

Now, we need to check if this Lewis structure of \(\mathrm{BeCl}_{2}\) satisfies the octet rule. We can see that both Cl atoms have 8 electrons around them (including the bonding electrons), so they satisfy the octet rule. However, if we examine the Be atom, it only has 4 electrons around it (2 bonding electrons from each single bond), which does not satisfy the octet rule. Therefore, the Lewis structure with only single bonds does not satisfy the octet rule.

Since our first structure with only single bonds does not satisfy the octet rule, we will now search for possible resonance structures that satisfy the octet rule. There's a possibility to satisfy the octet rule for the Be atom by having a double bond with one Cl atom and a single bond with the other. Here's one resonance structure: Cl :: Be : :Cl And here's another possible resonance structure with the double bond to the other Cl atom: Cl: : Be:: Cl

Now we need to analyze these resonance structures based on their formal charges to determine which structure is dominant. To calculate the formal charges: Formal charge = (Valence electrons) - (Number of bonding electrons) - (Number of nonbonding electrons) For resonance structure 1: - Be: formal charge = (2) - (3) - (0) = -1 - Cl (with a single bond): formal charge = (7) - (1) - (6) = 0 - Cl (with a double bond): formal charge = (7) - (4) - (4) = -1 For resonance structure 2, the formal charges are the same, but with the chlorine atoms swapped. Both resonance structures have a total formal charge of -2, but bearing the negative formal charge on the highly electronegative chlorine atoms is favorable. Therefore, it can be said that these resonance structures are dominant when compared to the initial Lewis structure with single bonds. The actual structure of \(\mathrm{BeCl}_{2}\) in the vapor phase could be a hybrid of these resonance structures, better satisfying the octet rule for all the atoms.