Use the formal charge arguments to rationalize why \(\mathrm{BF}_{3}\) would not follow the octet rule.

To calculate the formal charge of each atom in the BF3 molecule, we first need to know the number of valence electrons for each atom. The valence electrons are the electrons in the outermost shell of the atom. Boron (B) has 3 valence electrons and Fluorine (F) has 7 valence electrons.

Now, to determine the electron arrangement in the molecule, let's draw the Lewis structure of the BF3 molecule. We start by placing the central atom (Boron) in the middle and the three Fluorine atoms around it. Then, we connect each Fluorine atom to the central Boron atom with a single bond, indicating a shared pair of electrons. The resulting Lewis structure is as follows: ``` F | F--B--F ``` Each single bond represents two shared electrons.

The formal charge of each atom in a molecule can be calculated using the formula: Formal Charge = Valence Electrons - Non-bonding Electrons - (1/2 * Bonding Electrons) Now, let's calculate the formal charge of Boron and Fluorine in the BF3 molecule. For Boron (B): Valence Electrons = 3 Non-bonding Electrons = 0 (since all valence electrons are involved in bonding) Bonding Electrons = 6 (as it is connected to 3 Fluorine atoms with one single bond each) Formal Charge of B = \( 3 - 0 - \frac{1}{2}*6 = 0 \) For Fluorine (F): Valence Electrons = 7 Non-bonding Electrons = 6 (since each Fluorine shares 2 of its 7 electrons with Boron) Bonding Electrons = 2 (as it is connected to Boron with one single bond) Formal Charge of F = \( 7 - 6 - \frac{1}{2}*2 = 0 \)

The formal charges on the Boron and Fluorine atoms in the BF3 molecule are both 0. It indicates that the molecule is stable and has a minimum energy arrangement of electrons. However, the central Boron atom has only 6 electrons in its outer shell (3 F-B bonds with a shared pair of electrons each). This clearly indicates that the BF3 molecule does not follow the octet rule, where the central atom is expected to have 8 electrons in its outermost shell. The formal charge analysis shows that the BF3 molecule has a stable electron configuration despite not following the octet rule. This is because the addition of more electrons to the central Boron atom would result in an increased formal charge, leading to a less stable molecule. Therefore, in the case of BF3, the octet rule is not followed to maintain a stable electron configuration and a minimum energy state.