STUDIES
IN THE
HYDROLYSIS
01~ M E T A L
IONS
P~rt I. Cepper
BY S. MAHAPATRA AND R. S. SUBRAHMANYA
(Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 12, lnd/a)
Received October 13, 1966
(Communicated by Prof. M. R. A. Rao, t,,A.SC.)
ABSTRACT
The hydrolysis of cupric ion has been studied at various ionic
strengths (0"01, 0.05, 0.1 and 0- 5 M). The results are analyzed employing 'core-F links' theory, log-log plot, normalization plot, and extrapolation method for obtaining the pure mononuclear curve. The stability
eonstants of Cu~(OH)~++, Cus(OH)4++, Cu(OH) + and Cu (OH)a have
been reported.
INTRODUCTION
THE hydrolysŸ of cupric ion has be~n studied by Pederson, t Biedermann 2
and Perrin) Pederson has explained bis results assuming the formation of
CuOH +, Cuz.OH3+ and Cu~ (OH)2 ~+. Biederlnann has obtained evidence
[i0 mM < (Cu)t < i00 mM] Ÿ the formation of only Cu~ (OH)a-H- using
Sillen's 'core + links' method. Assuming the existence of Cu2 (OH)~.++
at low ¡ values Perrin obtained constant values for/~2~. Further, he showed
that Cua (OH)4 ~+ is present at higher ¡ values. It is therefore elear that there
is still obscurity about the nature of complexes. In the present paper ah
attempt is made to clear up these obscurities by the analysis of ¡
curves
[(Cu)t < lO mM] by independent mathematical techniques. Since evidence
is obtained for the formation of mononuclear species at low metal concentrations, ah extrapolation method has been used to obtain theoretical mononuclear curve.
EXPERIMENTAL
All the chemicals used were either extra pure or analar in quality.
Correction is applied for the small quanity of free acid, present in cupric
salt solution employing Brosett's method. 4 The pH of the various test solutions is determined with Beckman G pH meter employing the glass electrode,
standardized with hydrochloric acid or suitable buffers containing suPiicient
potassium nitrate to keep the ionic strength same as in the test solution.
283
284
S. MAHAPATRAAND R. S. SUBRAHMANYA
Cupric salt solution (100 c.c.) containing known amount of nitric acid
(pH = 3) and sufficient potassium nitrate to keep the ionic strength constant
(0.01, 0.05, 0.10 and 0.50 M) is titrated with carbonate free sodium hydroxide. After each addition of sodium hydroxide an equal volume of twice
the strength of the initial test solution is added to keep the total concentration
of cupric copper and ionic strength constant throughout the titration.
Equilibrium was attained immediately. However, the pH was read two
minutes after each addition. The titration is continued until a faint precipitate appears. Experiments have been conducted with different concentrations of cupric copper. The solution is deaerated with nitrogen anda magnetic stirrer is used to stir the solution. During pH measurements the stirring
is stopped.
The value of ¡ and pOH is calculated using the following relationS:
h--
B -- (Ca -- H+) ," pOH = pKw -- pH.
CM
The value ofpKw in 0.01, 0.05, 0.10 and 0.50 M potassium nitrate solutions
determined potentiometrically are 13.72, 13.69, 13.67 and 13.62 respectively.
NOTATIONS
B
Ca
¡
Concentration of sodium hydroxide added.
Total free acid of the initial solution.
Average number of hydroxylion per metal ion.
Total metal (copper) concentration.
Metal (copper) ion.
Cu
M
[OH-], [H+], [M] Concentrations of free hydroxyl, hydrogen and metal ions.
Stability constants of MOH, M (OH)~ and Mm (OH)/.
fl~, 1, fll, 2, fl,~i
Equilibrium constants of the hydrolytic reactions forming
MOH, (M) OH~ and Mm (OH)i.
Ionic product of water.
K1/)
k.k~,k~, . . . , k . are the constants for the hydrolytic reaction for the complexes containing 1, 2, 3... nth links in Cu ((OH)2Cu)r~++.
kl, 1, kl, 2, km~
RESULTS
The ¡
curves at various metal concentrations in solutions of ionic
strength 0.5, 0.1, 0.05 and 0.01 M a r e given in Figs. 1-4. The maximum
Studies in the HydroIysis of Metal Ions--I
285
value of ¡ reached diminishes both with an increase in metal concentration
at constant ionic strength and ah increase in ionic strength at constant metal
concentraª
4.91
~
I
H
I
5-17
5-67 P
91
HYDROLV~.I5 OF CUPRiC ION'~.~OH CURVES.
r
91
5[6 ~ t
O~
4"62
5.12
5.62
i
"'
~H
6"12
....
~
6"62
i
- HYDROLYSiS OF CUPRIC ION, ¡
0.15
CUPRIC ION CONC.
I IO.O mM
2 - 6"O mM
3 - 4"0 mM
4 - 2"O mM
O.iO
5 - I.O
6 - 0"5 mM
¡
7 - 0 . 2 5 mM
8 - THEORETICAL
,o,o,~c~~,,
CURVEs.
f,J.:O'5M
I
2
5-
0'5 mM
6 - O'25 m M
7 - THEORETICAL
MONONUCLEAR
777
//!
[
,3: ~-oo ~~
1
/
/~
6
mM
-
-
,.o.
CUPRIC ION CONC.
IO.O mM
6.0 mM
3
]
4
~i//
o.o:..~~/../2/~,
, ~
9"0
p.5
8-0
POH
7.5
7"0
95
9.0
91
/
s!69 ~H 91
91
D~
CUPPlC ION CONC
IO-OOmM
6.OO mM
4 . 0 0 mM
2.OOmM
I.OO mM
- 0,50 mM
- O-25 mM
8 - THEORETICAL
MONONUCLEAR
I
2
:}
4
5
67
I
1,0F
5,72
=-
,
i,,
I:>H
6.22
6';
i
~/
J- ¡ ~o~ CURVES.
U=o.o,.
s
0.81-
-
7.0
HYDROL~IS 01Ÿ CUPRiC ION
HYDROLYSIS OF CUPRIC ION
¡
CURVI.S. p = O , O S M
C,-z
Th5
FIo. 2
Fm. 1
s'.19
1>OH
2-
4
~4
CUPRIC iON CONC.
1.00
mM
,.o5o~~
h
O'
IlJ
4 * 0'25 mM
5-THEORETICAL
kAONON'dCLF.AR
¡
J
J
/
l
9
/
i
,
pOH7.5
7-0
O'4
D.;
32
;
2/
,
,
,
, ,
0"2
~'7
0-5
8-0
7. 5
bOH
Fin. 3
7-0
8-5
8.0
Fxo. 4
]
286
S. MAHAPATRA AND R. S. SUBRAHMANYA
DISCUSSION
1. Analysis o f ¡
Method 6
Curves for Polynuclear Complex Formation by Sillen's
The spaeing of the 11e~ ¡
curves indicates that the derivative
(~ log CM/b 1Og [H+])s is about 2 and the plots of
¡
(i) ~ vs. log {CM [OH-] ~} or
¡
CM
(ii) ~ vs. log [ii+] ~
[called y (x) curves] coincide indicating that the' core + links' complexes
have the formula Cu (Cu (OH)~)n++. A typical y (x) curve is given in Fig. 5.
The curve with 0.25 mM copper does not coincide indicating considerable
amount of mononuclear species. Direct analysis of plot (i) gives the value
of the equilibrium constant for the formation of the complex while that of
plot (ii) gives the value for the hydrolytic reaction, the two constants being
related by kmi = flmiKw ~. The function g (v) = f ( u ) = 27 knun and u are
determined from the arca of the y (x) curves using the following equations
log(1 + g) = Ÿ ydx + log (1-- y) + y log e
logu=x--yloge--
f ydx.
The plots of the log g vs. log u are straight lines with the slope near 1.2
at aU ionic strengths indicating that the most predominant complex contains
one link in the complex. The plots of gu--a vs. u (F,~g. 6) are straight lines
(lowest points very sensitive to small errors in y'have been disregardedT),
the intercept and the slope giving the values of k x and k~ (Table I).
2. Analysis of f~-pOH Curves by Log-log Plots 8, ~
At low values of ¡ where one can expeet only CuOH + and the lowest
polynuclear species Cuq (OH)p (~q-p)+, if CuOH + can be neglected as compared to Cuq (OH)p(~q-l~)+, one can write
¡ = P [Cu~ (o~p(',q-~) +]
(Cu)t
expressing Cuq (OH)p(aq-~)+ in terms of flqp, etc., noting that Cu ++ ~ (Cu)t,
and taking logarithms one gets
log ¡ = logp + log flqp + (q -- 1) log (Cu)t -]- p log [OH-].
Studies in the Hydrolysis of Metal lons--I
"
" v L~-II
HYDROLY51S OF CUPRIC ION ~'1
VS LOG C M + t.pH PLOT.
t
/J "O'O5M. t , 2 " O
~t
HYDROLYSIS OF CUPRtC ION
DIRECT ANALYSIS
INTERCEPT - k I
CONC. OF CUPRIC ION
) 0 mM
6 rnM
O&~
B"
Xe9
0,3
287
4
f~M
2 mM
, mM
o.SmM
f'j
J7
=91
t- 0"0| M
;I- O'O5 M
3 - O,;O M
....
,
r
,
,
,
,
,
# )) ~i
)
CM 9 tbH
2
4
u
Flo. $
XO
Fin. 6
LO~ r
LOG [OH']
9 THEORETICALPOtNTS
X IO91
I'~DROLYSI$ OF CUPRIC ION
INTERCEPT - ~l!
SLOPE- ,e 12
~
,-
¡
o,
9
o.~
./
3 o O'IOM
,
~ /
Y
-3.8
-4-1 ~
r
/
,
,
,
,
Ir
,
'" '
= 2i
Fio. 7
J
0
~
' ~
' 31X i~~7'
NORMALIZATKA~ I~.OT FOR~ CUIO[q)*
/'.NO CU(OH)-~ CC',MP,(NFn
l~o. 8
It follows from the abov• equation that the plot of log ¡ vs. log tOH-]
should be a straight lino, the slope giving the, valu• of p. The valur of q
is obtained from the differencc in the valur of the intercr
The averago
values of p and q aro 2 -4-0.1 indicating the most prr
spccics to
be Cuz (OH)~++ in agreement with Sillen's method. Tho valuo of log fls=
is obtaincd from the valuo of tho intercept (Table I),
288
S. MAHAPATRA AND R. S. SUBRAHMANYA
TABLE I
Stability constants of the mono and polynuclear hydrolytic
products of cupric copper
Method
Sp~ies
Log stability constant at of v a ¡
ionic
strengths(correct to with[a 4" 0-04 except Thermothose from Normalization plots where the), rdyaamic
are correct to 4- 0.2)
0.50 M
Cu~ ( 0 H h ++
Sillen plot
Cus (0H)~ ++
do.
.+
tu2 (OH)2 ++
Log-log plot
Cu~ (OH)~ ++
Norma~hation procedure
(under all conditions)
Extrapolation method
Cu OH +
ca (OHh
16.41
16.38
Normalization procedure
(CuOH + only)
Normalization procedur e
(CuOH+ + Cu(OH)~)
do.
Cu (OH) +
Cu (OH)z
Nonaali~tion l~'or
(only Cu(OH)2)
Cu (OH)2
0.01 M
t~=0
16.90
17.05
1'/.16
33.53
33.66
34.11
34.36
16.78
16.96
17.19
17.38
16-9
.o
5.38
5.69
6.11
6.43
12.85
13.09
13.1'/
13.30
5.7
I.
*.
.o
oQ
0.05 M
16.78
.e
do.
Ca OH +
0.I0 M
6.3 }
o+
12.6
13.1
ii
+*
3. Analysis of Data for Mononuclear Complexes
(i) Extrapolation procedure.--In the present work it was not possible
to obtain sufficient number of points for the mononuclear curve by extrapolating (at constant pOH) the values of ¡ at various Cm values to CM--+0.
In a system containing CuOH+, Cu(OH)2, Cue (OH)s ++, the following
equations for CM~ ¡ CM, [Cu++] and ¡ can be written.
CM = [Cu++] + [CuOH+] + [Cu (OH)s] + 2 [Cu~ (OH)e ~+]
¡
= [CuOH+] q- 2 [(Cu (OH)s] q- 2 [Cue (OH), ~-]
and
CM (1 -- ¡
[Cu++] = 1 -- 31, e [OH-] e
C u (1 -- ¡
[OH_]e
flll [OH-] + 2flx, ~ [ O H - ] ~ + 2fle, z i _ fil, ~ ~O--H-~a
h=
(t [OH-p
- ~) [oH_p+ ~1.1 [OH-] +/~1,~ [OH-] ~ + 2~~, ~ ~ _c .~~,e
289
Studies in the Hydrolysis of Metal Ions--I
It is therefore obvious that at constant ¡ the hydroxyl ion concentration
is a function of C,, only. H e n ~ the plot of the hydroxyl ion concentration
vs. CM when extrapolated to zero value of CM would give the value of the
hydroxyl ion concentration for the mononuclear cuve for the ¡ chosen. The
above treatment would be valid even when more than one polynuclear eomplex
is present but the expression for the metal ion would be a higher degree equation. Hence the hydroxyl ion concentration is a function of Ctt at constant
¡ In Figs. 1-4, the theoretical mononuclear curves obtained as described
above are given. The plots of ¡ 2 4 1
[OH-]) vs. ( ( 2 - - ¡ [OH-])/
(1 -- ¡ are straight lines (Fig. 7) the intercept giving the value of flz, z and
the slope giving the value of Ex, ~ (Table I).
(ii) Application of the normalization proeedurel~
plots of log Ca
vs. (log Cu + tpH)¡ have a slight curvature (Fig. 8) indicating the formation
of mononuclear complexes. Theoretical plots have been made assuming
the presence of (i) CuOH +, (ii) CuOH + + Cu (OH)2 and l ----=100 and (i¡
Cu (OH)v Good fits have been obtained in all cases obviously due to the
small amount of the mononuclear species present in the solution. Since
the formation of CuOH + and Cu (OH)2 is indicated in the analysis of the
theoretical mononuclear curve only the equations corresponding to this
eondition are given below.
C t a = k [ 3 1 , t "-~C~a = v a -~
log(CMa 9 ) = l o g v + l o g
(
1 +a
(
+
la ~ + l _vv
1 + a + la 2 + 1 ~
=X
Y = log C,,., = X -- 2 log a
where
a=~l,l[OH-]
and
l=~~,~St0~L
Also
log Cu = log C~ + logk -- 21og ~z,x
log (Caa 2) = log C M + 2 lo 8 [OH-] + log k.
v
+ (1
+
ov)")
v
(1--
)
290
S. MAHAPATRAAND R. S. SUBRAHMANYA
The values of a at various values of ¡ and v are calculated from the equa-
tion
1(2-¡
{yR__¡ [
"(1--¡
+a--
2o
"
1 +1--
,, + 0_-~~~)~]
}
0 - ,,)' (1 -W) = 0.
Theoretical plots (Y vs. X) can now be made for each value of 8 (0.05,
0.1, 0.2 and 0.4) giving suitable values of v, assuming different values for
the stability constant ratios (1 =- 0.1, 1, 10 and 100). In the position ofgood
fit
Y - - y = log k - - 2 l o g flx, 1
X - - x = log k -----log fl~, 3.
The normalization plot (l = 100) is given in Fig. 8 and the stability constants
are given in Table I.
ACKNOWLEDGEMENT
The authors wish to thank Professor M. R. A. Rao for helpful discussions.
REFERENCES
..
Kgl. danske Vldenxkab. $elskab, mat.-fys. Medd., 1943, 20, 7.
2. Biedermann, C.
..
Arklv geml, 1953, 5, 441.
3. Perrin, D . D .
..
4. Brosett, C.
..
5. Ahrland, S.
..
6. Sillen, L.G.
..
J. Chem. Sor 1960, 3189.
Acta C¡
Stand., 1952, 6, 910.
IbId., 1949, 3, 374.
Ibid., 1954, $, 299, 318.
Ibid., 1956, 10, 1327.
1. Pederson, K.J.
7. Biedermann, G., Kilpatrick,
M., Pokras, L. and
Sillen, L. G.
8. Jensen, B.S.
..
9. Rossotti, F. J. C. and
lbid., 1961, 15, 487.
Ibtd., 1955, 9, 1177.
Rossotti, H. S.
10. Biedermann, G. and Sillen,
L.G.
Ibid., 1956, 10, 101L