Problem 12 - Chemistry: The Central Science

Question

The diagram that follows shows the highest-energy occupied MOs of a neutral molecule \(\mathrm{CX},\) where element \(\mathrm{X}\) is in the same row of the periodic table as C. (a) Based on the number of electrons, can you determine the identity of \(X ?\) (b) Would the molecule be diamagnetic or paramagnetic? (c) Consider the \(\pi_{2 p}\) MOs of the molecule. Would you expect them to have a greater atomic orbital contribution from \(\mathrm{C}\), have a greater atomic orbital contribution from \(X\), or be an equal mixture of atomic orbitals from the two atoms? [Section 9.8\(]\) $$ \begin{array}{l|l|l|} \cline { 2 - 3 } \sigma_{2 p} & \multicolumn{1}{c} {1} \\ \cline { 2 - 3 } \pi_{2 p} & 1 \downarrow & 1 \downarrow \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The identity of X is Helium (He), as it has 2 electrons. The molecule CX (CH) is diamagnetic, as all electrons are paired. The π2p MOs of the molecule are expected to have a greater atomic orbital contribution from C than from He, due to the smaller energy difference between the atomic orbitals of C and He for the 2p orbitals compared to the 2s orbitals.

Step 1: Determine the identity of X based on the number of electrons

Let's count the number of electrons in the MO diagram. We can see a total of 8 electrons: one in the σ2p orbital, and two in each π2p orbital, for a combined total of 6 in the π2p orbitals. Carbon has 6 electrons. If the neutral molecule CX has 8 electrons, then X must have 8 - 6 = 2 electrons, which corresponds to an element with an atomic number of 2: Helium. Thus, X is Helium (He).

Step 2: Determine if the molecule is paramagnetic or diamagnetic

A molecule is paramagnetic if it has unpaired electrons, and diamagnetic if all electrons are paired. In the provided MO diagram, all electrons are paired (there is no single unpaired electron), so the molecule CX (CH) will be diamagnetic.

Step 3: Analyze the contributions of atomic orbitals from C and X to π2p MOs

Because C and X (He) are in the same row of the periodic table, their energy levels for the 2p orbital are similar. However, He has a larger effective nuclear charge than C, which means its 2s orbital would be more contracted and have a lower energy compared to the 2s orbital of C. Therefore, when they form molecular orbitals, the π2p orbitals of the molecule are expected to have a greater atomic orbital contribution from C than from He, as the energy difference between the atomic orbitals of C and He is smaller for 2p than for 2s orbitals.