Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 2 / Section B / 20 / b

For two independent identical ions at sufficiently high temperature, Curie's law gives $\chi T=2(N_A{\mu }_B^2/3k_B)g^{2}S(S+1)$. In the cgs units used here, $N_A{\mu }_B^2/3k_B\simeq 0.125\mathrm{c}{\mathrm{m}}^3\mathrm{K}\mathrm{mo}{\mathrm{l}}^{-1}$.

Fe(II), Co(II) and Ni(II) have $S=2$, $3/2$ and 1, respectively. The corresponding high-spin occupancies, ordered as $(e^{\prime \prime },e^{\prime },a_1^{\prime })$, areHund filling puts one electron in each orbital before additional pairing. Spin-only dimer values at $g=2$ would be 6.0, 3.75 and 2.0; the observed larger values anticipate orbital contributions. The spin assignments require the chemically appropriate high-spin states, rather than rounding the measured $\chi T$ directly to a spin-only integer.

Using the spin values above and accounting for two metal ions per formula unit,The deviations from 2 indicate spin-orbit coupling and incomplete quenching of orbital angular momentum. The partly filled $e^{\prime \prime }$ manifold in Fe and $e^{\prime }$ manifold in Ni permit orbital degeneracy in the ideal geometry. Co's high-spin orbital occupation is more orbitally balanced, but mixing with excited ligand-field states still produces a substantial effective $g$ shift. These fitted scalar values summarize a thermally averaged response; they do not determine the individual components of an anisotropic g tensor.