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[C
n
COO
í
]
eq
= [C
n
COO
í
]
i
- 2[Pb
2+
]
eq
(4)
where subscripts
eq
and
i
indicate the concentrations of species in equilibrium and
initially, respectively; from (3) and (4) and (2) we have:
[Pb
2
+
]
−
[Pb
2
+
]
i
eq
K
=
(5)
a
2
+
−
2
2
+
2
2
+
−
[Pb
]
([C COO ]
+
4[Pb
]
−
4[Pb
] [C COO ] )
eq
n
i
eq
eq
n
i
Using the experimental values of [Pb
2+
]
eq
, shown in Figure 4, and the initial concen-
tration of carboxylate, it is possible to calculate the association constants (
K
a
). The
K
a
values obtained were analyzed using the Grubbs method resulting the values 1.8
(±0.5) × 10
6
M
-2
, 5.2 (±0.6) × 10
6
M
-2
,
and 3.8 (±0.7) × 10
6
M
-2
for the formation of
lead octanoate, decanoate, and dodecanoate, respectively.
3.4 CONCLUSION
The interactions between the divalent cations Ca
2+
and Pb
2+
, and sodium carboxyl-
ates with different alkyl chain lengths were studied in water using conductimetric
and potentiometric techniques. In the case of Ca
2+
, the interaction with carboxylates
is not only affected by ionic interactions, but also by the interactions involving the
hydrophobic chain of the amphiphilic ion. The interaction between Ca
2+
and sodium
octanoate does not exist or is very weak. The Pb
2+
carboxylate interactions are not
significantly affected by the surfactant chain length, in agreement with the idea of
some specific interactions in the complexation due to the bonds having substantial co-
valent character. However, the presence of Pb
2+
markedly affects the physico-chemical
properties of the solutions when compared with Ca
2+
. The interactions C
n
COO
í
Pb
2+
and C
11
COO
í
Ca
2+
occur with a stoichiometry of 2:1, which is consistent with charge
neutralization. Considering this interaction stoichiometry, association constant values
are proposed for the lead carboxylate system.
KEYWORDS
Calcium(II)
•
Electrical conductivity
•
Lead(II)
•
Potentiometry
•
Sodium carboxylates
•
ACKNOWLEDGMENT
Rui F. P. Pereira thanks FCT for a PhD. grant (SFRH/BD/38696/2007).
REFERENCES
1. Stigter, D.
J. Phys. Chem.
,
79
, 1008-1014 (1975).
2. Stigter, D.,
J. Phys. Chem
.,
79
, 1015-1022 (1975).
3. Gunnarsson, G., Jonsson, B., and Wennerstrom, H.
J. Phys. Chem.
,
84
, 3114-3121 (1980).
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