Question

Valence Bond Theory Draw orbital diagrams (boxes with arrows in them) to represent the electron configuration of carbon before and after sp \(^{3}\) hybridization.

Short answer

Before sp³ hybridization, Carbon has the electron configuration of 1s² 2s² 2p². After hybridization, the electron configuration is four equivalent sp³ orbitals each containing one unpaired electron, ready for bonding.

Step-by-step solution

Determine the Electron Configuration of Carbon

First, determine the electron configuration of a neutral carbon atom which has 6 electrons. The configuration is 1s² 2s² 2p². The 1s orbital is filled with 2 electrons, the 2s orbital is filled with 2 electrons, and the 2p orbitals have 2 electrons out of a possible 6 electrons (as there are three 2p orbitals).

Draw the Orbital Diagram for Carbon Before Hybridization

Draw one box (or circle) for the 1s orbital with two arrows pointing in opposite directions (representing the two electrons). Draw a second box for the 2s orbital, again with two arrows pointing in opposite directions. Then draw three boxes for the 2p orbitals. Place one arrow in the first two 2p boxes to represent the two 2p electrons. Leave the third 2p box empty as it has no electron. The arrows in the same box point in opposite directions, signifying the Pauli exclusion principle that no two electrons in the same orbital can have the same spin.

Understand sp³ Hybridization

During sp³ hybridization, one 2s electron is promoted to the empty 2p orbital. This results in four orbitals with one electron each: one 2s and three 2p orbitals. These four orbitals hybridize to form four equivalent sp³ hybrid orbitals.

Draw the Orbital Diagram for Carbon After sp³ Hybridization

Draw four boxes of equal energy, signifying the four sp³ hybrid orbitals. Place one arrow in each box, indicating a single electron in each hybrid orbital. These hybrid orbitals are now ready to form four sigma bonds, as is the case in methane (CH₄).

Key concepts

Valence Bond Theory

Valence Bond Theory (VBT) is a fundamental concept in chemistry that explains how atoms bond with each other to form molecules. According to VBT, atomic orbitals of bonding atoms overlap to form a new kind of orbital that reflects a covalent bond between them. The theory suggests that a bond forms when electrons with opposite spins in different atoms are in close proximity, allowing their atomic orbitals to overlap.

To depict the overlap and the resulting covalent bonds, we use orbital diagrams – visual representations of the electrons in an atom's orbitals. In the case of carbon before sp³ hybridization, we have separate s and p orbitals. These orbitals are not equivalent, but upon hybridization, they combine and redistribute their energy to form equivalent sp³ hybrid orbitals. This results in carbon's capability to form four identical bonds, leading to the stable and tetrahedral structure commonly observed in organic compounds like methane.

Orbital Diagrams

Orbital diagrams are visual tools used to represent the electron configurations of atoms. They consist of boxes (or circles) with arrows to depict electrons. Each arrow represents an electron, while the direction of the arrow indicates the electron's spin. This is an illustration of the Pauli exclusion principle, which states that no two electrons in the same orbital can have the same spin.

The layout of these diagrams reflects the electron configuration of the atom. For a carbon atom before sp³ hybridization, two electrons fill the lowest energy level (1s), followed by two electrons in the second energy level (2s), and then two more electrons in the 2p orbitals. After hybridization, the electron from the 2s orbital is promoted, and the s and p orbitals mix to form four equivalent sp³ orbitals, each depicted by a box with a single electron.

Electron Configuration

The electron configuration of an atom describes the distribution of electrons in its atomic orbitals. For a neutral carbon atom, with six electrons, this configuration is noted as 1s² 2s² 2p². The numbers denote the energy level, 's' and 'p' indicate the type of orbital, and the superscripts show the number of electrons in those orbitals.

The electron configuration provides insight into an atom's reactivity and how it bonds with other atoms. For instance, in carbon, the two electrons in the 1s orbital are tightly bound to the nucleus and do not partake in chemical bonding. However, the electrons in the 2s and 2p orbitals are in a higher energy level and can be involved in bonds. The sp³ hybridization phenomenon arises when the 2s and 2p orbitals blend to accommodate extra electrons or create more favorable bonding conditions, like in the formation of four equivalent bonds we see in a molecule of methane.