Problem 100 - Chemistry The Molecular Science

Question

Ketene, \(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{O},\) is a reactant for synthesizing cellulose acetate, which is used to make films, fibers, and fashionable clothing. (a) Write the Lewis structure of ketene. Ketene does not contain an \(-\mathrm{OH}\) bond. (b) Identify the electron-region geometry and the molecular geometry around each carbon atom and all the bond angles in the molecule. (c) Identify the hybridization of each carbon and oxygen atom. (d) Is the molecule polar or nonpolar? Use appropriate data to support your answer.

Step-by-Step Solution

Answer

Ketene is nonpolar despite its polar bonds.

Step 1: Lewis Structure of Ketene

To draw the Lewis structure of ketene \((\mathrm{C}_2\mathrm{H}_2\mathrm{O})\), start by counting the total number of valence electrons. Carbon has 4 valence electrons, hydrogen has 1, and oxygen has 6. Thus, the total number of valence electrons is \(2(4) + 2(1) + 6 = 16\) electrons. Arrange the atoms as C=C=O with each carbon atom attached to a hydrogen. Distribute the electrons to satisfy the octet rule for each atom, forming double bonds between carbon-carbon and carbon-oxygen, and single bonds between carbon and hydrogen. This results in the C=C=O with \(\mathrm{H}-\) connected to each C.

Step 2: Electron-Region and Molecular Geometry

For the central \(\text{C}_1\) atom bonded to another Carbon (\(\text{C}_2\)) and hydrogen (\(\text{H}\)), the electron-region geometry is linear due to the presence of two regions of electron density. The molecular geometry is also linear, as there are no lone pairs. For \(\text{C}_2\) which is bonded to \(\text{C}_1\), \(\text{O}\), and \(\text{H}\), the geometry is also linear for similar reasons. There are no lone pairs impacting the bond angles, which are all 180°.

Step 3: Hybridization of Atoms

The hybridization of \(\text{C}_1\) and \(\text{C}_2\) in ketene is sp, as they're involved in forming two pi bonds with linear geometries. This is confirmed with the formation of two pi bonds: one between \(\text{C}_1\) and \(\text{C}_2\), and the other between \(\text{C}_2\) and \(\text{O}\). For the oxygen atom, the hybridization is also sp, due to its participation in forming a double bond with carbon.

Step 4: Molecular Polarity

To determine molecular polarity, consider the molecular shape and the difference in electronegativity between atoms. Despite the presence of polar bonds (C=O), the symmetrical linear geometry of C=C=O cancels out any dipoles along the molecule, rendering the overall ketene molecule nonpolar.

Key Concepts

Hybridization

Atoms undergo hybridization to form new hybrid orbitals. In ketene, both carbon atoms are involved in linear bonding, and the geometry leads to sp hybridization. This occurs because each carbon forms two pi bonds- one between the two carbons and another between carbon and oxygen.
To achieve this, each carbon mixes one s-orbital and one p-orbital, leaving two unhybridized p-orbitals for pi bond formation. This creates two sp hybrid orbitals for sigma bonding. The oxygen atom also partakes in this process, having an sp hybridization for its double bonding to carbon. Knowing the hybridization helps predict the molecule’s shape and type of bonds it will form.

Molecular Geometry

Molecular geometry explains the 3D arrangement of atoms in a molecule. For ketene, the molecular geometry around each carbon atom is linear. The C=C=O portion forms a straight line due to the sp hybridization of the carbon atoms. This linear structure dictates that the bond angles are 180°, which matches with the electron-region geometry.
The linear arrangement of atoms means there's no room for deviation in bond angles, as each carbon must satisfy the octet rule by sharing electrons with hydrogen, oxygen, and each other in a straight line. Understanding molecular geometry helps in predicting how compounds interact in reactions or how their physical properties manifest.

Molecular Polarity

The concept of molecular polarity revolves around the distribution of charges within a molecule. Ketene's polarity is determined by its linear molecular geometry and the polar bonds it contains. Even though the carbon-oxygen bond is polar due to the difference in electronegativity, the overall molecular geometry plays a crucial role.
In ketene, the symmetrical linear shape cancels out the dipoles created by the polar C=O bond, resulting in a nonpolar molecule. Polarity affects how a molecule interacts with other substances, influencing properties like solubility, boiling and melting points.

Electron-Region Geometry

Electron-region geometry considers both bonding and lone electron pairs around a central atom. In ketene, both central carbon atoms exhibit a linear electron-region geometry. This uniformity arises due to each carbon being surrounded by two regions of electron density corresponding to the two sigma bonds formed.
Understanding electron-region geometry aids in predicting molecular structure. With no lone pairs affecting shape, both electrons and atoms arrange themselves as far apart as possible to minimize repulsion, a principle derived from VSEPR (Valence Shell Electron Pair Repulsion) theory. This understanding helps in visualizing and modeling the 3D aspect of molecules.