5.03 Exam 5

Christopher C. Cummins

April 19, 2010

Instructions

Clearly write your name at the top of this front page, but otherwise do not write on this front pageas it will be used for scoring. This exam is closed-book and no calculators or electronic devicesmay be employed. There are five sections so please read over the exam before you begin and expectto take on average ten minutes per section. Read all questions carefully before writing down anyanswers. Enjoy the material!

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1 Ligand Field Stabilization Energy

The questions for this section are worth 4 points each.

1. At what four (θ, φ) values does a dxz orbital wavefunction attain a maximum absolute value?

2. Show that dz2 and dx2−y2 have the same energy in a tetrahedral complex by considering thevalues of θ and φ at the positions of the ligands. Explain your reasoning. Note: the equationfor dz2 is 3cos2θ − 1, while that for dx2−y2 is sin2θcos2φ.

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3. Explain why it is that low-spin tetrahedral complexes are extremely rare, in contrast to thesituation for octahedral complexes.

4. On going from d0 to d5 (high-spin octahedral case), there is a maximum in ligand field stabi-lization energy, LFSE, at d3. What is the magnitude of the LFSE for the d3 system in unitsof ∆o? Explain how this number can be arrived at.

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5. With reference to the following graphic showing hydration enthalpies for [M(H2O)6]n+ ions,what must be n, the value of the charge on the ion?

6. To what do the filled and open circles correspond in the above plot?

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2 Spectrochemical Series

The questions for this section are worth 4 points each.

1. The spectra below are for pseudo-octahedral copper(II) complexes with an O6, an N2O4, andan N4O2 set of donor atoms. Based on inspection of the spectra, which type of donor atomgenerally lies higher in the spectrochemical series, O or N?

2. Except for consideration of Jahn-Teller effects, spectra for pseudo-octahedral copper(II) com-plexes are as simple as those for what other 3d ion?

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3. What is the ligand that is typically listed highest in the spectrochemical series? Give tworeasons why this ligand gives rise to such large values of ∆o.

4. Is there a red spectral shift or is there a blue spectral shift when en is added to a solutioncontaining aqueous nickel(II) ion? Explain what is happening chemically and why the spectrumshifts as it does.

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3 Tanabe-Sugano Diagrams

The questions for this section are worth 4 points each.

1. For a nickel(II) complex three bands are observed at energies of 8000, 13200, and 22800 cm−1.what is the value of ∆o? Shown below is the Tanabe-Sugano diagram for the d8 case.

2. Using the values from the preceding question, what is the approximate value of ∆o/B that isindicated by the ratio ν2/ν1?

3. Given the value of ∆o/B you obtained in the previous question, what value of B′ is indicated?

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4. In the Tanabe-Sugano diagram for the d8 case, it can be seen that two of the triplet statesare curved due to configuration interaction. Which triplet states are these, and what are theconfigurations that give rise to them?

5. How many spin allowed bands are there for a manganese(II) complex in the case where ∆o/Bis about 20?

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4 Magnetism

The questions for this section are worth 4 points each.

1. Upon addition of en to an aqueous solution of manganese(III) ion in an NMR tube configuredfor Evans’s method magnetic susceptibility measurements, measurements of ∆ν taken as afunction of time show that the magnitude of ∆ν is decreasing substantially. To what valuesof µ should the initial and final values of ∆ν correspond? Assume that spin-only behavior isobserved, wherein µs = g

√S(S + 1).

2. When making an Evans’s method determination of the molar magnetic susceptibility of adissolved substance, what are the three quantities needed in order to do the calculation?

3. After carrying out a calculation of the molar magnetic susceptibility as referred to in the pre-ceding problem, correction for diamagnetism must be carried out in order to obtain χcorr

M (thisis the same thing as χP, the paramagnetic susceptibility). Is the value of the sample’s dia-magnetism (obtained using Pascal’s constants or otherwise estimated) added to or subtractedfrom the molar magnetic susceptibility in order to arrive at χcorr

M ?

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4. What is an approximate relationship between the molecular weight of a substance and itsdiamagnetic susceptibility, χD?

5. Using the relationship µ = 2.84√χPT , what is the approximate molecular weight at which the

measured magnetic susceptibility of a substance having two unpaired electrons per moleculegoes to zero at 298 K?

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5 Single-Molecule Magnets

The questions for this section are worth 4 points each.

1. To what point group does the molecule [Mn12O12(O2CCH2Br)16(H2O)4] belong (see graphic)?

2. In the case of [Mn12O12(O2CCH2Br)16(H2O)4], how many manganese ions are present for eachof the oxidation states +2, +3, and +4?

3. For [Mn12O12(O2CCH2Br)16(H2O)4], show how the result from the preceding question leadsto the observed value of S.

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4. Using single-crystal measurements, Sessoli et al. showed that the magnetic susceptibility for[Mn12O12(OAc)16(H2O)4] measured parallel to the crystallographic c axis was about fourteentimes greater than that measured perpendicular to the c axis. Note that the crystallographicc axis is aligned with the highest order principal rotation axis of the cluster molecules. Thisanisotropy of the magnetic susceptibility is attributed to what structural attribute of themanganese(III) ions within the cluster?

5. The presence of a large, negative, value for D means that in the absence of an applied mag-netic field only two states are populated at low temperature for the molecular magnet of thepreceding problem. Which are these states?

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Structure

Linear orlow symmetry

highly symmetric(octahedral,tetrahedral,icosahedral)

Normalsymmetry

Sure? More than oneCn axis of C3

or higher?

linear i

i

D

C

C

C

C

8h

8v

s

i

1

6C5

3C4

3S4

i

I

I

h

i

O

O

h

i

T

T

h

Td

C C2 nDnh

Dnd

Dn

S

v

2n

Cnh

Cnv

S2n

Cn

Yes

Yes

Yes

Yes

Yes

YesYes Yes

Yes

YesYes

Yes

Yes

Yes Yes Yes

Yes

Yes

Yes

Yes

No

No

No

No

No

No

No

No

No

No

No

No

NoNo

No

No

Spe

cial

G

roup

Ele

men

ts

Hig

h S

ymm

etry

Ele

men

ts

Nor

mal

Sym

met

ryE

lem

ents

(m

ost

com

mon

)

linea

rsi

ngle

ele

men

t

icos

ahed

ral

octa

hedr

alT

etra

hedr

alD

ihed

ral

S i

n g

l e

A

x i

s

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