Mo¨ssbauer spectroscopy in inorganic chemistry

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2.12 Mo¨ssbauer spectroscopy in inorganic chemistry

ﬂuxional. On going from the low to high temperature limit, the two signals coalesce to give a single resonance.

The usual dynamic process in which 5-coordinate species are involved in solution is Berry pseudo-rotation.^†Although ligand–ligand repulsions are minimized in a trigonal bi-pyramidal arrangement, only a small amount of energy is needed to convert it into a square-based pyramid. The interconversion involves small perturbations of the bond angles subtended at the central atom, and continued repeti-tion of the process results in each substituent ‘visiting’ both equatorial and axial sites in the trigonal bipyramidal struc-ture (Figure 2.13).

Exchange processes in solution

A number of hydrated cations in aqueous solution undergo exchange with the solvent at rates slow enough to be observed on the NMR spectroscopic timescale by using

17O isotopic labelling; ¹⁷O has I¼⁵₂, while both ¹⁶O and

18O are NMR inactive. Diﬀerent chemical shifts are observed for the¹⁷O nuclei in bulk and coordinated water, and from the signal intensity ratios, hydration numbers can be obtained. For example, Al^3þhas been shown to be present as [Al(H₂O)₆]^3þ.

Reactions such as that in equation 2.41 are known as redistribution reactions.

PCl₃þ PðOEtÞ₃Ð PCl₂ðOEtÞ þ PClðOEtÞ₂ ð2:41Þ A redistribution reaction is one in which substituents

exchange between species but the types and numbers of each type of bond remain the same.

The position of equilibrium can be followed by using ³¹P NMR spectroscopy, since each of the four species has a

characteristic chemical shift. Rate data are obtained by following the variation in relative signal integrals with time, and equilibrium constants (and hence values of G^o since G^o¼ RT ln K) can be found from the relative signal integrals when no further change takes place (i.e.

equilibrium has been established); by determining Gô at different temperatures, values of Hô and Sô can be found using equations 2.42 and 2.43.

Gô¼ Hô TSô ð2:42Þ

d ln K dT ¼H^o

RT² ð2:43Þ

Values of H^o for these types of reactions are almost zero, the redistribution of the groups being driven by an increase in the entropy of the system.

2.12 Mo¨ssbauer spectroscopy in

a radioactive source, a solid absorber with the ⁵⁷ Fe-containing sample and a g-ray detector. For⁵⁷Fe samples, the radioactive source is ⁵⁷Co and is incorporated into stainless steel; the ⁵⁷Co source decays by capture of an extra-nuclear electron to give the excited state of ⁵⁷Fe which emits g-radiation as it decays to its ground state. If

57Fe is present in the same form in both source and absorber, resonant absorption occurs and no radiation is transmitted.

However, if the⁵⁷Fe in the source and absorber is present in two diﬀerent forms, absorption does not occur and g-radiation reaches the detector. Moving the source at diﬀerent velocities towards or away from the ⁵⁷Fe absorber has the APPLICATIONS

Box 2.6 Magnetic resonance imaging (MRI) Magnetic resonance imaging (MRI) is a clinical technique to obtain an image of, for example, a human organ or tumour.

The image is generated from information obtained from the

1H NMR spectroscopic signals of water. The signal intensity depends upon the proton relaxation times and the concentra-tion of water. The relaxaconcentra-tion times can be altered, and the image enhanced, by using MRI contrast agents. Coordina-tion complexes containing paramagnetic Gd^3þ, Fe^3þ or Mn^2þ are potentially suitable as contrast agents, and of these, complexes containing the Gd^3þ ion have so far proved to be especially useful. To minimize toxic side-eﬀects in patients, Gd^3þmust be introduced in the form of a com-plex that will not dissociate in the body, and chelating ligands are particularly suitable (see Chapter 6 for a discussion of stability constants). Excretion is also an important consid-eration; complexes must not remain in the body any longer than is necessary. One of the successful ligands in use is derived from H₅DTPA; after the intravenous injection to introduce [Gd(DPTA)]², clearance through the kidneys takes about 30 min.

N N N

HO2C

HO₂C CO2H

CO2H CO2H

H5DTPA

If an image of a certain organ is required, it is important to ﬁnd a contrast agent that targets that organ, e.g.

gadolinium(III) complexes are used to target the liver.

Dependence upon the observation of proton signals in some organs (e.g. lungs) presents problems with respect to MRI. The use of¹²⁹Xe magnetic imaging has been tested as a means of overcoming some of the diﬃculties associated with proton observation. Under the right conditions, gaseous¹²⁹Xe taken into mouse lungs allows excellent images to be observed.

What can isomer shift data tell us?

The isomer shift gives a measure of the electron density on the ⁵⁷Fe centre, and isomer shift values can be used to determine the oxidation state of the Fe atom. Similarly, in

197Au Mo¨ssbauer spectroscopy, isomer shifts can be used to distinguish between Au(I) and Au(III). Three speciﬁc examples are chosen here from iron chemistry.

The cation [Fe(NH₃)₅(NO)]^2þhas presented chemists with an ambiguity in terms of the description of the bonding which has, in some instances, been described in terms of an [NO]^þunit bound to an Fe(I) centre. Results of⁵⁷Fe Mo¨ss-bauer spectroscopy have revealed that the correct description is that of an [NO]ligand bound to an Fe(III) centre.

The formal oxidation states of the iron centres in [Fe(CN)6]⁴and [Fe(CN)6]³ areþ2 and þ3; however, the closeness of the isomer shifts for these species suggests that the actual oxidation states are similar and this may be interpreted in terms of the extra electron in [Fe(CN)₆]⁴

being delocalized on the cyano ligands rather than the iron centre.

Diﬀerences in isomer shifts can be used to distinguish between diﬀerent iron environments in the same molecule:

the existence of two signals in the Mo¨ssbauer spectrum of Fe₃(CO)₁₂ provided the first evidence for the presence of two types of iron atom in the solid state structure (Figure 2.14), a fact that has been confirmed by X-ray diffraction methods.

Glossary

The following terms were introduced in this chapter. Do you know what they mean?

q neutron q proton q nucleon q nuclide q mass number q mass defect q binding energy q radioactive decay q ﬁrst order rate equation q ﬁrst order rate constant q half-life

q a-particle q b-particle (b) q g-radiation q positron (b^þ) q neutrino (n_e) q antineutrino

q transmutation of an element q nuclear ﬁssion

q nuclear fusion

q slow (thermal) neutron q fast neutron

q transuranium element q isotopic enrichment q zero point energy

q isotope exchange reaction q kinetic isotope eﬀect q spectroscopic timescale

q nuclear spin quantum number, I q chemical shift (in NMR spectroscopy) q spin–spin coupling (in NMR spectroscopy) q proton-decoupled NMR spectrum

q multiplicity of an NMR spectroscopic signal q satellite peaks (in an NMR spectrum) q stereochemically non-rigid

q ﬂuxionality

q Berry pseudo-rotation q redistribution reaction q Mo¨ssbauer eﬀect

q isomer shift (in Mo¨ssbauer spectroscopy)

Problems

2.1 For each of the following isotopes, state the number of neutrons, protons and electrons present: (a)¹⁹₉F; (b)⁵⁹₂₇Co;

(c)²³⁵₉₂U.

2.2 What do you understand by the terms: (a) atomic number;

(b) mass number; (c) mass defect; (d) binding energy per nucleon?

2.3 Using the data in Appendix 5, plot a representation of the mass spectrum of naturally occurring atomic Ba.

2.4 Radium-224 is radioactive and decays by emitting an a-particle. (a) Write an equation for this process. (b) The decay of radium-224 produces helium gas. Rutherford and Geiger determined that a-particles were emitted from

224

88Ra at a rate of 7:65 10¹²s¹mol¹, and that this corresponded to a rate of helium production of

2:90 10¹⁰dm³s¹at 273 K, 1 bar. If 1 mole of helium occupies 22.7 dm³(273 K, 1 bar), estimate a value for the Avogadro constant.

2.5 Use the following data to determine the half-life of²¹⁸₈₄Po and the rate constant for the decay of²¹⁸₈₄Po.

Time / s 0 200 400 600 800 1000

Moles²¹⁸₈₄Po 0.250 0.110 0.057 0.025 0.012 0.005

2.6 The half-life of strontium-90 is 29.1 years. Determine the rate constant for the decay of strontium-90 in units of s¹. [The SI unit of time is the second.]

2.7 Complete the following table, which refers to possible nuclear reactions of a nuclide:

Reaction type

Change in number of protons

Change in number of neutrons

Change in mass number

Is a new element formed?

a-particle loss b-particle loss Positron loss (n,g) reaction

2.8 For each step in Figure 2.3, identify the particle emitted.

2.9 Interpret the following notational forms of nuclear reactions: (a)⁵⁸₂₆Feð2n;bÞ⁶⁰₂₇Co; (b)⁵⁵₂₅Mnðn;gÞ⁵⁶₂₅Mn;

(c)³²₁₆Sðn;pÞ³²₁₅P; (d)²³₁₁Naðg;3nÞ²⁰₁₁Na.

2.10 Identify the second ﬁssion product in the following reactions:

(a)²³⁵₉₂Uþ¹₀n^"¹⁴²₅₆Baþ ? þ 2¹₀n

(b)²³⁵₉₂Uþ¹₀n^"¹³⁷₅₂Teþ ? þ 2¹₀n

2.11 In each of the following reactions, are the incoming neutrons ‘fast’ or ‘slow’ ? Give reasons for your choices.

(a)¹⁴₇Nþ¹₀n^"¹⁴₆Cþ¹₁H

(b)²³⁸₉₂Uþ¹₀n^"²³⁹₉₂Uþ g

2.12 Determine the half-life of Bk given that a plot of ln N against t is linear with a gradient of0.0023 day¹where N is the number of nuclides present at time t.

2.13 The IR spectrum of naturally occurring CO shows an absorption at 2170 cm¹assigned to the vibrational mode of the molecule. If the sample is enriched in¹³C, what change do you expect to see when the IR spectrum is re-recorded?

2.14 If the oxide P₄O₆is dissolved in an aqueous solution of sodium carbonate, compound A of formula Na₂HPO₃ may be crystallized from solution. The IR spectrum of A contains a band at 2300 cm¹. The corresponding band in the IR spectrum of B (obtained by an analogous method from P₄O₆and Na₂CO₃dissolved in D₂O) is at 1630 cm¹. On recrystallization of A from D₂O, however, its IR spectrum is not aﬀected. Discuss the interpretation of these observations.

2.15 Why is the method of isotope dilution analysis used to determine the solubility of sparingly soluble salts rather than a method depending upon mass determination?

2.16 A small amount of the radioactive isotope²¹²₈₂Pb was mixed with a quantity of a non-radioactive lead salt containing 0.0100 g lead (A_r¼ 207). The whole sample was dissolved

in aqueous solution and lead(II) chromate (PbCrO₄) was precipitated by the addition of a soluble chromate salt.

Evaporation of 10 cm³of the supernatant liquid gave a residue having a radioactivity of 4:17 10⁵that of the original quantity of²¹²₈₂Pb. Calculate the solubility of lead(II) chromate in mol dm³.

In questions 2.17 to 2.27, refer to Table 2.3 for isotopic abundances where needed.

2.17 Why is a coupling constant measured in Hz and is not recorded as a chemical shift diﬀerence?

2.18 Long range couplings are often observed between³¹P and

19F nuclei, between³¹P and¹H nuclei, but not between remote non-equivalent¹H nuclei. What does this tell you about the relative magnitudes of values of J_PF, J_PH and J_HHfor the respective pairs of nuclei when they are directly attached?

2.19 Rationalize the fact that the¹³C NMR spectrum of CF₃CO₂H consists of two binomial quartets with coupling constants of 44 and 284 Hz respectively.

2.20 How might you use³¹P NMR spectroscopy to distinguish between Ph₂PH and Ph₃P?

2.21 The³¹P NMR spectrum of PMe₃consists of a binomial decet (J 2.7 Hz). (a) Account for this observation. (b) Predict the nature of the¹H NMR spectrum of PMe₃.

2.22 The²⁹Si NMR spectrum of compound 2.5 shows a triplet with a coupling constant of 194 Hz. (a) Rationalize these data and (b) predict the nature of the signal in the¹H

Fig. 2.15 Figure for problem 2.23.

Chapter 2 ^. Problems 77

NMR spectrum of 2.5 that is assigned to the silicon-bound protons. [²⁹Si: 4.7% abundant; I¼¹₂]

H H

(2.5)

2.23 Figure 2.15 shows the¹¹B NMR spectra of (a) THF BH₃ (2.6) and (b) PhMe₂P BH₃. Interpret the observed coupling patterns and mark on the ﬁgure where you would measure relevant coupling constants.

O BH3

(2.6)

2.24 (a) Predict the structure of SF₄using the VSEPR model. (b) Account for the fact that at 298 K and in solution the¹⁹F NMR spectrum of SF₄exhibits a singlet but that at 175 K, two equal-intensity triplets are observed.

2.25 The¹⁹F NMR spectrum of each of the following molecules exhibits one signal. For which species is this observation consistent with a static molecular structure as predicted by VSEPR theory: (a) SiF₄; (b) PF₅; (c) SF₆; (d) SOF₂; (e) CF₄?

2.26 Outline the mechanism of Berry pseudo-rotation, giving two examples of molecules that undergo this process.

2.27 Is it correct to interpret the phrase ‘static solution structure’ as meaning necessarily rigid? Use the following molecules to exemplify your answer: PMe₃; OPMe₃; PPh₃; SiMe₄.

Further problems on NMR spectroscopy

2.28 Account for the fact that the²⁹Si NMR spectrum of a mixture of SiCl₄and SiBr₄that has been standing for 40 h contains ﬁve singlets which include those assigned to SiCl₄ ( –19) and SiBr₄( 90).

2.29 The structure of [P₅Br₂]^þis shown in diagram 2.7.

Account for the fact that the³¹P NMR spectrum of this cation at 203 K consists of a doublet of triplets (J 321 Hz, 149 Hz), a triplet of triplets (J 321 Hz, 26 Hz) and a triplet of doublets (J 149 Hz, 26 Hz).

P P

P Br Br

(2.7)

2.30 Tungsten hexacarbonyl (2.8) contains six equivalent CO ligands. With reference to Table 2.3, suggest what you would expect to observe in the¹³C NMR spectrum of a

13C-enriched sample of W(CO)₆.

W OC

OC CO

CO OC

CO (2.8)

2.31 The compounds Se_nS_{8 n}with n¼ 1–5 are structurally similar to S₈. Structure 2.9 shows a representation of the S₈ ring (it is actually non-planar) and the atom numbering scheme; all the S atoms are equivalent. Using this as a guide, draw the structures of SeS₇, 1,2-Se₂S₆, 1,3-Se₂S₆, 1,2,3-Se₃S₅, 1,2,4-Se₃S₅, 1,2,5-Se₃S₅and 1,2,3,4-Se₄S₄. How many signals would you expect to observe in the

77Se (I¼¹₂, 7.6%) NMR spectrum of each compound?

S S

S S S S

1 2

3 4 5 6 7 8

(2.9)

2.32 Explain why the¹⁹F NMR spectrum of BFCl₂consists of a 1 : 1 : 1 : 1 quartet. What would you expect to observe in the¹⁹F NMR spectrum of BF₂Cl? Data for the spin-active nuclei in these compounds are given in Table 2.3.

2.33 Rationalize the fact that at 173 K,¹H NMR

spectroscopy shows that SbMe₅possesses only one type of Me group.

2.34 MeCN solutions of NbCl₅and HF contain a mixture of octahedral [NbF₆], [NbF₅Cl], [NbF₄Cl₂],

[NbF₃Cl₃]and [NbF₂Cl₄]. Predict the number and coupling patterns of the signals in the¹⁹F NMR spectrum of each separate component in this mixture, taking into account possible isomers. (Assume static structures and no coupling to¹⁹³Nb.)

An introduction to molecular symmetry

Dalam dokumen INORGANIC CHEMISTRY (Halaman 110-116)