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8.1 Assuming the Cr3+ ions have the same μeff as in CrCl3 calculate a molar susceptibility, in cm3mol−1, for Cr2(SO4)3 bearing in mind that one mole of this compound contains two moles of chromium ions.
The RMM of Cr2(SO4)3 is (2×52) + (3×(32+64)) = 392 g mol−1. Rewriting as a formula containing one chromium ion i.e. Cr(SO4)3/2 the RMM is 392/2 = 196 g mol−1 . Using 
= 3.89 μB will give χM = 6350 × 10−6 cm3 mol−1 so for Cr2(SO4)3 with twice as many chromium ions χM will be doubled at 12700 × 10−6 cm3 mol−1 ( the experimental value is 11800 × 10−6 cm3 mol−1).
8.2 The experimental magnetic moment of the complex K4[Mn(NCS)6] is 6.06μB. What is the electron configuration of the manganese centre in this compound?
From the spin only formula
6.062 = n(n+2) gives n ~ 5. The oxidation state of manganese in the compound is Mn(II) which has a d5 configuration so these five electrons must all be unpaired. In the octahedral [Mn(NCS)6]4− anion the high spin configuration t2g3eg2 would be consistent with the observed experimental magnetic moment.
8.3 Would the spin-only formula be likely to predict the observed magnetic moment for the nickel centre in Cs2NiF6, which contains [NiF6]2− anions?
The [NiF6]2− anion will be octahedral with the electronic configuration d6, and could be predicted to be high spin with the weak field fluoride ion so t2g4eg2. In this case there will be expected to be a significant orbital contribution to the magnetic moment for the one unpaired electron in the t2g orbital set (Table 8.1(a)). The level of orbital contribution will be temperature dependent.
Experimentally the [NiF6]2− anion is found to be low spin ion so t2g6eg0 and, therefore, diamagnetic. As with low spin octahedral Co3+ (also t2g6eg0) mixing in of higher energy levels with a magnetic moment would be expected to give a small Temperature Independent Paramagnetism (TIP) with µeff ~ 0.05µB
8.4 By consideration of the spectrochemical series (Section 5.4.3) and Eqn. 8.10 explain the following measured magnetic moments [CoI4]2− 4.77, [CoBr4]2− 4.65μB, [CoCl4]2− 4.59μB, [Co(NCS)4]2− 4.45μB.
Co2+ is d7 and in tetrahedral coordination give the configuration e4t23, ( Table 8.1(b)) which will have an A ground state term symbol.
The observed µeff value will be increased, noting that λ is negative for the more than half-filled shell, from the spin-only value by an orbital contribution amount inversely dependent on the crystal field splitting parameter Δoct. The spin only value for three unpaired electrons is 3.87μB. In the spectrochemical series Δoct values vary in order I− < Br− < Cl− < NCS− and, therefore, the we would expect the µeff values to be in the order [CoI4]2− > [CoBr4]2− > [CoCl4]2− > [Co(NCS)4]2−, as is observed.
8.5 Estimate room temperature μeff values for the octahedral low spin, d4 ions Cr2+, Mn3+, Ru4+, and Re3+ by consideration of their spin-orbit coupling constants, λ, (59, 89, 350, and 630 cm−1 respectively) and the spin-only μeff value for a d4 ion. Assume a similar form for the Kotani plot for a d4 system to that shown for the d1 system in Figure 8.7.
The spin-only μeff value for a low spin, octahedral d4 ion, t2g4, is 2.83μB. Experimental μeff values for the first row transition metals with small values of λ would be expected to be close to this value. For second row Ru and third row Re the 
values of kT/λ will be 208/350 =0.59 and 208/630=0.33 respectively. If the curve has a similar form to that for a d1 configuration then for kT/λ a μeff value of around 60% of the spin only value would be expected for Ru4+at 1.7μB and of around 45%, i.e. 1.3μB, for Re3+.
8.6 The measured magnetic moment of Pr2(SO4)3 is 3.50μB. Show that this value is consistent with the presence of the Pr3+ ion (f2, ground state term symbol, 3H4, with L = 5, S = 1, and J = 4) in this compound.
Using
Eqn 8.11
where the Landé gj factor is
Eqn 8.12
gj = 1 + [ ( (1×2)−(5×6)+(4×5) )/ 2(4×5) ] = 1 + [(2−30+20)/40] = 4/5
Therefore µeff = 4/5 (20)½ μB = 3.58 μB.