Question

A molecule that has the formula CH2X2 has a X-C-X bond angle that is 111°. What is the hybridization of this carbon toward each X atom if only s and p orbitals are hybridized? In other words, what is the lambdaX value to the nearest hundredth? An explanation would be great, thank you!

Answer 1

Solution:

Determining the hybridization of carbon atom

The carbon atom in CH₂X₂ is covalently bonded to 4 other atoms: 2 hydrogen atoms and 2 halogen atoms (represented by X). To determine the kind of hybridization of atomic orbitals of carbon atom, let's look at its ground state. Its ground state is:

₆C: 1s² 2s² 2p_x¹ 2p_y¹ 2p_z⁰

or

To accommodate 4 electrons of the 4 other atoms, the four orbitals of carbon must be singly filled. To accomplish this, an electron from the 2s orbital jumps to 2p orbital by absorbing energy. This is feasible as the energy gap between 2s and 2p orbital is not much and it is believed to easily come from the lower energy (or stable) state that the system as a whole achieves. The state of electrons is called excited which has an electronic configuration of:

₆C: 1s² 2s¹ 2p_x¹ 2p_y¹ 2p_z¹

or

The 2s and 2p orbitals of the excited state attain the same energy and no longer retain characteristics of s and p orbitals. They become degenerate and have the same shape. It is these 4 hybrid orbitals that bond to four other atoms. Since one s and 3 p orbitals combine to form these 4 hybrid orbitals, the hybridization of carbon in the case of CH₂X₂ is said to be sp³.

Bond angle:

The four hybrid orbitals arrange themselves in space such that they are a maximum distance apart (so that there is minimum repulsion). In case the four identical atoms are attached (as in CH₄), the H-C-H bond angle is 109.5⁰ (called a tetrahedral angle). But in the case of CH₂X₂, all the four atoms are not same and halogen atoms being bigger in size have more repulsion, so the X-C-X bond angle is found to be greater than 109.5⁰ (111⁰, to be exact). Nevertheless, the shape around the central carbon atom is tetrahedral (but not a regular tetrahedron as in the case of CH₄).

is the parameter to determine the degree of hybridization of each bond. It is the coefficient of p when the hybrid orbital is written in the form of s + .p. It is related to hybridization index, n, which is the exponent of p in spⁿ, by the relation: n =

Clearly, in the present case, n=3