Chemistry Reference
In-Depth Information
The calculation of diffusion coef¿ cients from equations based on some models de-
scribing the movement of matter in electrolyte solutions is, in the end, a process con-
tributing to the knowledge of their structure, provided we have accurate experimental
data to test these equations. Thus, to understand the behavior of transport process of
these aqueous systems, experimental mutual diffusion coef¿ cients have been com-
pared with those estimated using several equations, resulting from different models.
Assuming that each ion of the diffusing electrolyte can be regarded as moving
under the inÀ uence of two forces: (i) a gradient of the chemical potential for that ionic
species and (ii) an electrical ¿ eld produced by the motion of oppositely charged ions,
we come up to the Nernst-Hartley equation [20, 21].
D
= [(v
1
+v
2
) Ȝ
1
° Ȝ
2
° / (v
1
|Z
1
| (Ȝ
1
° + Ȝ
2
°))] (R T / F
2
) [1 + (d lng
±
/ d lnc)]
(12)
where Ȝ° are the limiting ionic conductivities of the ions (subscripts 1 and 2 for cation
and anion, respectively), Z is the algebraic valence of the ion, v is the number of ions
formed upon complete ionization of one solute “molecule”, T is the absolute tempera-
ture, R and F are the gas and Faraday constants, respectively, and g
is the mean molar
±
activity coefficient.
Equation (12) is often written as:
D
=
D
° [1 + (d lnȖ
±
/ d lnc)]
(13)
where D° is the Nernst limiting value of the diffusion coefficient.
Onsager and Fuoss [23] improved Equation (13) by taking into account the elec-
trophoretic effects (Equation 14):
D = (D° +¦¨
n
)[1 + (d lnȖ
/ d lnc)]
(14)
±
The difference between Equations (13) and (14) can be found in the lectrophoretic
term, ¨
n
, given by:
¨
n
= K
B
T A
n
(Z
1
n
t
2
° + Z
2
n
t
1
°)
2
/ (a
n
|Z
1
Z
2
|)
(15)
where K
B
is the Boltzmann's constant, A
n
are functions of the dielectric constant, of
the viscosity of the solvent, of the temperature, and of the dimensionless concentra-
tion-dependent quantity (k
a
), being k
the reciprocal of average radius of the ionic
atmosphere; t
1
° and t
2
° are the limiting transport numbers of the cation and anion,
respectively.
Since the expression for the electrophoretic effect has been derived on the basis of
the expansion of the Boltzmann exponential function, because that function had been
consistent with the Poisson equation, we only, in major cases, would have to take into
account the electrophoretic term of the ¿ rst order (n = 1). For symmetrical electrolytes
we can consider the second term. Thus, the experimental data can be compared with
the calculated
D
on the basis of Equations (16) and (17) for symmetrical and non-
symmetrical electrolytes, respectively.
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