Problem 75 - Chemistry The Central Science In Si Units

Question

A carbene is a compound that has a carbon bonded to two atoms and a lone pair remaining on the carbon. Many carbenes are very reactive. (a) Draw the Lewis structure for the simplest carbene, \(\mathrm{H}_{2} \mathrm{C}\). (b) Predict the length of the carbon-carbon bond you would expect if two \(\mathrm{H}_{2} \mathrm{C}\) molecules reacted with each other by a combination reaction.

Step-by-Step Solution

Answer

The Lewis structure for \(\mathrm{H}_{2}\mathrm{C}\) is \(\mathrm{H}-\mathrm{C}: \mathrm{H}\). The expected \(\mathrm{C-C}\) bond length in the reaction product is around 154 pm.

Step 1: Understanding Carbenes

Carbenes are compounds with a carbon atom bonded to two other atoms and possessing a lone pair. In this exercise, we are considering the simplest carbene, \(\mathrm{H}_{2}\mathrm{C}\), where carbon is bonded to two hydrogen atoms and carries a lone pair of electrons.

Step 2: Drawing the Lewis Structure for \(\mathrm{H}_{2}\mathrm{C}\)

Start by placing the carbon atom as the central atom. Attach two hydrogen atoms to the carbon. Since carbon forms four bonds or has an octet of electrons, for \(\mathrm{H}_{2}\mathrm{C}\), there are also two non-bonding electrons (a lone pair) on carbon to complete its octet. The Lewis structure is: \(\mathrm{H}-\mathrm{C}: \mathrm{H}\).

Step 3: Reaction of Two Carbenes

When two \(\mathrm{H}_{2}\mathrm{C}\) molecules react, the lone pairs on each carbon atom can form a new \(\mathrm{C-C}\) bond. This type of reaction is known as a combination reaction.

Step 4: Predicting the Carbon-Carbon Bond Length

After the combination reaction, the \(\mathrm{H}_{2}\mathrm{C}\) molecules form \(\mathrm{H}_{2}\mathrm{C}-\mathrm{CH}_{2}\) with a \(\mathrm{C-C}\) single bond. The typical carbon-carbon single bond length is approximately 154 pm (picometers). Thus, the expected \(\mathrm{C-C}\) bond length in the resulting molecule would be around 154 pm.

Key Concepts

Lewis Structure

A Lewis structure is a simple way to represent the arrangement of electrons in a molecule. It helps visualize how atoms are bonded together and the presence of any lone pairs of electrons. For the simplest carbene, \(\mathrm{H}_{2}\mathrm{C}\), the Lewis structure shows carbon in the center. This carbon atom bonds with two hydrogen atoms and also carries a lone pair of electrons. This lone pair is essential for completing carbon's valence shell with eight electrons, following the octet rule.

• The carbon atom is central, connected to two hydrogen atoms.
• A lone pair of electrons sits on the carbon.
• The structure is depicted as \(\mathrm{H}-\mathrm{C}:\mathrm{H}\).

Lewis structures are crucial for understanding molecular structure, as they provide insight into the bonding and electron pairs within a molecule.

Combination Reaction

A combination reaction involves two or more substances coming together to form a single product. In this exercise, two \(\mathrm{H}_{2}\mathrm{C}\) carbene molecules react by combining their lone pairs of electrons to form a new carbon-carbon bond.
This results in the production of a larger molecule, \(\mathrm{H}_{2}\mathrm{C}-\mathrm{CH}_{2}\).

• Lone pairs from each carbon in \(\mathrm{H}_{2}\mathrm{C}\) facilitate the formation of a \(\mathrm{C-C}\) bond.
• The molecules align such that carbon atoms are adjacent, allowing bond formation.
• The result is a single, larger molecule with a new covalent bond.

Combination reactions are fundamental in chemical synthesis, as they allow simple molecules to come together and form complex structures.

Carbon-carbon bond length

The carbon-carbon bond length is a critical measurement in chemistry, as it influences the properties and stability of a molecule. When two \(\mathrm{H}_{2}\mathrm{C}\) react to form \(\mathrm{H}_{2}\mathrm{C}-\mathrm{CH}_{2}\), a single \(\mathrm{C-C}\) bond is created. The typical length for a carbon-carbon single bond in stable organic molecules is approximately 154 picometers (pm). This length can vary slightly based on the surrounding atoms and molecular environment, but 154 pm is a reliable average.

• The bond originates from the overlap of \(sp^3\) hybrid orbitals on each carbon atom.
• Stable \C-C\ single bonds form the backbone of many organic compounds.
• The precise length can influence chemical reactivity and physical properties.

Understanding bond lengths is pivotal in predicting and explaining the behavior of organic and inorganic compounds in various environments.