Inorganic Chemistry Tutoring

Inorganic chemistry covers the whole periodic table, and the course changes character halfway through. The first part is theory: symmetry, group theory, and molecular orbitals. The second is the chemistry of the elements: coordination compounds, organometallics, solids, and the descriptive chemistry of main-group elements. Students who did well in organic chemistry by drawing mechanisms often find that inorganic rewards a different skill, which is picturing three-dimensional structure and counting electrons carefully. STEM Tutor 360 provides one-on-one inorganic chemistry tutoring built around that skill.

Sessions follow your textbook and syllabus, and we use a shared whiteboard to draw point-group flow charts, orbital diagrams, and crystal structures together. You do the drawing, and your tutor checks each step. A good deal of the course is pattern recognition, so we practice the kinds of problems your instructor writes: assigning a point group, building an MO diagram, or predicting the magnetic behavior of a complex.

A typical inorganic chemistry problem, worked

Compare $\ce{[Fe(H2O)6]^2+}$ and $\ce{[Fe(CN)6]^4-}$. For each one, find the oxidation state of iron, the $d$ electron count, the octahedral electron configuration, the number of unpaired electrons, and the crystal field stabilization energy (CFSE).

Water is neutral, so iron is $+2$ in $\ce{[Fe(H2O)6]^2+}$. In $\ce{[Fe(CN)6]^4-}$, six $\ce{CN-}$ ligands contribute $-6$ and the complex is $-4$, so iron is $+2$ again. Iron is $[\text{Ar}]\, 4s^{2}\, 3d^{6}$, and the 4s electrons leave first, so $\ce{Fe^2+}$ is $d^{6}$ in both.

In an octahedral field, the d orbitals split into a lower $t_{2g}$ set and a higher $e_g$ set, separated by $\Delta_o$. Water is a weak-field ligand, so $\Delta_o$ is small and the electrons spread out before pairing. That gives $t_{2g}^{4} e_{g}^{2}$, with 4 unpaired electrons. $$\text{CFSE} = 4(-0.4\Delta_o) + 2(+0.6\Delta_o) = -0.4\Delta_o$$ The spin-only moment is $\sqrt{4 \times 6} = 4.90$ Bohr magnetons.

Cyanide is a strong-field ligand, so $\Delta_o$ is large and the electrons pair in the lower set. That gives $t_{2g}^{6}$, with no unpaired electrons. $\text{CFSE} = 6(-0.4\Delta_o) = -2.4\Delta_o$, and the complex is diamagnetic. In general, a $\Delta_o$ larger than the pairing energy gives low spin.

Where students usually get stuck

• Counting d electrons before finding the oxidation state. The charge on the complex and the ligands come first.
• Removing the wrong electrons. For first-row metal cations, $4s$ electrons leave before $3d$.
• Point groups: skipping the flow chart, or missing a $C_2$ axis or a mirror plane.
• Building MO diagrams for polyatomic molecules without first finding the symmetry-adapted combinations.
• Mixing the neutral and ionic electron-counting methods in organometallics. Pick one and stay with it.
• Memorizing crystal structures instead of checking coordination numbers and ion size ratios.

Shared ground with quantum chemistry

Group theory and molecular orbital theory use the same ideas as quantum mechanics in physical chemistry. Students taking both courses can use sessions to connect them.