Why is \(\mathrm{BeCl}_{2}\) molecule linear, but \(\mathrm{BF}_{3}\) is trigonal planar?

Both BeCl2 and BF3 have a central atom with multiple bonded atoms around. In BeCl2, the central atom is Be (beryllium) and in BF3, the central atom is B (boron). Let's determine each central atom's electron configuration: For Be (atomic number 4): 1s^2 2s^2. For B (atomic number 5): 1s^2 2s^2 2p^1.

To understand the shape of the molecules, we need to determine the number of valence electrons they have. We will calculate the valence electrons considering the number of shared electrons in each bond: For BeCl2: Be (2 valence electrons) + 2 Cl atoms (each has 7 valence electrons) = 2 + (2 × 7) = 16 valence electrons. For BF3: B (3 valence electrons) + 3 F atoms (each has 7 valence electrons) = 3 + (3 × 7) = 24 valence electrons.

In BeCl2, there are 16 valence electrons. The central atom Be is bonded with two Cl atoms using two electron pairs to form two shared bonds. Thus, there are no lone pairs of electrons on the central atom. According to the VSEPR theory, if there are two electron pairs and no lone pairs on the central atom, they will arrange themselves linearly to minimize repulsions. Therefore, BeCl2 has a linear molecular shape.

In BF3, there are 24 valence electrons. The central atom B is bonded with three F atoms using three electron pairs to form three shared bonds. Similar to BeCl2, there are no lone pairs of electrons on the central atom. According to the VSEPR theory, if there are three electron pairs and no lone pairs on the central atom, they will arrange themselves in a trigonal planar shape to minimize repulsions. Therefore, BF3 has a trigonal planar molecular shape. To summarize: - BeCl2 has a linear shape because there are two electron pairs with no lone pairs on the central atom (Be), which creates a linear arrangement. - BF3 has a trigonal planar shape because there are three electron pairs with no lone pairs on the central atom (B), which creates a trigonal planar arrangement.