Question

(a) Make a model of allene, \(\mathrm{CH}_{2}=\mathrm{C}=\mathrm{CH}_{2}\), a cumulated diene. What is the spatial relationship between the pair of hydrogens at one end of the molecule and the pair of hydrogens at the other end? (b) Substituted allenes of the type \(\mathrm{RCH}=\mathrm{C}=\mathrm{CHR}\) have been obtained in optically active form. Is this consistent with the shape of the molecule in (a)? Where are the cbiral centers in the substituted allene? (c) Work out the electronic configuration of allene. (Hint: How many atoms are attached to the middle carbon? To each of the end carbons?) Does this lead to the same shape of molecule that you worked out in (a) and (b)?

Short answer

In summary, allene has a unique Y-shaped molecular structure, with the hydrogen atom pairs on both ends being non-planar and perpendicular to each other. The molecule indeed possesses optical activity, as substituted allenes have chiral centers at the end carbon atoms connected to the "R" groups. Lastly, the electronic configuration (sp2 hybridization) and the molecular geometry we determined from it matches the shape of the molecule we observed in the previous parts.

Step-by-step solution

Molecular structure and spatial relationship of allene

We can start by drawing the Lewis structure for allene, \(\mathrm{CH}_{2}=\mathrm{C}=\mathrm{CH}_{2}\). C: 4 valence electrons H: 1 valence electron The molecule has a total of 12 valence electrons (4x2 for C and 1x4 for H). Here is the Lewis structure: H-C=C=C-H H H To know the spatial relationship, we need to study the molecular geometry. In allene, the C=CH\(_{2}\) double bond and the C=C=CH\(_{2}\) double bond create a unique Y-shape. In this structure, the pair of hydrogen atoms at opposite ends of the molecule is non-planar and perpendicular to each other. (b)

Optical activity and chiral centers of substituted allenes

Optical activity is a characteristic of chiral molecules. We know that a molecule is chiral when it does not have a plane of symmetry or a center of inversion. To be optically active, the molecule should have a stereochemistry that does not have internal symmetry or a superimposable mirror image, hence having a chiral center. Let's examine the substituted allene, \(\mathrm{RCH}=\mathrm{C}=\mathrm{CHR}\). The central carbon atom has a double bond with the two end carbon atoms, and they form a plane. Both end carbon atoms are attached to two different groups (R and H), and they are perpendicular to the main plane. Since the molecule lacks internal symmetry and cannot be superimposed with its mirror image, it has chiral centers at the end carbon atoms. So, the chiral centers are at the end carbon atoms, connected to "R" groups. (c)

Electronic configuration of allene

We need to find the number of atoms attached to each central carbon. - There are 2 atoms attached to the middle carbon (C) - There are 3 atoms attached to each end carbon (CH\(_{2}\)) Now, let's consider the hybridization of each carbon: End Carbon: Middle Carbon: End Carbon: 3 atoms, sp2 2 atoms, sp 3 atoms, sp2 In this case, the end carbons are sp2 hybridized, while the middle carbon is sp hybridized. Both end carbons are trigonal and planar, while the middle carbon is linear. Based on these hybridizations, the shape of the allene molecule is as we worked out in parts (a) and (b): The end carbon – central carbon – end carbon bond is linear (180° bond angle), while the two hydrogen atoms on the end carbons are perpendicular to the plane formed by the central carbon, creating non-planar geometry. So, yes, the electronic configuration leads to the same shape of the molecule that we worked out in (a) and (b).

Key concepts

Cumulated diene

Allene, or \( \mathrm{CH}_{2}=\mathrm{C}=\mathrm{CH}_{2} \), is known as a cumulated diene because it possesses two sequential double bonds shared with a common carbon atom; the central carbon is sp hybridized. This arrangement differs from conjugated dienes, where the double bonds are separated by a single bond, and isolated dienes, where the double bonds are separated further.

The significance of allene's structure as a cumulated diene lies in its unique molecular geometry. It causes adjacent double bonds to be perpendicular to each other, due to the linear sp hybridization of the central carbon. The perpendicular arrangement of these pi bonds means that each end of the molecule experiences distinct spatial environments. This geometry is essential for understanding the molecule’s reactivity and properties.

Chiral centers

Chirality is a fundamental concept in stereochemistry, referring to the geometric property of a molecule having a non-superimposable mirror image. Molecules with this property have what are known as chiral centers - atoms holding groups of substituents in such a way that the structure cannot be superimposed on its mirror image.

In substituted allenes, \(\mathrm{RCH}=\mathrm{C}=\mathrm{CHR}\), two chiral centers can appear at the terminal carbon atoms when the substituents (denoted as 'R') are different. These chiral ends of the molecule cannot be aligned with their mirror images, conferring optical activity to the molecule - it can rotate plane-polarized light. This characteristic challenges students to think beyond the simple tetrahedral model of chiral centers, as the geometry around the chiral carbon in an allene is not tetrahedral, but rather trigonal planar.

Molecular geometry

The molecular geometry of a compound such as allene is determined by the spatial arrangement of its bonds. For allene, this is notably unique due to the linear configuration determined by the sp hybridization of the central carbon atom. The hybridization of an atom in a molecule corresponds with the atom's bonding situation - the central carbon in allene forms two sigma bonds, aligning with the sp hybridization model.

Each hydrogen at both ends of the molecule is located in a plane that is perpendicular to the plane of the other pair of hydrogens, making the molecule's shape distinctly non-planar. This geometrical feature is pivotal for students to understand as it influences the molecule's properties, such as reactivity and interaction with polarized light - key points for anyone studying the physical and chemical behavior of organic compounds.