Download Chapter 20. - Bryn Mawr College

265
21.1
configuration of w^^
, ^ ,^ , .
•
. Consider formation of octahedral complex [ML,]'-. Crystal field theory • •
treats metal ion and ligands as point charges; repulsions between electrons,,,
in M"-" d orbitals and L donor electrons.
. Ligands create a 'crystal field' around M"^ In a spherical field, the energy
of ^ orbitais is raised with respect to energy in gas phase W^ See left-hand
side ofFigure 21.2 in H&S.
. An octahedral crystal field leads to splitting of d orbitals mto 2 sets (21.i).
(i) higher energy rf,. and d^_^., and (ii) lower energy d^. d^^ and d^,. The d2
and d, , orbitals point directly at the ligands while d^, d^^ and d^^ orbitals
point between the ligands. Therefore, repulsion between ligand electrons
and electrons in d^ and ^,._^is greater than between ligand electrons and
- d- m6d yz orbitals. See right-hand side of Figure 21.iin
electrons in d^,
H&S.
. The raising and lowering of energies is measured with respect to the energy
level in the spherical crystal field, this is the barycentre (see diagram 21.14).
0 Include redrawn Figures 21.2 and 21.3 from H&S in your answer.
V-y2
«n
d.., d..
(21.1)
21.2
2L3
NH,
H,N
Refer to Section 21.3 in H&S. Points to include:
- Gas phase metal ion M"- has degenerate nd atomic orbitals, and a valence
(21.2)
Look at Table 20.2 in H&S. X^,, is the wavelength of the absorption maximum; a
value of A - 510 nm corresponds to absorption of green light and transmittance
of red and'iolet, so solutions of [Ti(Hp),]^^ actually look purple.
(a) en = 1,2-ethanediamine; NJ^'-donov, 21.2. Usually bidentate; forms 5-membered
chelate ring (chelate effect, see Section 6.12 in H&S). Occasionally monodentate.
(b) bpy - 2 2'-bipyridine; iV,/V'-donor, 21.3. Bidentate; 5-membered chelate nng.
(c) Cyanide, [CN]" (21.4); usually C-donor, rnonodentate; sometimes bndges m an
M ^ s N~M mode (see examples in Chapter 22 of H&S).
(d) Azide, [N3]', (21.5); usually monodentate N-donox; sometimes bridges.
(e) CO (21.6); monodentate, C-donor (see Section 24.2 in H&S).
(f) phen = 1,10-phenanthroIine (21.7); iVA'-donor; bidentate forming 5-membered
(sUoxl"^= oxalate (21.8); 0,0'^donor; bidentate forming 5-membered chelate ring.
(h) [NCSr (thiocyanate, 21.9) can be an N- or S-donor; usually monodentate but
sometimes bridges in an M-N=C=S-M mode.
(i) PMe3 (tnmethylphosphine, 21.10) is usually a monodentate, F-donor, but see
structure 24.18 in H&S and the accompanying discussion.
_
The order is as ligands appear in the spectrochemical senes (Section 21.3 m H&b).
(21.3)
;N
(21.4)
O
0
Me'
N:
]<i:=i<i:=ii
(21.5)
c=o
(21.6)
0
Me
0
N-
(21.7)
.P'"<; Me
(21.8)
(21.9)
(21.10)
266
(i-Block metal chemistry: coordination complexes
21.4
B r < F- < [OH]- < H2O < NH3 < tCN]weak field
21.5
Factors to look for ai-e different oxidation states of metal, different field strengths
of ligands, or metals with same oxidation state and in the same triad.
(a) [Cr(On^)^f^ should have larger A^, than [CriOH^)^]^^-(+3 is higher ox. state)
(b) [Cr(NH3)g]3^ should have larger A^, than [CrF^J^- (both Cr(ni), but NE, is a
stronger field ligand than F~).
• •
(c) [Fe(CN)g]3- is Fe(ni), [Fe(CN)g]^ is Fe(n); [Fe(CN),]3- will havp larger A ,
(d) [Ni(en)3]2^ should have larger A^^^ than [NiCOJ-I^^]'-^ (en is stronger field ligand).
(e) [MnFg]^- and [ReF^j^- both contain M(IV) with M from group 7; [ReFg]^- should
have larger A^^^ because Re is 3rd row metal, Mn is 1st row.
(f) [Co(en)3]3-^ and [Rh(en)3]3^ both contain M(m) with M from group 9; [Rh(en)3]3-^
should have larger A^^, because Rh is 2nd row metal, Co is 1st row.
21.6
(a) Diagram 21.11 shows the d^ configuration in an octahedral field. There is no
vacant e^ orbital and so no possibility of promoting an electi'on from a fully occupied
t^^ orbital to generate a high-spin configuration. .-. Only one configuration.
(b) Consider an example, e.g. octahedral d-^, that can be low-spin (21.12) or highspin (21.13). Preference for high-spin or low-spin configuration depends on which
configuration has the lower energy. This, in turn, depends on whether it is
energetically preferable to pair the fourth electron (21.12) or promote it to the e
level (21.13). Need to consider the energy required to transform two electrons with
parallel spins in different degenerate orbitals into spin-paired electrons in the same
orbital - the pairing energy, P, depends on (1) the loss in the exchange energy on
pairing the electrons (see Box 1.8 in H&S), and (ii) the coulombic repulsion between
the spin-paired electrons.
For high-spin:
A^^^ < P
weak field
•-f~~f- e^
"If-"IT 4^ !g
(21.11)
-XI
1
1—
strong field
?
_ For low-spin:
(21.12)
A^^^> p
strong field
(c) Different numbers of unpaired electrons give rise to different effective magnetic
moments (^^^j), e.g. low-spin d^ has 2 unpaired electrons, high-spin d"^ has 4. Use
the spin-only formula to estimate the magnetic moment for n unpaired electrons:
In the case of an octahedral d^ ion, low-spin is diamagnetic, high-spin is paramagnetic.
(21.13)
21.7
+0.6A
barycenlre
-^.4A
%
(21.14)
For a given d'^ configuration, CFSE is difference in energy between d electrons in
octahedral crystal field and (^electrons in spherical crystal field. From diagram 21.14:
CFSE - (-0.4A^J(number of electrons in t^^ level)
+ (0.6A^,)(Eumber of electrons in t^ level)
Examples of use of this equation:
^
d'
CFSB = (-0.4A^J(Z) -f 0 = -0.4A^,
d' high-spin
CFSE =^ (-04A^J(3) -f (O.6A^J(1) = -0.6A^^^
d' high-spin
CFSE =. (-0.4A^J(3) + (0.6A^,)(2) := 0
But for, for example, low^spin d\ CFSE consists of two terms: the four electrons
in the t^^ orbital give rise to a -1.6A^, term and a pairing energy, P, must be included
to account for the spin-pairing of two electrons:
-1.6A^, + P
^^M^^^if^
*^»-
rf-Block metal chemistry: coordination complexes
Figure 21.1 For answer 21,8:
rationalizing numbers of unpaired
electrons in problem 21.8. For the
ground state electronic
configurations of the metal atoms,
see Table 20.1. p, 256.
267
j||^_ll__l^ -I-H-^- "f-|-~h -|-4Hfln(CN)/-
(a) fMniCNy*-
mcmr
octahedral Fe{lll}, high-
octahedral Cr(ll), high-
spin d^
octahedral Mn(IV), d^
ocEahedral Mn(H), iowspin d^
spin rf*
^
^
44
^
t
(e) iPd(CN),F'
square planar Pd{ll)
(21.15)
(DECoCI,ptetrahedrai Co{!l), cf
"if ""tf
(g) muftefrahedral Ni(ii),
21.8
See Figure 21.1.
21.9
(a) Define an axis set; by convention, take
the axial ligands to lie on the z axis (21.15
^j?-)j2
and 21.16).
Trigonal bipyramid: the d^2 orbital points
directly at 2 ligands and is destabilized the
most (Figure 21.2). The equatorial ligands
lie in the xy plane, and the d^z^^^z and d^
d^. d-.
orbitals are degenerate and higher in
energy than the d^^ and d^^ orbitals which
point between the ligands. Square-based
square-based
pyramid: 1 ligand lies on the z axis, 2 lie
trigonal
« along the x axis, 2 lie s* on the y axis; the
pyramid
bipyramid
d^2^f orbital (points » at the basal ligands)
is destabilized the most, the d^i orbital is
Figure 21.2 For answer 21,9:
destabilized to a lesser extent (Figure 21.2);
crystal field splitting diagrams for
trigonal bipyramidal and squaresince the basal ligands lie in the xy plane,
based pyramidal fields.
the d._. orbital lies at higher energy than
xy
orbitals.
the d... and d.
yz
(b) Ni(n) is d^ and both trigonal bipyramidal and square-based pyramidal complexes
will be diamagnetic (place 8 electrons in the levels shown in Figure 21.2).
(21.16)
21.10
(a) On going from gaseous M'"^ to complexed M"*^, interelectronic repulsion between
metal d electrons decreases - pairing energies reduced. This is caused by an increase
in effective size of metal orbitals ~ the nephelauxetic effect ('cloud expanding')For a common M"^, nephelauxetic effect of ligands follows series:
F- < H P < NH3 < en < [ox]^- < [NCS]- < CI- < [CN]- < Br-< IFor metal ions (with a common ligand) nepheiauxetic effect follows series:
MnCn) < NiOO « Co(ro < Mo(n) < Re(IV) < Fe(in) < IrOm) < CoOOI) < MnaV)
•^
268
f/-Biock metal chemistry: coordination complexes
Parameters for ligands (h) and metal ions (k) (see Table 21.10 in H&S) are used to
estimate the reduction in electron-electron repulsion upon complex formation:
metal ion )
Where B is the Racah pai-ameter, B, is interelectronic repulsion.in, free ion^
(b) From nephelauxetic series for ligands: F- < H,0 < NH^ < en < [CN^ < r
21.U
-f \~
(a) [CoCy2- is Co(II), cP. [ C u C y ^ is Cu(II), d^.
Tetrahedral Co2M2U7), t^
orbitals are all singly
occupied; in tetrahedral Cu^^
+„ J
(21.18), ^2 orbitais are
asymmetrically filled. Thus,
the complex suffers a JahnTeller distortion leading to
the observed flattened
I
i|
L-t,
I
]
"^
(21.17)
i| ' k
-4i- -li- "i—
1?
IT
I
(21.18)
l?{octh?draUCoF,]3-is Co(m), d^ F-is weak M
spL(21.19).A^nonmightbeexpected to giveasingle absorption intheelectronic
(21.19)
spectrum (see diagram in Figure 21:19 in H&S). The excited ^^ate of Co^] (t ^e 5) suffers a Jahn-Teller effect because the e^ level is asymmetncally filled.
Small splitting of e^ level leads to 2 possible transitions: 11500 and 14500 cm-.
21.12
The electron configuration of Si is 1.^.^2/3.^3^^ but only the 3p^ (/ = D
configuration contributes to the term symbol. The working is as for carbon m
Section 21.6 in H&S. There are 15 microstates. The table of microstates for a p
configurationis given inTable21.6inH&S.T^emicrostatesaregrouped according
tovaluesofM,andM,.ValuesofLand5arederivedbylookmgforsetsofM,and
M5 values:
allowed values of M^:
O,...-iL'll ~L
L,{L' •1)
5, (S • I),... -(5-1),--5
allowed values of My:
Term symbols are assigned as follows:
c^ /r . c
• L - 2,5 = 0 gives the singlet term, 'D; J can take values {L + 5), (L + S 1)
L^S\ so only / = 2 is possible; the term symbol is ^D^. 1 = 1 , 5 - 1 corresponds to a doublet term; possible values of i are 2,1,0
giving the terms ^F ^F, and ^PQ.
_
. L =. 0,5 = 0 con-esponds to a singlet term, and only / - 0 is possible; the
term s y m b o l i s t
,
The predicted energy ordering (from the rules above) IS 3P,< P^< t'^< u^< ^o21.13
3F and 3F are triplet terms. •/>, 'G and ^S are singlet terms. Electronic transitions
obey the spin selection rule:
A5 = 0
i.e.transitions may occur from singlet to singlet, or triplet to triplet states, but a
change in spin multiplicity is forbidden.
. „w,1nH'.
The relativeenergies of the3F,^F,^A^Gand^Sterms are determined usmgHunds
rules. The terms with the highest spin multiplicity are the ^F and ^P and of these
the term with higher value of L has the lower energy. Therefore, ^F is the ground
term Th^ other terms are singlets and their relative energies depend on the values
ii~Block metal chemistry: coordination complexes
269
of L. The energy ordering of the terms for a <^ configuration is therefore ^F<^P<
^G<^D< ^S. The most probable transitions originate from the ground state. The
allowed transition (triplet to triplet in an absorption spectrum) is ^F-(r~ ^P. Transition
from ground to excited states are much more likely that from excited to excited
states, and therefore you can ignore the latter on statistical grounds.
21.14
i/"0 is a closed shell configuration and gives only a '5 term. For this term, L = 0,5
=- 0, and therefore / := 0. Using the following formula:
S,P,D,F,G ...term
Multiplicity
of the term "
X.J -»—j value
the ground (and only) term is therefore %. Examples ofd^° ions: Zn2+, Cu+.
21.15
Russell-Saunders coupling is a spin-orbit coupling scheme and it is not valid for all
elements, in particular those with high atomic numbers. For heavier elements where
spin-orbit coupling is particularly latge, a more appropriate approach is to use a j / coupling scheme.
For detailed discussions, see:
T.P. Softley (1994) Atomic Spectra, Oxford University Press, p. 68;
M. Gerloch (1986) Orbitals, Terms and States, Wiley, p. 73.
21.16
The quantum number / takes values (L + S),(L + S
- 1)... \L - S\. For the ^F term, I, - 3 and 5 = 1.
Therefore, J = 4,3,2. Different values of/denote
different levels within the term (diagram 21.20),
and the energy differences between successive
pairs of energy levels are 3X and 4X where X is the
spin-orbit coupling constant. The degeneracy of a
/ level is (2/ -i-1). For 7 - 4, degeneracy - 9; for J
= 3, degeneracy = 7; for J = 2, degeneracy = 5. In
a magnetic field, each J state splits into the (2J +
I) levels separated by g^Ms^o ^SJ ^^ *® Land6 ^factor, fj.^ is the Bohr magneton, and SQ is the
magnetic field). The splitting of the levels in a
magnetic field (shown in diagram 21.21) is called
the Zeeman electronic effect, and the small energy
separations between these levels are the basis for
Energy
(21.20)
LS
coupling
(21.21)
electron paramagnetic resonance (EPR)
spectroscopy (see Box 20.1 in H&S).
21.17
Term
Components in
octahedral field
-^ig + ng + Tig
The splitting of terms in an octahedral field is tabulated in the margin.
(a) The ^ term will split to %^ and ^E^.
(b) The ^P term does not split but becomes the %^.
(c) The 3F term splits to become the ^r,^, %g and ^A^^.
See Figure 21.20 in H&S.
effect of
magnetic
field
270
d-B\ock metal chemistry, coordination complexes
Table 21.1 Table of microstates
for a d' ion
^ -2
t
f' ~2
-1
t
0
t
+1
+2
M,
21 18
nil
t
t
t
t
K
t
t
t
t
t
0
t
t
t
t
t
t
+2 +1 0 - 1 - 2
•<
t
t
t
t
t
t t
+3 +2 +1 0 - i -2 -3 +i 0 —1
/
'Y"
The construction of tables of microstates is described in detail m Section_21.6 m
H&S Assume for this answer that you need only consider the weak field limit, i.e.
termsof maximum spin multiplicity(see discussion in H&S,Section21.6).Setup
the table of microstates as in Table 21.1. The left-hand column ^^J^^ i « P J ^ <>
Table 21.1 gives m, values for arforbital; the row in the lower part of Table 2 U
gives M, values for a d^ ion. In a tetrahedral field, the ^ term has E and T
components (see Orgel diagram in Figure 21.19 in H&S) The rnultxphaty o the
term (the 2 in the ^D symbol) is determined frona 2S + 1; for 1 electron, S= I,,
(b) Set up the table of microstates for the d^ ion remembermg that the electrons
singly occupy orbitaIs(Table21.2).TheM, values are obtained by summing them,
values in each column. Your tablemaynotlooHdenticaltoTable21.2because the
columns may come in a different order; the columns here are
^^^^fj^f^^'
values ofM, in an order from which the term symbols are easily found. H^e^Ptem
does not split (see answer 21.17) and gives a T, component in a tetrahedral field,
and a T, component in an octahedral field. In an octahedral field the components
of the 3F term are A,,, T,, and T,^; in a tetrahedral field, they are A , T, and T,
21.19
(a) Equations needed:
Wavenumber (in cm" )
Remember: lower
wavenumber corresponds to
longer wavelength
1
Wavelength (in cm)
I cm = W nm
10 000 cm-' - 1000 nm; 20 000 cm-' = 500 nm; 30 000 cm-^ - 333 nm.
(b) Visible range-400-750nm (25 000-14 285 cm-').
c Look at X corresponding to the visible part of spectrum. [mOH^),]
absorDs
.660 nm, so appears green; mm.)er ^ ^ ^ ^ ^ ' ' ^ " " v t - S T s ^ X
Visible range of spectrum
and absorption/transmittance
of light:
see Table 20.2 in H&S
wavenumber, the absorptions for [Ni(OH,),]=^ appear at lower wavenumbers
those for [Ni(NH3)6]2^
21.20
(a) Crdll) is d\ Sketch an Orgel diagram for an octahedral d^ ^ ^ ^ " J ! " '
Corresponds to the left-hand side of Figure 21.20 in H&S. Three absorption
transitions are expected:
(i-Block metal chemistry: coordination complexes
centre of symmetry
N.^^.oN
F
(21.22)
271
(b) tmns-[Co(en\V^]-^ (21.22) has a centre of symmetry, but the cw~isomer does
not; loss of centre of symmetry penrats greater p-ii mixing and, therefore, a greater
probability of transitions, leading to more intense colour for the c/5-isomer.
Comparing chloro and fluoro rran^'-complexes: charge transfer from Ch to Co^*
(LMCT) accounts for the more intense colour of chloro complex; LMCT for F" is
unlikely. LMCT occurs when a ligand that is easily oxidized is bo-ttrtd to a metal
centre (usually one in a high oxidation state) that is readily reduced..
21.21
(a) LMCT bands are at 282 nm for [OsClg]^- and at 348 nm for [RnCl^J^-. The
LMCT band moves to longer wavelength (smaller energy) because it is easier to
reduceRu(in)thanOsdll).
'
' '-^•''
(b) The bpy ligand easily accepts an electron and therefore charge transfer will .be
in the direction M(n) to L, not L to M(n), i.e. an MLCT band rather than an LMCT
band is observed.
21.22
ETi(OH2)6]^^ is a d^ ion. Its electronic spectrum consists of two bands close together
(observed as one band with a shoulder) because of a Jahn-Teller effect in the excited
state, t^'^e '. Single occupancy of the e^ level lowers the degeneracy, but the energy
separation between the fj^ and e^ levels is small. Two 'd-d' transitions from ground
to excited state are therefore possible, but they are close in energy and give rise to
absorptions at similar wavelengths.
iri(0n2)ef* is a £^ ion. Three 'd-d' transitions are predicted (Figure 21.20 in H&S):
r,, - r./F)
A.
T^AF)
If
TAP)^T,XF)
but only two, well separated bands are observed in the absorption spectrum (see
answer 21.38b).
2L23
Figure 2L23b in H&S shows the ^F and "F terms arising from a d^ configuration.
There are three transitions and their energies, measured from the electronic spectrum,
are given by:
F. ~ A
E= 1.2A^^j-f \5B + x
See:A.B.P.Lever(1968)J,
Chem. Educ, vol. 45, p. 711
21.24
f-f44
(21.23)
Limitations:
(i) The figure refers only to the extreme weak field limit and this is a severe limitation
of the method outlined here for determining the Racah parameter B.
(ii) The method is easiest to apply if all three transitions are observed. If only two
bands are observed (e.g. one absorption is hidden under an intense charge transfer
band), it becomes more difficult to abstract a value for B from the observed data.
(a) Co(n) is cf, and the Orgel diagram for octahedral d'^ is the same as for octahedral
d^ (Figure 21.20 in H&S). Absorption data in the question are reported in.cm-^
and the smallest wavenumber corresponds to the lowest energy transition. H^O is a
mid-field iigand; an assumption has to be made about the crossing of the lines in
the Orgel diagram. {Co{On^^^'- is high-spin (21.23) with 3 unpaired electrons:
Multiplicity == (2 x Vj) + 1 = 4
ifisiKt^swsiimissmisi^^m
272
t^-Block metal chemistry: coordination complexes
The assigments are:
8100 cm-' •
%g^%gif)
16000 cm->
%^iP)^'T,^(F)
19400 cm-'
%g^%s(P^
(b) From Figure 21.23a in H&S:
0.8A^,, + x = 8100cm-'
(i)
1.8A^,, + x - 1 6 0 0 0 cm-'
(ii)
- ••
Eqiiation (ii) ~(i) gives:
' A =16000-8100 = 7900 cm-'
oct
This value does not agree with the value listed in Table 21.2 because the method is
applicable only to a limiting case where field strength of the ligands is extremely
weak.
21.25
Racah parameters provide information aboutelectron-electronrepulsions. Ongoing
from a gaseous metal ion to a metal complex, there is an effective expansion of
'metal' orbitals associated with metal-ligand bond formation. This results in a
reduction in the electron-electron repulsions and, therefore, a reduction in the Racah
parameter B. Parameters for ligands and metal ions (see answer 21.10a, p. 267)
may be used to estimate this reduction.
21.26
Use the spin-only fomula to find the number of unpaired electrons, or fit values
calculated from the spin-only formula to the experimental values (assume you can
ignore contribution of the orbital angular momentum to the magnetic moment):
Table 2X.3 Calculated values
of /i(spin-only) for n unpaired
electrons.
n
1
2
3
4
5
//(spin-only) =
;i(spin-only) / ^
From values in Table 21.3:
(a) [VCl_^(bpy)] has 1 unpaired electron; d^ coiTesponds to V(IV), therefore x :=: 4.
(b) KJV(ox)3] has 2 unpaired electrons; d"^ corresponds to V(ni); the complex
anion is therefore [V(ox)3p-and so X - 3.
(c) [Mn(CN)g]^- has 3 unpaired electrons; d^ con-esponds to Mn(IV); since the
cyano ligand is [CN]", the overall charge must be 2~, i.e. x-2.
1.73
2.83
3.87
4.90
5.92
21.27
For an electron to have orbital angular momentum, it must be possible to transform
the orbital containing the electron into an equivalent and degenerate orbital by
rotation. For a fuller explanation, refer to Section 21.9 in H&S, the subsection
entitled 'Spin and orbital contributions to the magnetic moment'.
21.28
(a) K3[TiFg] contains [TiFg]^-, therefore Ti(ni), d^.
^(spin-only) = - / K " T 2 ) - V 3 = 1.73 ^^
d'-Biock metal chemistry: coordination complexes
273
(b) In a d^ ion (r,^0> there is one electron in one of the d. d^ or d^^ orbitals. These
orbitals can be interconverted by rotations through 90°, and therefore the electron
has orbital angular momentum. This results in an orbital contribution to the magnetic
moment.
21.29
Octahedral Ni^^ {d^) should have no orbital contribution, and jx^^^ is expected to be
close to spin-only value. Tetrahedral Ni^* has an orbital contribution because ground
state configuration is e\^, and so spin-orbit coupling occurs. This results in jx^^^ >
^(spin-only). In a square planar Ni^*complex, all electrons are paired leading to a
diamagnetic complex; look at Figure 21. le, p. 267 - the promotion energy to the
d^2 orbital (highest level) is too large for a high-spin complex to form.
-'•"•'
21.30
Consider for which ions you expect there to be an orbital contribution to the magnetic
moment. Orbital contributions to the magnetic moment are important only for the
tj J (see answers 21.28b and 21.35c), LJ; US} and t^H} configurations.
(a) [Cr(NH3)g 3-1(b) [V(0H,),]3(c) lCoV,f~
octahedral (P (/j/)
no orbital contribution
orbital contribution
octahedral (f- {t^?)
octahedral, high-spin d*^ ^h^^^) orbital contribution
Therefore, only for (a) will the spin-only formula give a reasonable estimate of the
magnetic moment. An octahedral d^ ion has a '^A^ ground term, and a better
estimate of the magnetic moment can be obtained by using equation 21.23
inH&S.
21.31
All the examples in the question are octahedral complexes.
Co(ni), low-spinrf^,diamagnetic.
(a) [Co(OH,),]3-^
Co(ni), rare example of high-spin d^, paramagnetic.
(b)[CoF,]3Ni(rV), low-spin (i^, diamagnetic.
(c) [NiF,FFe(ni), strong-field ligand, low-spin i^, paramagnetic.
(d) [Fe(CN)gF(e) [Fe(CN),]'^
Fe(II), strong-field ligand, low-spin d^, diamagnetic.
(f) [Mn(OH2)g]2*
Mn(n), high-spin d^, paramagnetic.
21.32
(a) Tj^^ is estimated from ionic lattice; r^^^ values for high-spin, octahedral ions are:
Ti2-^
V2^
Cr2+
Mn2+
d^
d'^
d^
79
80
2^
86
Fe^-^
d^
Co2^
Ni^-^
Cu2+
Zn2+
d'^
d^
d^
d"^
75
69
73
74pm
S
83
78
Plot of r.^^^ against number of d electrons shows an 'inverse' double-humped
curve. Radii increase at points in series when electrons enter d^ or d^ ^
orbitals - these point directly at the ligands, and interelectronic repulsion increases,
(b) The trend is the inverse of that for lattice energies (Figure 21.33 in H&S).
Lattice energy is inversely proportional to the intemucleai' separation and is therefore
inversely related to r^^^.^^. The double hump is rationalized in terms of variation in
LFSE (include a graph or table of LFSE vs d"- electrons, Figure 22.32 in H&S).
Hydration enthalpies (Figure 21.34 in H&S) behave similarly to lattice energies.
21.33
^m^Ml^^^^i^M^^^^^^^^^^i^^^sm,
Normal spinel has tetrahedral Ni^^ {d^) and 2 octahedral Mn^"^ {d^)\ inverse spinel
has tetrahedral Mn^"^, octahedral Mn^"^ and octahedral Ni^+. One octahedral Mn^'^ is
^BS
^ i
ssss
wiff™pm»«B
l»yi^»p!|ITHMMLMI>»Mll!<(IB«IW!WI^^
274
£/-Block metal chemistry: coordination complexes
common to both types of spinel and can be neglected. Compare LFSE values:
^.^%K.
spinels ABp^: see Box 13.6
and Section 21.10 in H&S
21.34
Refer to Section 8.3 in H&S
Refer to Section 21.12 in H&S
21.35
LFSE tet. Ni^-^ + oct. Mn^^ =^ -(0.8 x % x 8500) - (0.6 x 21 000) = --15 622 cm-'
LFSE oct. Ni^-^ + tet. Mn^^ := ~(1.2 x 8500) - (0.4 x % x 21 000) = -13 933 cm-'
Therefore, one predicts a normal spinel; the factor not taken into .account is the
Jahn-Teller effect for Mn^* (d^); although one predicts a normal spinel by a small
margin, the structure is, in practice, an inverse spinel.
(a) LFSEs can be estimated as in answer 21.7 - see also Table 21.3 in H&S..The
difference in LFSE on going from octahedral [Co(OH2)6]^'^ to tetrahedral [Co'Cl-;,]^is much less for Co^"^ (d'') than for Ni^* (d^). Remember that A^^^ ^ '^^9\a(b) Data are consistent with H^[Fe(CN)g] being a weak acid with respect to the 4th
acid dissociation constant; H'*" complexing of [Fe(CN)g]*" makes reduction easier.
(c) LFSE plays only a minor part. There is a loss of LFSE on reduction of Mn^+
(d% a gain on reduction of Fe^+ (d^), and a loss on reduction of Cr^"^ (d^); the
decisive factor is the large value of the 3rd ionization energy for Mn.
(a) Information for this answer comes from Section 21.3 in H&S. Points to include
in your answer:
«• relationship between x, y, z axes and positions of 6 L in octahedral [MLg]"*;
• crystal field theory assumes point charges;
»metal orbitais that point directly at ligands are d^z and d^i^^t,
• repulsions between electrons in d^z and d^-2_yi orbitais and ligand electrons
greater than between electrons in d^^, d and d orbitais and ligand
electrons;
" include a sketch of Figure 21.2 in H&S;
' energies of d^ and d^ 2 orbitais raised with respect to barycentre, and
energies ofd^^, ^^y^nd (i orbitais lowered.
(b) First, note that each complex in the question contains Fe. To detemiine the
ordering, consider the oxidation state of the Fe centre, and the field strength of the
Hgands: CN"" is a much stronger field ligand than H p ; A^^.^ is largest for combination
of strong field ligand and higher oxidation state, and smallest for weaker field
ligand and lower oxidation state. Order is:
[FeCCN)^]^- > [Fe(CN),]'*- > [FeCOH^),]^"^
(c) Tetrahedral d^ has configuration e\'^ (21.24). For an electron to have orbital
angular momentum contribution, it must be possible to transform the orbital it
occupies into an equivalent, degenerate orbital by rotation - the three t^ orbitais
can be interconverted by rotations through 90°; if all the t^ orbitais in the tetrahedral
complex are either singly or doubly occupied (i.e. fj^ or ?2^), an electron cannot be
transferred from one of the ?2 orbitais to another. In the tetrahedral d^ ion, there is
one fully and two singly-occupied ?2 orbitais and so there is an orbital contribution
to the magnetic moment. Refer to Section 21.9 in H&S for greater detail.
(21.24)
21.36
(a) The complexes in the question are all octahedral Jahn-Teller distortions are
observed for # and high-spin d'^ configurations where there is asymmetric filling
of the e, level:
Cr(n)
high-spin d^ Jahn-Teller distortion expected
[CrL 14~
J-Block metal chemistry: coordination complexes
275
[Cr(CN), 14CT(IJ)
low-spin d^ no Jahn-Teller distortion expected
[CoR]3"
Co(ni)
high-spin # no Jahn-Teller distortion expected
[Mn(ox)3]3~ Mn(III)
high-spin d^ Jahn-Teller distortion expected
(b) In [Et4N]2[NiBrJ and K^tP^Br^], complex ions are [NiBr^p- and [PdBrJ^-;
[NiBr^]2j^^(ix)
^
[PdBrJ2Pddl)
d^
Two possible geometries: tetrahedral and square planar. The splitting of iorhitals
and electronic configuration depends on the arrangement of the ligands. Splitting
diagrams and orbital occupancies for tetrahedral and square planar d^ configurations
are shown in 21.25 and 21.26, respectively. If [NiBr4]^" is paramagnetic, then it
must have a tetrahadxal structure. Since [PdBr^]^- is diamagnetic, it is square plaqar.
(c) Information for this answer is in Section 21.4 in H&S. Points to include:
• valenceorbitalsof Ni are3J,45'and4p;
• '"•
• each ligand provides one orbital (consider as outward pointing hybrid of
NH3 that contains the lone pair);
" assume 0^ symmetry for the complex;
• in O^ point group, metal s orbital has a, symmetry, p orbitals are
degenerate with t^^ symmetry, d orbitals split into two sets, e (d^2 and d^2_-2)
'•indt^^(d^,d^^,dj;
• in 0|j point group, 6 LGOs for the Lg-fragment have a, , f,,^ and e
symmetries (see Figures 5.27 and 21.12 in H&S);
• by matching symmetries, form 6 bonding MOs (a-^ , t^^ and e ) , 6
antibonding MOs (a^^*, t^/ and e^*) and 3 non-bonding MOs (tyj;
* effectively, the d orbitals of Ni split into two levels, lower energy /^gand
higherenergy e *,
(21.25)
V
(21.26)
21.37
2+
(a)
2+
H2
^^^ I S'
. Fe.
Enantiomers of complex with pyridine N donors/oc, and NH^ groups fac
2+
r-
^^
«^^
IT
-12+
H2
^
if IT
(21.27)
Enantiomers of complex with pyridine N donors mer, and NHj groups mer
(21.28)
(b) Complex contains Fe(II), d^; for octahedral complex, low-spin cfi is diamagnetie
(21.27) and high-spin is paramagnetic (21.28). At 120 K, the compound undergoes
a change from low to high-spin; specifying a single temperature rather than a range
implies that the change is abrupt rather than gradual (see Figure 21.28 in H&S).