Download Aquo complexes of simple Cu+, Ag+ and Aut ions and the acidities

Indian Journal of Chemistry
Vol. 44A, November 2005, pp. 2202-2207
Aquo complexes of simple Cu+, Ag+ and Aut ions and the acidities of
metal aquo ions. A heat of hydration analysis and PM3 calculations
lnan Prakash Naskar & Dipankar Datta*
Department of Inorganic Che mi stry, Indian Association for the Cultivation of Science, Calcutta 700 032, India
Emai l: [email protected]
Received 5 Janu ary 2005; revised 14 September 2005
It is shown that the heats of hydration (l!..Jfl) of some 37 metal ions (ex.c ludin g Cu+, Ag+ and Au+) with charge Z on
them varying from + I to +4 can be reproduced with an average erro r of 3.8 (± 2.7) % by the fo llowing eq uati on :
Application of thi s equation to th e l!..Jfl values of Cu+, Ag+ and Au+ reveals that while no aquo complex is possible
for simple Au+ ion in water, simple Cu+ ion can be 2 or 4 coordinated and Ag+ io n 2 coordinated in water. This indicates
that the appearance of the factor of 53 pm in the above equation is a consequence of the hydration structure around a metal
ion. Further, the experimenta l pKa va lues for some 2 1 metal aquo ions are fO llnd to correl ate linearly (corre lation coefficien t
= 0.975) with the gas phase enthalpy changes l!..Jfl for the reaction [M(H 2 0)nf+ + m H 20 ~ [M(H 2 0)n+m.p.I (OH)](Z. I)+ +
p H 20 + H+ calculated at the PM3 level. In exceptional cases, so me metal ions (e.g. Hg 2+) undergo expansion of the
coordination spheres upon de protonation and some metal ions (e.g. TI 3+) lose water molecule(s) with deproto nation.
For quite some time we have been interested in the
theoretical and experimental aspects of Pearson's
Hard Soft Acid Base (HSAB) principle i •2. One of the
special points of interest has been the chemical
bond(s) between a "hard" and a "soft" species.
Though hard-soft interactions are not particularly
favoured in terms of the HSAB principle, the
principle does not preclude the possibility of the
existence of a bond between them altogether. We
have provided examples (in addition to several other
examples by other workers) of this aspect by
synthesizing first, a few examples of copper (I)
complexes containing a discrete bond between "soft"
Cu+ and "hard" H20 .2 In this connection we have
been interested in the interaction of water with two
additional soft iO metal ions, Ag+ and Au+. In order
to gain some insights into the nature of the aquo
complexes of simple Cu+, Ag+ and Au+ ions, we
analyse herein the heats of hydration of these three
metal ions.
Theory
Aquo complexes of simple metal ions undergo loss
of a proton in water to form hydroxo ones (Eq. 1)
where Z is the charge on the metal ion and n the
number of water molecules bound to the simple metal
ion in its hydrated form.
Consequently aqueous solutions of many si mpl e
metal salts (e.g. perchlorates) are acidic of measurable
strengths . The pKa values are known experimentally
for a number of metal ions3aA .5 . However, the acid
dissociation behaviour of the metal aquo ions is still
not very well understood. When the pKa values are
plotted agai nst Z21r (r is the ionic radius), it is found
that there are many significant deviants, e.g., Hg2+,
Te+ etc 3a . There have been several attempts recently
to explain the variation of the pK" values at molecular
level with little success 6.7. The second objective of our
work is to provide a rationale for the acid dissociation
behaviour of the metal aquo ions.
Results and Discussion
From various X-ray techniques, e.g., extended Xray absorption fine-structure spectroscopy (EXAFS),
large-angle X-ray scattering (LAXS), etc. , it is now
recognised that there exists a discrete hydration
structure around a metal ion in water8. However,
NASKAR & DATIA : HEAT OF HYDRATION AND ACIDITIES OF METAL AQUO IONS
hydration is by no means a static phenomenon. It is a
dynamic process, where bulk water molecules are
constantly in exchange with those coordinated to the
metal ions, with a "time of residence" depending on Z
and r of a metal ion. There has been some controversy
in the number (n) of water molecules in the first
coordination sphere of a metal ion, partly because this
n is somewhat dependent on the concentration of the
metal salt. For example, from large angle neutron
diffraction coupled with molecular dynamics calcula9
tions , Pasquarello et al. have recently concluded that
2
hydrated Cu + ion is five coordinated, in contradiction
to the general view of a Jahn-Teller distorted octalo
hedral configuration. Later, Persson and co-workers
have reaffirmed by means of EXAFS and LAXS
techniques that for Cu 2+ ion in water, n is six. We
have collected the most accepted values of n for some
37 metal ions (Cu+, Ag+ and Au+ not included) with Z
.
f rom + 1 to +4 f rom recent I'Iterature8' 10· 12
varymg
(Table I), It may be noted that no monoatomic ion
with Z> +4 can exist as a hydrated ion in water.
It was surprising to find that despite the importance
of the subject, so far the theoretical reproduction of
the heats of hydration (/'t.J-f) of the metal ions has not
been studied properly. It was clear from the beginning
that Born equation 13 [Eq. (2)], which is equally
applicable to anions and cations in a solvent of
relative permittivity, c, works satisfactorily for the
anions but fails miserably in cases of cations.
W 10
12
O
•
N(Ze)~
81t£0
r
(.!.-1)
c
... (2)
In Eq. (2), N is Avogadro's number, e charge of an
electron and co the permittivity of vacuum; the factor
12
of 10 is introduced so that r is expressed in pm. The
value of c of water at 298.15K is 78.54 (ref. 14). In
order to improve the applicability of Born equation to
cations, earlier Stokes has considered the variation of
c of water in the vicinity of cations 15. [n his approach,
effective c values of water were worked out in a
somewhat arbitrary manner for cations with various Z
values. No cations with Z > +3 or transition metal
ions were considered in his studies. Later Rashin and
l6
Honig advocated the use of "covalent radius" of a
cation as the r value in Eq. (2). However, their
approach gave rise to errors> I 0% for the transition
metal ions, While working with Eq. (2) for the alkali
metal ions in water, Latimer and co-workers l7 were
the first to realise that cations apparently undergo a
sort of uniform expansion in their ionic radius in
2203
solution. They could reproduce the experimental heats
of hydration (/'t.J-fexp) of the alkali metal ions quite
well by adding a factor (c) of 85 pm to their Pauling
ionic radii. Later, Phillips and Williams (see ref. 18)
have tried to correlate Z2/(r + 85) with I"1WcxP for
some 29 metal ions with Z varying from +1 to +3.
While the overall correlation is reasonably linear, the
bivalent ions of the first row transition metals and
Zn 2+ seem to lie on a separate line branching off the
main one. Further, in some cases like TI 3+, the
ls
observed deviations are significant .
We now re-examine the applicability of Eq. (2) to
metal ions. In deriving Eq. (2), the solvent is treated
as a dielectric continuum ignoring possible solvation
structures around ions. In recognition of the now
known hydration structures of the metal ions in water,
we decided to use the crystal ionic radii designated by
Shannon l9 , which are coordination number specific.
In the cases of the transition metal ions, we have used
the radii in their high spin configurations since their
aquo complexes are all high spin . Thus, our choice of
the r values allows us to incorporate some effects of
ligand fields indirectly in Born equation. Since
Shannon's crystal ionic radii are numerically different
from Pauling's, the factor c is expected to be different
from 85 pm. In order to evaluate c, we fit the !':..Wexp
dataSb via Eq . (3) for every metal ion of Table I. The
average of the c values so obtained (Table I) is found
to be 53 pm. The standard deviation (0') is only 7 pm
showing that c is fairly a constant. With c = 53 pm in
Eo . (3), we then calculated the !':..W value for a metal
lon, I.e.
12
10 . N(Ze) 2
!':..H o - - - - ' - - 811:c[) (r+c)
!':..H~al c .
(I )
-E- I
l--I
1012. N(Ze)2 / 1
811:co (r+53)
c
)
... (3)
... (4)
The average error in our I"1Jflcalc (Table I) is found
to be 3.8 % with 0' of 2.7 . The correspondence
between I"1Wcxp and our l"1fI)calc is shown in Fig. I.
There are no offshoots like deviations. This is very
significant when compared with the observations of
Phillips and Williams (see ref. L~).
We now analyse the heats of hydration for Cu+,
Ag+ and Au+. According to statistical theories2o , all
the data in a given set lie within ± 30' of the average
value. Thus, since the value of 0' in the average in our
calculated !':..W's is 2 .7%, the maximum error
INDIAN 1 C HEM. SEC A. NOVEMBER 2005
2204
Table I- Heats of hydration and other data for so me metal ions (exr;l udin g Cu· , Ag+ and Au+) "
Metal
Ion
-111-f'«p
(~J mor l )
n
r
(pm)
cb
(pm)
-l1l-f'calc
(kJ mor l )
Erro{
(0/0 )
Li +
Na +
K+
Rb+
Cs+
Mg2+
Ca 2+
Sr 2+
Ba 2+
V2>
Cr2+
Mn2+
Fe 2+
Co 2+
Ni 2+
Cu 2+
Zn 2+
Pd 2+
Ag2+
Cd 2+
Pb 2+
Pt 2+
AI' +
Sc 3+
T i'+
V 3+
Cr3+
Mn 3•
Fe'+
Co' +
Ga 3+
In 3+
TI'+
La 3+
Ce 3+
Sn 4 +
Ce4 +
523
418.4
330.5
3 13.8
284.5
1941.4
1598.3
1464.4
1322. 1
1895.3
1924.6
186 1.9
1958. 1
2079.4
2 12 1.3
2 121.3
2058.5
2 112.9
171 9.6
1828.4
1502. 1
2 188.2
4694.4
3962.2
4297
4405 .8
4623.3
4594
4485.2
4711.2
4702.8
4163.1
4117 . '
33 17.9
3502
7644.2
6451.7
4
4
4
6
6
6d
8c
8
9d
6
6d
d
6
6d
6d
6d
h
6
6
4
4
6
6d
4
6
6
6
6
6
6
6d
6
6
6
6
9d
9d
6d
9d
73
114
151
166
18 1
86
126
140
16 1f
93
94 g
97 g
92 g
88.5 g
83
87
88
78
93
109
133
74
67.5
89
81
78
75.5
78.5 g
78.5 g
75 g
76
94
164
135.6
133.6
83
1J6 f
58
50
56
53
60
55
46
47
46
52
48
50
48
43
46
42
45
52
66
41
50
51
64
67
63
59
58
56
59
56
55
54
47
50
43
61
54
544.0
413.0
336.0
313.8
293.3
1973.6
1532.6
1421.3
1282.0
1879.6
1866.5
1828.8
1892.0
1938.9
20 17. 1
1959.8
1945.6
2094.1
1879.0
1693.3
1474.9
2 160.2
5122.5
4362.2
4606.6
4712.0
4803.7
4694.0
4694.0
4822.5
4784.8
4199.1
3969.4
3272.7
3307.9
8068 .8
6493. 1
4.0
1.2
1.7
0.0
3.1
1.6
4.1
2.9
3.0
0.9
3.0
1.8
3.4
6.8
4.9
7.6
5.5
0.9
9.3
7.4
1.8
1.3
9.1
10. 1
7.2
6.9
3.9
2.2
4.6
2.4
1.7
0.9
3.6
1.4
5.5
5.5
0.6
Meanings of the symbols are same as in the tex t. Sources of data: n, ref. 11 unl ess otherwise specified; I1Ffcxp , ref. 5b; r, ref. 19.
A vcrage value: 53 (± 7) pm.
e Average value: 3.8 (± 2.7).
d From ref. 8.
C From ref. 12.
f Average of radii for coordination numbers 8 and 10.
g High spin value.
h From ref. 10.
a
b
permitted in l1I-fcalc is 3.8+3x 2.7=11.9%. For ready
reckoning, we mention that the maximum error
encountered by us in Table 1 is only to. I % (for Sc3+),
which is less than the maximum error permitted. In
Table 2, we find for Cu+ that the coordination
numbers 2 and 4 are possible as the errors in these
two cases are <1 1.9 % . However, the coordination
number 6 is not possible as the error in thi s case is
>11.9 %. Consequently, Cu+ can exist in water as
Cu(H 20h + or Cu(H20)/. Also, no copper(l) complex
with coordination number of six is known in the
literature 1I. Similarly, for Ag+, we fi nd from Table 2
that onl y Ag(H 20 )z + can exist in water as the errors in
M-tcalc . for n = 4 and 6 exceed 11.9%. There has been
some controversy in the results of the EXAFS studies
on Ag+. Some workers have concluded that only
NASKAR & DATIA: HEAT OF HYDRATION AND ACIDITIES OF METAL AQUO IONS
Ag(H 20h+ exists in solution while others feel that
simple Ag+ ion in water is four coordinate with two
mol ecules of water held firmly and two more loosell.
In the case of Au+, Shannon has given its ionic radius
(151 pm) only for n = 6 which leads to an error of
47.8 % in l1!fcalc. Our calculations show that for Au+,
l
an !1Ffcxp of 644.3 kJ mor ± 11.9% yields an r value
in the range 95-121 pm and c = O. (With c = 53 pm,
the same range of l1!fexp yields an r value in the range
of 42-68 pm, which is unrealistically small for Au+).
Shannon's crystal ionic radius for a metal ion
decreases with the decrease in n. For examples, see
the data for Cu+ and Ag+ in Table 2. When we
compare the radius range of95-121 pm with Pauling
ionic radius of 137 pm for Au +, we realise that n is 0
for Au+ in water, i.e., no hydrated species is possible
for simple Au+ ion . Such a situation has been
21
suspected earlier by other workers als0 . No solution
X-ray studies are reported for Cu+ and Au+ since they
disproportionate in water [Eqs (5) and (6)] with large
disproportionation constants (K)11.1 4. It may be noted
in this context that Ag+ does not disproportionate in
water. This is in keeping with the order of Pearson's
hardness 22 for these three ions: Ag+ > Cu+ > Au+.
K= 10
6
== Cu + Cu 2+
K = 10
3 Au+ == 2 Au + Au 3+
10000
2205
2 Cu+
. . . (5)
10
8000
6000
0
E
-,
0
.><
o
I
~ 4000
<;1
2000
o
2000
4000
6000
8000
10000
-6HO.,p I kJ mol"
Fig. I-Correspondence between 6J·f e,p and 6.Jfealc for some 37
metal ions (Cu+, Ag+ and Au+ not included) with charge on them
varying from + I to +4. For data, see Table I. The line is drawn
with a slope of unity to emphasize the fit.
Table 2-Heats of hydrati on and other data for
Cu+, Ag+ and Au+"
Metal
ion
-6.Jfe ,p
n
(kJ mor l )
Cu+
581.6
Ao+
0
485.3
Au+
644.3
2
4
6
2
4
6
6
-6.Jfcalc
(kJ mor l )
% error
(pm)
60
74
91
81
114
129
151
607.1
540.2
476.1
511.7
410.9
377.0
336.0
4.4 b
7. 1b
18. l c
5.5 h
15.4c
22.4 c
47.8 c
r
a Meanings of the sy mbols are same as in Table I. Sources of
data: 6.JIle,p, ref. 5b; r, ref. 19.
b The va lue of n is compatible with the value of t..If ew See text.
c The value of n is not compatible with the value of 6.Jfexp. See
tex t.
... (6)
We now come to our second objective, i.e., to
rationalise the acid dissociation behaviour of the
metal aquo ions. We have attempted to calculate the
!1Ff values for reaction (l) in the gas phase for so me
21 metal ions with Z varying from 1 to 4 by PM3
23
method. This method, as developed by Stewart ,
belongs to the family of semi-empirical MO
techniques of the MNDO-AM 1 series. The parameters
set in PM3 are much better optimised within the
basic framework of modified neglect of diatomjc
overlap and the AMI theory. The parameter optimjsation is carried out by a modified method involving
the derivatives of the computed properties with
respect to the adjustable parameters. Better optimjsation and much larger data set make these parameters
much more reliable as compared to the original
MNDO-AMI parameters. All computations were
done by using the HyperChem program (version 7.5).
We could not carry out PM3 calculations on all the
metal aquo ions for which the pKa values are available
due to lack of necessary parameters. Attempts are sti ll
on to optirruse the PM3 parameters for many metal
24
ions . The metal ions for which PM3 calculations
have been done here are given in Table 3. The value
4
of n for Zr + in water, for which no X-ray data are
available, has been set equal to 8 (Table 3) since 8 is
the most common coordination number for Zr4+
(ref. 11). For Sn 2+, PM3 parameters are available. Still
it is not included in our study because it seems to
behave in a very peculiar manner in water8 . In our
calculations, the aquo ions of all the transition metals
listed in Table 3 and their monohydroxo species were
treated as high spin complexes 3b .
IND IAN.J CHEM , SEC A, NOVEMB ER 2005
2206
The calcu lated gas phase !1H) values of reaction ( I)
for some 19 meta l ions are plotted against their pK"
values in Fig. 2. The plot is somewhat scattered with
L J,
'+ Be2+, Mn 2+ and Hg2+ deviating conspicuously .
This calcu lation could not be done for Cd 2+ and Te+
since according to our PM3 calcu lations the con'esponding monohydroxo species are not stable in the
gas phase. From Fig. 2, it is apparent that the aqueous
solution of a simple metal salt becomes more acidic as
the gas phase thermochemical feasibility of the loss of
a proton from its aquo compl ex increases.
In o rder to explain the deviations, we now cons ider
a general deprotonation reaction of the type (7) where
we assume that deprotonation is accompanied with
aquation or release of water molecule(s). It may be
noted that when m = p = 0, the reaction (7) becomes
reaction (I) on ly. The gas phase M·f values calculated at the PM3 level for some 21 meta l ions with
various optimised values of m and p are given in
Table 3. As seen from Table 3, for most of the metal
ions, m = p = 0 . On ly in some exceptional cases, m or
p is non-zero. A non-zero value of m indicates that the
concerned metal ion undergoes further aquation with
deprotonation wh ile a non-zero value of p means loss
of water molecule(s) from the metal aquo ion with
deprotonation. When the M-f values for reaction (7 )
are plotted against the pK" values, a ve ry satisfactory
linear correlation is obtained (Fi g. 3) with Mn 2+ being
the only signi ficant deviant.
15
Table 3-The acid constants (PK,,) and oth er re levant data for
the deproto nation reacti o n of some metal aquo ions"
OLI '
O\1g 2•
Mn:o
Metal ion
pK"
n
m
p
-I">.H'
Fc2~;O
10
(kJ mor l )
CO:!i O
O Zo:::'
Cu2i O
Li +
13.8
Be 2+
5.5"
Mg2+
Ca 2+
M n2
Fe 2+
C0 2+
Ni 2+
C u2+
Zn 2+
Cd 2+
11.4
12.8
II b
9.5
b
9
8.0
9 .0
10.1
Hg2+
3.4
Pb 2+
b
0
Ti 3+
Cr3 +
Fe J +
C0 3+
AI J +
In 3 +
T1 3+
Zr4 +
IO b
8
2.2d
4 .0
2.2
I"
5.0
d
4.4
0.6
-0.3
4
4
4
4
6
8
6
6
6
6
6
6
6
6
2
2
6
6
6
6
6
6
6
6
6
6
8
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
I
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
256.5
303 .3
867 .3
1112.9
726.8
623.0
941.4
869.4
878.2
839.3
829. 3
787.8
c
723 .0
889. 1
1383.6
732.2
786.6
1370.3
1345.6
1444.3
1394.5
1197.0
1182.0
c
1474.0
1613.4
" Meanings of the symbols used are same as in the text. The
pK" va lues are taken from ref. 3a unless otherwise specified.
The va lue of n for Hg2+ is taken from ref. 3a and for other
metal ion s are from ref. I I.
b From ref. 4.
C According to o ur PM 3 calculations, [M(H 0)n.,(OH)](z,,)+ is
2
not stabl e in th e gas phase.
d Fro m ref. Sa.
OPb :! '
-:.:."
Q
Olk :! <
5
o
i
-1600
-1200
-800
-400
l>1I"/ kJ mol "
Fig. 2-Variation of pK" w ith M-f' calculated for the reaction (I )
[o r for reaction (7) with 111 =P = 0]. For data, see Ta ble 3.
15
OL"
C:. 21 0
/
M,"o
Mn:?'.
Nil;
10
c~~:g
/
Cd :?'
a Zul'
., OO Pb~ '
Cu-'
A I,I +
5
Cr.lO
Be :?'
OI " Jt
1I ~21 0
FeJ O Q T. J •
o
,
-1600
-1200
-800
-400
l>H'/ kJ mol "
rig. 3- Variation o f pK" with M-f' calcu lated fo r the reacti o n (7)
with the o ptimi sed values of 111 and p . For data. see Table 3.
Mn(H zO)62+ marked by a fi lled circle is exc luded from the least
squares fit. Correlation coeffi cient = 0 .975 .
NASKAR & DATTA : HEAT OF HYDRA nON AND ACIDITIES OF METAL AQUO IONS
[M(H20),i+ + m H 2 0--7 [M(H 2 0)n+lI1_p_ I(OH)] (Z-ll+
+ p H20 + H+ . . . (7)
Conclusions
We have shown that Eq . (4) can reproduce the
experimental heats of hydration of a number of metal
ions very well when appropriate Shannon's crystal
ionic radii are used . Analysis of the heats of hydrati on
for Cu+, Ag+ and Au+ by thi s equation reveals that
while no aquo complex is possible for simple Au+ ion
in water, simple Cu+ ion can be 2 or 4 coordinated and
Ag+ ion 2 coordinated in water. Since c is 0 for Au+,
its solvation in water can be adequately described in
the true spirit of Born equation (Eq. (2). This finding
for Au+ indicates that appearance of c in Eq. (4) is a
consequence of the hydration structure around a metal
ion . Here we have also examined the acid di ssoc iation
behaviour of the aquo ions of many metal ions by
means of PM3 calculations on reaction (7) . From our
study , it is evident that the metal ions like Hg2+, Be2+
etc., which are found to deviate in Fig. 2, actually
undergo a change in the coordination sphere with
deprotonation . In the case of Lt, Be2+, Hg2+ and Pb 2+,
the coordination sphere around the metal ion expands
with deprotonation. For Cd 2+ and TI 3+, loss of water
molecule(s) occurs with deprotonation. The ac id
di ssociation behaviour of the aquo ion of Mn2+ in
relation with other metal aquo ions is not understood
at present.
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I
2
Hati S & Datta D, Proc Indian Acad Sci. Chem Sci. 108
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2207
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7
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