35 The Computation of Pourbaix Diagrams
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T. I. BARRY Chemical Standards Division, National Physical Laboratory, Teddington, Middlesex, TW11 OLW, UK
Pourbaix diagrams illustrate graphically the dominant solu tion or precipitate species of a component or components as a function of pH and oxidation potential (1). They are particu larly useful for defining the conditions for selective precipita tion or solution in hydrometallurgical extraction (2) and for passivation of metals. However, they are tedious to produce manually, especially when a number of components are present. The purpose of this paper is to demonstrate the principles of automatic computation for simple and complex systems and to illus trate these by reference to the copper and sulphur systems both separately and combined. The same methods are applied to the delineation of the conditions under which various chloride com plexes of copper will predominate as a function of chloride activity rather than pH. Principles Figure 1 shows a Pourbaix diagram for sulphur compounds in water. The point of the diagram is to indicate which compound of sulphur has the highest activity at combinations of pH and oxidation potential. It shows for example that in oxidising, alkaline solutions the sulphate ion dominates, whereas in reducing, acid solutions aqueous hydrogen sulphide is the major sulphur compound. In acid conditions of intermediate oxidation potential a wedgeshaped region is found which defines the circumstances under which precipitation of sulphur can occur. An odd feature of the diagrams, as described here, is that unless the solution compounds have equal and constant activity coefficients, the concentrations of these compounds in their respective zones are not equal and could in principle be very different. To remove this anomaly the activity coefficients could readily be incorporated provided they were independent of pH and pE, the variables of the system. O-8412-0569-8/80/47-133-681$05.00/O Published 1980 American Chemical Society In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
Downloaded by CORNELL UNIV on May 29, 2014 | http://pubs.acs.org Publication Date: October 29, 1980 | doi: 10.1021/bk-1980-0133.ch035
THERMODYNAMICS
OF AQUEOUS
SYSTEMS W I T H INDUSTRIAL
APPLICATIONS
+
Figure 1. A pH-pE diagram for the S-H 0-H -e system at 298.15 K. The activities of the predominant sulphur compounds in solution are 10' . 2
1
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
35.
Computation of Pourbaix Diagrams
BARRY
683
The diagrams c a l c u l a t e d by the methods d e s c r i b e d d i f f e r t o some extent from many a v a i l a b l e i n the l i t e r a t u r e i n t h a t they omit the predominant s o l u t i o n compound i n areas where a condensed compound a l s o forms. This g r e a t l y s i m p l i f i e s t h e diagrams w i t h out i m p a i r i n g t h e i r u s e f u l n e s s f o r most purposes. The system d e f i n e d by f i g u r e 1 has f o u r components, S - H 2 O - H - e. I t i s important t o note t h a t these f a l l i n t o two c l a s s e s . Sulphur w i l l be c l a s s i f i e d as a type 1 component to s i g n i f y t h a t we are i n t e r e s t e d i n what compounds i t forms. Condensed type 1 compounds, have an a c t i v i t y o f 1 i f present and > 1 i f absent. The a c t i v i t i e s o f the predominant type 1 compounds i n s o l u t i o n can be f i x e d at any d e s i r e d value. I n f i g u r e 1 they are s e t a t 1 C T . Thus t h e sulphate i o n has an a c t i v i t y o f 1 0 " i n i t s area and HS~ has an a c t i v i t y o f 1 C T i n i t s area. On t h e l i n e between these areas HS and the sulphate i o n c o e x i s t w i t h equal a c t i v i t i e s and t h e p o s i t i o n o f the coexistence l i n e between these two compounds can be obtained by s o l u t i o n o f t h e equation f o r the e q u i l i b r i u m +
1
1
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1
so£~
=
HS
+
kK 0
-
2
9H
-
Be.
The remainder o f the components are o f type 2 . Their a c t i v i t i e s are e i t h e r f i x e d , as f o r H 0 , or they form the i n d e pendent v a r i a b l e s o f the system, H and e. The a c t i v i t i e s o f H and t h e n o t i o n a l a c t i v i t y o f the e l e c t r o n are expressed i n l o g a r i t h m i c form as pH and pE where pE i s r e l a t e d t o the o x i d a t i o n p o t e n t i a l , E , by t h e r e l a t i o n 2
+
h
RT I n F
10
pE
There are 6 sulphur compounds t o be considered and t h e r e f o r e 15 p o s s i b l e c o e x i s t e n c e l i n e s o f which o n l y 9 represent s t a b l e equilibria. Moreover, even these 9 l i n e s are v a l i d ( i . e . c o r r e s pond t o s t a b l e coexistence) along only p a r t o f t h e i r p o s s i b l e extents. The problem then i s t o determine t h e equations f o r t h e l i n e s and the range over which they are v a l i d , and t o p r o v i d e a method f o r p l o t t i n g them. Methods f o r a simple case The p r i n c i p l e s o f t h e method become much c l e a r e r i f a p p l i e d to a p a r t i c u l a r r a t h e r than t h e general case. 1 The f i r s t step i s t o l i s t t h e compounds o f t h e type 1 compon ent together w i t h t h e i r Gibbs energies o f formation at t h e chosen temperature, o r t h e f u n c t i o n [ΔΗ°(f, 298) + G°(T) - H ° ( 2 9 8 ) ] which i s much e a s i e r t o c a l c u l a t e i n a data-bank. The two f u n c t i o n s must not be used f o r d i f f e r e n t substances i n the same c a l c u l a t i o n . The data used i n t h i s paper are taken from t h e monograph by Duby {3) on aqueous systems o f copper.
In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
684
THERMODYNAMICS
OF
AQUEOUS
SYSTEMS
Table
WITH
Formula
1
S
2
HS0 ~
A G°(298)
mole"
1
0 -756.01
4
3
Downloaded by CORNELL UNIV on May 29, 2014 | http://pubs.acs.org Publication Date: October 29, 1980 | doi: 10.1021/bk-1980-0133.ch035
f
/kJ
2
s
