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8.1 Predict spin-only magnetic moments for the following species
(a) High spin tetrahedral [FeCl4] 2−
(b) Octahedral V3+ in (NH4)V(SO4)2.12H2O
(c) Low spin octahedral Fe(III) in K3Fe(CN)6
(d) [Fe(CN)6]4−
(e) [Ru(NH3)6]3+
(f) [Cr(NH3)6]2+
(a) Fe(II) so d6 and e3t23 configuration with four unpaired electrons, n=4 S=2. A spin-only μeff of 4.90μB.
(b) Octahedral V3+ t2g2eg0 n=2 S=1. A spin-only μeff of 2.83μB
(c) Low spin octahedral Fe(III) t2g5eg0 n = 1 S = ½, A spin-only μeff of 1.73μB
(d) [Fe(CN)6]4− will contain, with the high field cyanide ligand, low spin octahedral Fe(II) t2g6eg0 n = 0 S = 0, A spin-only μeff of 0μB.
(e) [Ru(NH3)6]3+ . Second row transition metal, octahedral complexes are usually low spin even with weak field ligands such as ammonia. Low spin octahedral Ru(III) t2g5eg0 n = 1 S = ½, A spin-only μeff of 1.73μB
(f) [Cr(NH3)6]2+ will contain, with the low field ammonia ligands, high spin octahedral Cr(II) t2g3eg1, n = 4 S = 2. A spin-only μeff of 4.90μB.
8.2 The experimental magnetic moment of [NiCl4]2− in various salts has been measured as 2.85μB. Use this information to determine whether the [NiCl4]2− species is tetrahedral or square planar.
The [NiCl4]2− ion contains Ni2+ with a d8 electron count. In a tetrahedral ion the crystal field splitting will lead to a e4 t24 configuration with n = 2 S = 1, and a predicted spin-only μeff of 2.83μB. In square planar configuration the dx2−y2 will lie at high energy and be empty so that the electrons will be paired in the four other d orbitals – this configuration will have n = 0, S = 0, and a spin-only μeff of 0μB. Therefore the experimental evidence support a tetrahedral geometry for the [NiCl4]2− ion.
8.3 The measurement magnetic moment of [Co(tripyridylamine)2](ClO4)2 is 3.82μB at 373 K and 1.75μB at 4 K. Tripyridylamine is a tridentate ligand. Explain how a change in the electron configuration on cobalt at 200 K can explain these data.
The complex [Co(tripyridylamine)2](ClO4)2 contains Co2+ d7 and would have octahedral coordination around cobalt with two tridentate tripyridylamine ligands. Possible configurations are high spin, t2g5eg2 n=3, S=3/2 and low spin t2g6eg1 n=1, S=1/2. The spin only predicted μeff values are, therefore, 3.87μB and 1.73 μB respectively and these values tally with those at high temperature, 373 K, and low temperature, 200K. Thus [Co(tripyridylamine)2](ClO4)2 undergoes a spin-crossover from high spin to low spin on cooling from 373 K to 200K
8.4 A student mixes up samples of (a) MnSO4.7H2O and (b) CoSO4.7H2O both of which are pink in colour. How could magnetism measurements help them determine which sample is which?
Both these complexes contain the hexaaquo cations [M(OH2)6]2+ . For manganese, Mn2+, d5 high spin t2g3eg2 n=5, S=5/2 μeff = 5.92μB. For cobalt, Co2+, d7 high spin t2g5eg2 n=3, S=3/2 μeff = 3.87μB . These two magnetic moments would be easily distinguished from experimental data
8.5 Explain the following experimental magnetic moments by considering any orbital contributions to the theoretical magnetic moments and their likely temperature dependence.
(a) VCl4 μeff (77K) = 1.62μB μeff (300 K) = 1.62μB
(b) Cs[CoCl4] μeff (77K) = 4.54μB μeff (300 K) = 4.62μB
(c) K2[VCl6] μeff (77K) = 1.42μB μeff (300 K) = 1.83μB
(a) V4+ has a d1 configuration and an expected spin only μeff = 1.73μB A small orbital contribution would be expected as vanadium is in an octahedral coordination in solid VCl4
- for the t2g1 configuration with the ground state term symbol 2T2g. This would reduce the observed magnetic moment slightly from the spin-only value and be consistent with the 1.62μB value given, however a temperature dependence would also be expected. In a tetrahedral coordination e1 ground state term symbol 2E there would be no expected orbital contribution, though spin-orbit coupling would be expected to reduce the observed magnetic moment slightly (similar to Eqn 8.10 for tetrahedral complexes). The 2E ground state would also not be expected to produce a significant variation with temperature. In fact vanadium does have tetrahedral coordination in VCl4 as might be expected from the formula.
(b) Cs[CoCl4] has tetrahedral Co2+ d7 e4 t23 ground state term symbol 4A2 The spin only predicted magnetic moment is 3.87μB though spin orbit coupling would likely increase the observed value – as in seen in the experimental value of 4.62μB. No orbital contribution would be expected and little or no temperature dependence expected – as is observed.
(c) K2[VCl6] contains V4+ in octahedral coordination: d1 t2g1eg0 ground state term symbol 2T2g spin only μeff = 1.73μB and orbital contribution would be expected which would be small at room temperature but show significant temperature dependence. The variation with should follow the Kotani plot for a d1 system.
8.6 Calculate a theoretical magnetic moment for the Bk3+ ion. Is this in agreement with the experimental value of 9.69μB found for berkelium compounds?
As a mid- to late- actinide cation we can assume the electronic configuration of the Bk3+ will be 5f8 (and not have 6d electrons). The ground state of a 5f8 is 7F6 ( see Table 8.4 for the equivalent 4f8 configuration of Tb3+) and the calculated μeff = 9.72μΒ. This value is in very good agreement with the experimental values confirming the electronic ground state of Bk3+ is 5f8
8.7 Interpret the following observations on the magnetic susceptibility data of the cobalt chalcogenides CoS2 and CoSe2 in terms of cooperative magnetism phenomena.
For both CoS2 and CoSe2 the inverse susceptibility data obey the Curie-Weiss law above room temperature.
CoSe2 shows a minimum in a plot of χM−1 versus temperature at 90 K and the Weiss temperature determined from data above this temperature is −160 K.
CoS2 shows a rapid increase in χM below 124 K and the Weiss temperature is +220 K.
These data are consistent with CoSe2 undergoing a transition to antiferromagnetic behaviour with a TN of 90 K. Above this temperature the negative Weiss temperature implies local antiferromagnetic interactions between cobalt centres in a paramagnetic state.
CoS2 undergoes a transition to a ferromagnet with a Curie temperature of 124 K. The positive Weiss temperature is also indicative of ferromagnetic interactions between spins in the paramagnetic regime above 124 K
