Question

Write orbital diagrams (boxes with arrows in them) to represent the electron configuration of carbon before and after \(s p^{3}\) hybridization.

Short answer

Before sp3 hybridization, Carbon has the electron configuration: 1s2 2s2 2p2. After hybridization, it has four sp3 hybrid orbitals each with one unpaired electron.

Step-by-step solution

Write Down the Electron Configuration of Carbon

Identify the electron configuration of a carbon atom before hybridization. Carbon has 6 electrons with the configuration 1s2 2s2 2p2. The first two electrons occupy the 1s orbital, the next two occupy the 2s orbital, and the last two are in separate 2p orbitals, following Hund's rule.

Draw the Orbital Diagram of Carbon Before Hybridization

Draw a diagram with one box for the 1s orbital containing two arrows pointing in opposite directions (representing the two electrons with opposite spins), another box for the 2s orbital also with two arrows, and three boxes for the 2p orbitals; populate the first two p orbitals with single arrows, again opposite in direction from each other, and leave the third p orbital empty.

Understand the Concept of sp3 Hybridization

Recognize that in sp3 hybridization, one 2s orbital and three 2p orbitals mix to form four equivalent sp3 hybrid orbitals, each capable of holding one pair of electrons and having a tetrahedral geometry.

Draw the Orbital Diagram of Carbon After sp3 Hybridization

Draw four boxes to represent the sp3 hybrid orbitals. Place one arrow in each box to represent the single electron in each hybrid orbital after hybridization. This shows that the carbon atom has four unpaired electrons available for forming bonds.

Key concepts

Understanding Orbital Diagrams

Orbital diagrams are essential tools for visualizing the arrangement of electrons within the atom's orbitals. Think of them as a visual aid, like a floor plan that shows how the electrons are distributed in their 'rooms' or orbitals. For carbon, an atom that plays a central role in organic chemistry, we start by placing its six electrons into the corresponding energy levels. The first two electrons fill the lowest energy level - the 1s orbital, presented as one box with two arrows pointing in opposite directions, to indicate the electrons' opposite spins.

Then, we fill the 2s orbital with the next two electrons, depicted similarly with another box and two opposite arrows. Here is where it gets interesting: carbon has two more electrons that need a place in the 2p orbitals. According to Hund's rule, these electrons occupy separate orbitals. So, we draw three boxes for the 2p orbitals, populating two of them with single arrows. This visualization clarifies electron arrangements before any hybridization occurs.

Decoding Electron Configuration

Electron configuration is like the address of an electron, specifying exactly where it lives in an atom. This address is written in a sort of shorthand that describes which orbitals the electrons are in and how many are in each. For carbon, before any bonding happens, its electron configuration is denoted by 1s² 2s² 2p². The numbers represent the energy levels, the letters (s and p) indicate the type of orbital, and the superscripted numbers tell you how many electrons are in each orbital.

Remember, the 1s can hold up to 2 electrons, as can the 2s. The 2p level consists of three separate orbitals (pₓ, pᵧ, pᶻ), each capable of holding 2 electrons, yet only two of those are filled for carbon before it undergoes sp³ hybridization. Understanding this electron configuration sets the stage for grasping changes during chemical bonding.

Applying Hund's Rule

Electron Placement and Stability

Under Hund's rule, we fill up orbitals in a way that's sort of like public transportation protocol; electrons will fill empty seats first before having to share. Imagine a bus with three empty seats and two passengers. Naturally, each passenger would take their own seat rather than share one. Similarly, electrons occupy separate orbitals of the same energy (in this case, 2p orbitals) before pairing up. This separation minimizes electron repulsion and adds stability.

For carbon, the two 2p electrons occupy separate orbitals, represented by arrows in individual boxes (p orbitals). This follows Hund's rule and explains why, even though two of the p orbitals have just one electron each, those electrons do not pair up in the same orbital. Observing this rule helps predict how an atom will interact with others when forming bonds.

Exploring Tetrahedral Geometry

The Shape of Molecules

The concept of sp³ hybridization brings us to the formation of tetrahedral geometry. This shape is pivotal in understanding how atoms like carbon bond in molecules. Upon undergoing sp³ hybridization, carbon’s one 2s and three 2p orbitals merge to form four equivalent sp³ orbitals, pointing towards the corners of an imaginary tetrahedron.

Each orbital takes a pair of electrons - in our case, one from the original s orbital and one from a p orbital - and spaces out evenly to minimize repulsion. This arrangement is what gives molecules like methane (CH₄) its shape, with four hydrogen atoms bonded symmetrically around a central carbon atom. The beauty of tetrahedral geometry in molecules is that it provides maximum separation between electron pairs, leading to a stable structure fundamental in many chemical compounds.