The effect of additives on activities in cryolite melts
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I.
INTRODUCTION
W H E N a third component is added to a cryolite (Na3A1F6) melt, the activities of NaF and A1F3 are changed. The changes, in principle, can be measured in a number of different ways. The purpose of this paper is to analyze the 'theoretical situation and apply the resuits to the rather sparse data in the literature. No new experimental work has been done. In the following, NaF is defined as component 1, A1F3 as component 2, and the additive as component 3. This simplifies the writing of subscripts. The quantities sought are 0 In a~/ON3 and 0 In a2/ON3, where a is activity and N is mole fraction, it being understood that the derivatives are taken with a constant ratio of N~/N2. The experimental quantities available are vapor pressures and concentration-cell emf's, supplemented in a few cases by other sources of information. In no case have the desired quantities been measured directly, and it is only by a thermodynamic approach that the disparate experimental data can be reduced to a common form. II.
In the limiting dilute solution, N1 = 0.75, and Nz = 0.25, so that 3 0 In al -
[1]
N1 d In al + N2 d In a2 + N3 d In 3'3 = -dN3
[2]
3
0 In al
O In a 2 + - -
ON 3
ON3
1
[3]
In dilute solutions of 3 in cryolite, not only is N3 small but, if Henry's law applies, 0 In 3"3/0N3 = 0, so that the third term is negligible, and 0 In a~
0 In a 2 + N2 - = - 1
ON 3
0N3
4
I -- IV3
[6]
[7]
so that F 9
aA~F3
l n p = lnKp + l n a , + In a2
[8]
[9]
and 0 lnp -
-
ON3
0 In al -
-
0 In a2 +
-
ON3
-
[10]
-
ON3
Combination with Eq. [6] gives
ON3
ON3
[5]
NaF + AIF3 = N a A I F ;
- - -
O In a, 0 In a2 0 In 3'3 N ~ - - + N 2 - - + N 3 - - -
-4
where A73 is the value of N3 at the center of the range. The vapor over cryolite melts is predominantly NaAIF4 formed by
0 In a2
Hence,
N1
=
-
ON3
p = Kp 9 a N a
The term a 3 can be replaced by N3Y3, where 3' is the activity coefficient, and N a d In N3 = dN3, so
ON3
-
This is the fundamental link between the two activities. However, from the experimental point of view, it is often impossible to evaluate the necessary derivatives at zero concentration; rather, a mean slope may be obtained between zero and some finite concentration such as N3 = 0.1. In this case, the more general form of Eq. [5] is
THEORY
+Nzdlna2+N3dlna3=O
ON3
+
ON3
The Gibbs-Duhem equation for the ternary system is Nldlnal
0 In a2
-
3 0 In p - -
2 +
2 ON3
-
[11]
1 - 1V3
Thus, the variation of vapor pressure with addition of 3 gives the required quantity. ~ The treatment of concentration cells is analogous. For the cell AI Na3A1F6
Na~A1F61AI
[4] the transport number of Na + ions is effectively unity, and the e m f is
ERNEST W. DEWING, Principal Scientist, is with Alcan International Laboratory, P.O. Box 8400, Kingston, ON K7L 5L9, Canada. Manuscript submitted November 29, 1988. METALLURGICAL TRANSACTIONS B
E = (RT/3F) [ln (aE/a)~ - 3 In (al/a[)]
[12]
where a and a ' represent activities on the two sides of VOLUME 20B, OCTOBER 1989--675
the cell.
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