Chapter 10: Problem 45

Sketch the shapes of these molecular orbitals: \(\sigma_{1 s}\), \(\sigma_{1 s}^{\star}, \pi_{2 p},\) and \(\pi_{2 p}^{\star}\) How do their energies compare?

Short Answer

Expert verified

The \(\sigma_{1s}\) and \(\sigma_{1s}^{\star}\) molecular orbitals consist of symmetrical lobes along the internuclear axis, with the antibonding orbital featuring a node in the middle. The \(\pi_{2p}\) and \(\pi_{2p}^{\star}\) molecular orbitals consist of lobes above and below the plane of the atoms, with additional nodes for the antibonding orbital. In terms of energy, the order from lowest to highest is \(\sigma_{1s}\), \(\sigma_{1s}^{\star}\), \(\pi_{2p}\), \(\pi_{2p}^{\star}\).

Step by step solution

Sketch the \(\sigma_{1s}\) molecular orbital

The \(\sigma_{1s}\) orbital results from the overlap of two 1s atomic orbitals along the internuclear axis. The sketch should represent two lobes of equal size symmetrically positioned along a connecting axis, looking almost like a dumbbell or a figure eight shape.

Sketch the \(\sigma_{1s}^{\star}\) molecular orbital

The \(\sigma_{1s}^{\star}\) is the antibonding counterpart of the \(\sigma_{1s}\). This orbital also consists of two lobes, but there is a node, or a planar region with no electron density, at the nucleus. This gives it a donut conformation around the nuclear axis, with positive and negative phases (usually shown with different colors or shading) on either side of the node.

Sketch the \(\pi_{2p}\) molecular orbital

The \(\pi_{2p}\) orbital is formed by the side-on overlap of two 2p atomic orbitals. This should be sketched as two vertically aligned lobes on each atom, indicating the location of electron density above and below the plane of the atoms.

Sketch the \(\pi_{2p}^{\star}\) molecular orbital

The \(\pi_{2p}^{\star}\) is the antibonding version of the \(\pi_{2p}\). There are two nodes, creating three lobes for this orbital. The central lobe lies between the two atomic nuclei, and the other two lobes project above and below this central lobe.

Compare the energies of the molecular orbits

In terms of energy, antibonding orbitals (\(\sigma_{1s}^{\star}\) and \(\pi_{2p}^{\star}\)) are higher in energy than their bonding counterparts (\(\sigma_{1s}\) and \(\pi_{2p}\)). In addition, 2p orbitals (both bonding and antibonding) are higher than the 1s orbitals due to the increased energy level and distance from the nucleus. Thus, the order of increasing energy is \(\sigma_{1s}\), \(\sigma_{1s}^{\star}\), \(\pi_{2p}\), and \(\pi_{2p}^{\star}\).

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Sketch the shapes of these molecular orbitals: \(\sigma_{1 s}\), \(\sigma_{1 s}^{\star}, \pi_{2 p},\) and \(\pi_{2 p}^{\star}\) How do their energies compare?

Short Answer

Step by step solution

Sketch the \(\sigma_{1s}\) molecular orbital

Sketch the \(\sigma_{1s}^{\star}\) molecular orbital

Sketch the \(\pi_{2p}\) molecular orbital

Sketch the \(\pi_{2p}^{\star}\) molecular orbital

Compare the energies of the molecular orbits

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