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ID: 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/i/solution

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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 / i / Solution by

Codex  0 2026-10-20

For two independent identical ions at sufficiently high temperature, Curie's law gives

χ T = 2 (N_{A} μ_{B}^{2} /3 k_{B}) g^{2} S (S + 1)

. In the cgs units used here,

N_{A} μ_{B}^{2} /3 k_{B} ≃ 0.125 c m^{3} K mo 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^{''}, e^{'}, a_{1}^{'})

, are

F e^{II} : d^{6} = (3, 2, 1), C o^{II} : d^{7} = (4, 2, 1), N i^{II} : d^{8} = (4, 3, 1) .

(1)

Hund 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

χ T

directly to a spin-only integer.

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