Problem 172 - Chemistry: An Atoms-Focused Approach

Question

In the typical Lewis structure of \(\mathrm{BF}_{3}\) there are only six valence electrons on the boron atom and each \(\mathrm{B}-\mathrm{F}\) bond is a single bond. However, the length and strength of these bonds indicate that they have a small measure of doublebond character-that is, their bond order is slightly greater than 1. a. Draw a Lewis structure of \(\mathrm{BF}_{3}\), including all resonance structures, in which there is one \(\mathrm{B}=\mathrm{F}\) double bond. b. What is the formal charge on the \(\mathrm{B}\) atom, and what is the average formal charge on each \(\mathrm{F}\) atom? c. Based on formal charges alone, what should be the bond order of each \(\mathrm{B}-\mathrm{F}\) bond in \(\mathrm{BF}_{3} ?\) d. What factor might support a bond order slightly greater than \(1 ?\)

Step-by-Step Solution

Answer

Answer: The bond order of each B-F bond in BF3 is approximately 1.67, based on formal charges and considering the resonance structures. This bond order is slightly greater than 1 due to the influence of resonance structures and the electronegativity difference between B and F, which results in polar bonds. These factors lead to stronger and shorter bonds than expected for single bonds alone.

Step 1: Draw the Lewis Structure with a B-F double bond

First, let's draw the Lewis structure of \(\mathrm{BF}_{3}\) with a double bond between B and F. To do this, put the B atom in the center and arrange the three F atoms around it. The B atom has 3 valence electrons, and each F atom has 7 valence electrons. We can use one of the valence electrons from B to form a bond with each F atom. Then, we will use the remaining 6 electrons from the central B atom to form a double bond with one of the F atoms. ``` F || F--B--F ```

Step 2: Draw the Resonance Structures

Now, we will draw all the possible resonance structures that have the same atoms and one double bond. ``` F F || || F--B--F and F--B--F ```

Step 3: Calculate the Formal Charges

The formal charge of an atom in a molecule is the difference between the number of valence electrons in the atom and the number of electrons it effectively uses. For \(\mathrm{BF}_{3}\) with a double bond, the formal charges are: - Formal charge of B: \((3 - (0 + \frac{6+2}{2})) = 3 - 4 = -1\) - Formal charge of F with double bond: \((7 - (6 + \frac{2}{2})) = 7 - 7 = 0\) - Formal charge of F with single bond: \((7 - (6 + \frac{2}{2})) = 7 - 7 = 0\)

Step 4: Calculate the Average Formal Charge on each F

As there are three equivalent resonance structures, the average formal charge on each F atom is zero since they all have a formal charge of 0.

Step 5: Calculate Bond Order Based on Formal Charges

Based on formal charges alone, and considering that there are three resonance structures, the bond order of each B-F bond in \(\mathrm{BF}_{3}\) should be: $$\frac{1 \times (1+1+1) + 2 \times (1)}{3} = \frac{5}{3} \approx 1.67$$

Step 6: Identify Factors Supporting a Bond Order Slightly Greater than 1

In this case, resonance structures contribute to the bond order slightly greater than 1. The resonance structures reduce the overall energy of the molecule and stabilize it, leading to stronger and shorter bonds than expected for single bonds alone. Additionally, in the actual structure of \(\mathrm{BF}_{3}\), the electronegativity difference between B and F can result in polar B-F bonds which also can contribute to a bond order slightly greater than 1.

Key Concepts

Resonance Structures

Resonance structures are different ways to arrange electrons in a molecule, without altering the positions of the atoms. In \(\mathrm{BF}_3\), resonance illustrates possible structures where electrons in the molecule are distributed differently. By having resonance structures, electrons can be delocalized, stabilizing the molecule.
For example, in \(\mathrm{BF}_3\), instead of having just one structure with a single B-F double bond, we can draw several resonance structures. Each alternative shows the double bond moved to a different fluorine atom.

• This means the double bond character isn't fixated between just one boron and one fluorine but can be shared among all BF bonds.
• Such sharing of electron density across multiple bonds enhances molecular stability, leading to bonds that appear to be somewhere between a single and a double bond in nature.

Formal Charge

The formal charge is a concept that helps predict the stability and distribution of electrons in a molecule. Formal charges can be calculated using the formula:\[\text{Formal Charge} = (\text{Valence Electrons}) - (\text{Non-bonding Electrons}) - \frac{1}{2}(\text{Bonding Electrons})\]In the case of \(\mathrm{BF}_3\), the formal charge for each atom is critical to understanding its electron sharing and stability.

• The boron atom in one of the resonance structures will have a formal charge of \(-1\) because it has effectively used four electrons while having three valence electrons.
• Fluorine atoms typically end with a formal charge of \(0\) in these resonance forms as they complete their octet by using electrons efficiently.

Overall, calculating formal charge helps reveal which resonance structure may be more prominently contributing to the actual electron arrangement in the molecule.

Bond Order

Bond order offers insights into the number of bonds between two atoms and influences bond strength. For \(\mathrm{BF}_3\), bond order calculations incorporate resonance structures to provide a more detailed view of molecular interactions. Bond order is calculated as the average number of bonds between pairs of atoms:\[\text{Bond Order} = \frac{\text{Total Number of Bonds in all Resonance Structures}}{\text{Number of Resonance Structures}}\]In the case of \(\mathrm{BF}_3\), each B-F bond is the result of averaging bonds over all resonance forms.

• If including one double bond in the calculation, the bond order for B-F bonds is approximately 1.67, deviating from the perceived single bond character.
• A bond order greater than 1 indicates partial double bond character, explaining the shorter bond lengths observed in \(\mathrm{BF}_3\).
• This nuanced bond order underscores the significance of resonance and formal charge in understanding molecular structure.