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and chromium(III), but also by a further hydrogen ion À ux, according to Equation.
(19).
x
Cr
3+
+ 2
y
H
2
O
'
Cr
x
(OH)
y
(3
x
-
y
)+
+
y
H
3
O
+
(19)
Similar situations have been found for the systems BeSO
4
/water [3], CoCl
2
chloride/
water [4], and Pb(NO
3
)
2
/water [5].
In fact, comparing the estimated diffusion coef¿ cients of Pb(NO
3
)
2
,
D
OF
, with the
related experimental values [5], an increase in the experimental D values is found in
lead(II) nitrate concentrations below 0.025 M. This can be explained not only by the
initial Pb(NO
3
)
2
gradient, but also by a further H
3
O
+
À ux. Consequently, as H
3
O
+
dif-
fuses more rapidly than NO
3
-
or Pb
2+
, the lead(II) nitrate gradient generates “its own”
HNO
3
À ux. Thus, the Pb(NO
3
)
2
/water mixture should be considered a ternary system.
However, in the present experimental conditions we may consider the system as pseu-
dobinary, mainly for c0.01 M, and, consequently, take the measured parameter,
D
av
,
as the main diffusion coef¿ cient, D
11
.
For c<0.01 M, we can estimate the concentration of H
3
O
+
produced by hydrolysis
of Pb(II) using Equations (20) and (21), assuming that: (a) the À uxes of the species,
HNO
3
and Pb(NO
3
)
2
, are independent, (b) the values of the diffusion coef¿ cients,
D
OF
,
come from Equation (3). The percentages of H
3
O
+
(or the amount of acid that would
be necessary to add to one solution of Pb(NO
3
)
2
in the absence of hydrolysis, result-
ing in this way a simulation of a more real system) are estimated from the following
equations [5].
Į
D
of
(HNO
3
) + ȕ
D
of
(Pb(NO
3
)
2
) =
D
av
(20)
Į + ȕ = 1
(21)
where Į
100 are the percentages of nitric acid and lead nitrate, respec-
tively. From those data, we can conclude that, for c0.01 M, Į becomes very low,
suggesting that either the hydrolysis effect or the contribution of
D
of
(Pb(NO
3
)
2
) to the
whole diffusion process, can be neglected. Tables (1-3) give the estimated percentage
of hydrogen ions,
Į
, resulting from the hydrolysis of Pb
2+
,
Be
2+
, and Co
2+
ions in aque-
ous solutions of lead(II) nitrate, beryllium sulfate, and cobalt chloride, respectively.
×
100 and ȕ
×
TABLE 1
Estimated percentage of hydrogen ions,
Į
, resulting from the hydrolysis of Pb
2+
in
aqueous solutions of lead (II) nitrate at 298.15K, using Equations (20) and (21) [5].
[Pb(NO
3
)
2
]
/(
mol dm
-3
)
Į/%
0.001
0.005
0.01
0.05
26.0
7.2
2.5
α
)
(a) For this concentration we can consider Į as nonrelevant.
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