Question

Describe the geometry about a carbon atom that forms: (a) four single bonds (b) two single bonds and one double bond (c) one single bond and one triple bond

Short answer

Part A: Tetrahedral geometry with 109.5-degree angles. Part B: Trigonal planar geometry with 120-degree angles. Part C: Linear geometry with 180-degree angles.

Step-by-step solution

Part A: Geometry with Four Single Bonds

When a carbon atom forms four single bonds, it undergoes sp3 hybridization. This leads to a tetrahedral geometry where the bond angles are approximately 109.5 degrees, with each hydrogen atom at the corners of a tetrahedron and the carbon atom at its center.

Part B: Geometry with Two Single Bonds and One Double Bond

For a carbon atom with two single bonds and one double bond, it features sp2 hybridization. This results in a trigonal planar geometry with bond angles of 120 degrees. The molecule lies in a single plane with the double bond providing rigidity.

Part C: Geometry with One Single Bond and One Triple Bond

A carbon atom with one single bond and one triple bond is sp hybridized. This leads to linear geometry with bond angles of 180 degrees. The atoms involved are in a straight line with the triple bond consisting of one sigma and two pi bonds.

Key concepts

sp3 Hybridization

Imagine a carbon atom as a tiny central hub with four equally spaced spokes shooting out in different directions. That's the essence of sp3 hybridization: it describes the carbon atom's ability to form four equivalent bonds widely separated in space. This occurs because one s-orbital combines with three p-orbitals to create four new equivalent orbitals called sp3 hybrid orbitals. When a carbon atom undergoes sp3 hybridization, as seen in molecules like methane (CH₄), it ensures that the bonds formed are as far apart as possible for minimal repulsion between electron pairs, leading to the distinctive tetrahedral shape.

Tetrahedral Geometry

The tetrahedral geometry of a carbon atom isn't just some theoretical concept; it's the spatial arrangement that maximizes the distance between the pairs of electrons in the bonds. This occurs when a carbon atom forms four single bonds. Picture a tripod with a central stick rising from the middle — that's your basic mental model of tetrahedral geometry. Each 'leg' and the central stick represent a bond. The angle between each bond is approximately 109.5 degrees, creating a three-dimensional shape that's symmetric and sturdy. It's like the carbon atom at the center is wearing a hat with equally long brims pointing out in four directions.

sp2 Hybridization

Now, let's turn our attention to the sp2 hybridization. Think of a table with three equally spaced legs; this is akin to the carbon atom's structure when it undergoes sp2 hybridization. In this form, the carbon atom mixes one s-orbital with two p-orbitals, resulting in three sp2 hybrid orbitals and one remaining p-orbital. When a carbon atom is sp2 hybridized, like in ethene (C₂H₄), it can make three sigma bonds and keep one p-orbital free. This type of bonding allows one of those bonds to be a double bond, giving the molecule a flat, trigonal planar geometry with 120-degree bond angles.

Trigonal Planar Geometry

The sheer simplicity of trigonal planar molecules is beautiful. They lie flat, in one plane, with a central carbon atom bonded to three other atoms in a triangle, much like a fan with blades spread out evenly. This setup is not just aesthetically pleasing, but it's a natural consequence of sp2 hybridization that triggers the 120-degree separation between bonded electron pairs. This shape allows for a double bond, too, which is comprised of one sigma bond — like the sturdy spine holding the molecule together — and one pi bond — like the additional reinforcing bar that keeps the molecule's planar shape rigid.

sp Hybridization

For a moment, consider a ruler or a straight highway stretching to the horizon; this straight line is akin to the sp hybridization. It occurs when a carbon atom combines one s-orbital and one p-orbital, forming two sp hybrid orbitals, with two remaining p-orbitals free. This hybridization happens when the carbon atom just doesn't want all that spatial complexity and opts for simplicity: it forms two bonds in a straight line. This is the case in molecules like acetylene (C₂H₂), where the carbon forms a single bond and a triple bond, leading to a stripped-down, no-frills linear geometry with a bond angle of 180 degrees.

Linear Geometry

Think of linear geometry as the ultimate in minimalist design for molecules. There's no need for any fancy angles or multiple directions — everything is streamlined. With sp hybridization, the carbon atom can create two bonds that are 180 degrees apart, often with one bond being a triple bond, comprised of one central sigma bond and two flanking pi bonds. This arrangement forms a direct and unwavering line, much like railroad tracks cutting across a landscape. Such linear molecules, devoid of any bend or curve, are an eloquent demonstration of the simplest spatial arrangement atoms can achieve.