Heterogeneous Equilibria Involving Oxides, Hydroxides, Carbonates

9

Downloaded by UNIV ILLINOIS URBANA on May 31, 2013 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/ba-1967-0067.ch009

Heterogeneous Equilibria Involving Oxides, Hydroxides, Carbonates, and Hydroxide Carbonates P A U L W. S C H I N D L E R

1

National Bureau of Standards, Washington, D . C. Some major and minor constituents of sea water can be classified with respect to possible control of their concentrations by simple solubility equilibria. Comparing calculated and observed data leads to the conclusion that the ocean represents a steady-state system, where the degree of oversaturation bears a reasonable relationship to the rate of sedimentation. 'T^his paper discusses some applications of the law of mass action to systems consisting of solids, a liquid phase—mainly water—and a gaseous phase essentially similar to the earth's atmosphere. The success of such discussions is always limited by our present knowledge concerning (a) the chemical properties of the different phases, (b) some intensive properties such as temperature and pressure, and (c) the extent to which chemical equilibrium is approached. These restrictions hold whether we are involved in experimental work using small vessels or in studies of gigantic natural systems as represented by the sea and its surroundings. W e begin, therefore, by summarizing some recent laboratory work on heterogeneous systems. Finally, a brief discussion of some properties of sea water in terms of solubility equilibria is given, based on the results of these experimental studies. The chemical species under consideration belong to ternary systems M e * - H 0 - C 0 . Their generalized formulae are given in Table I. The general symbol Me(OH) _2.r>(C03)a; represents a hydroxide carbonate; it includes the corresponding hydroxide (x = 0) and the neutral carbonate (x = 0.5z). Solid solutions ( M e i , M e ) ( O H ) , . ^ ( C 0 ) x w i l l not be considered at the moment. Furthermore, the possible occurrence +

2

2

U

2

1

2

2

Present address: University of Bern, Bern, Switzerland.

196 In Equilibrium Concepts in Natural Water Systems; Stumm, W.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

3

9.

Table I.

Chemical Species i n Ternary Systems M e * - H 0 - C ( > 2 +

( z

-

2 x )

(C0 )

(Me Me ) (OH) l f

2

3

-

2

2

(C0 )x 3

( C 0 , H C 0 ) , HCO3- C 0 2

2

3

Me' , M e (0H) Me (CO ) 0);

0

d = d(E +

R

1

d -


d

3

+

(d(E

2

=

£

T

R

r

(3E/aB)

l

p

1

log

0

n

1 0

H)/dH

logH)/3g)i.

H

Table II summarizes the different kinds of equilibrium constants with which we shall be concerned. Besides these few equilibrium constants we have already mentioned, there are other constants: _[Me„(OH),' "-"][C03 r [OH-]("- "'

„

2

!

M , a

„ _ [Me^CO,),'—">+] [ O H - ] " — " iS>Sqp [C03 ~] ~ 2

{q

PX)

describing equilibria between the solid and particular hydroxo and carbonato complexes. Since it is often easier to investigate homogeneous equilibria in homogeneous systems (since the homogeneous system has at least one more degree of freedom), we shall restrict ourselves by assuming all homogeneous equilibria to be known. A l l the heterogeneous constants are then available once one of them has been determined as follows: log Ks = ^ 0

(log Ks

nm

-

log ß )

== i - (log Ks

ttm

log *Ks + (z - 2a) log K

qp

0

log fKs

0

w

+ (x — z) log Kpa

t

- log ß )

+ x log (Kpa^Ka.)

+ x log Ka

2

=

qp

=

+ (z — 2x) log K

w

Now we must select the one appropriate solubility constant whose numerical value w i l l serve as a basis for all subsequent calculations. Some considerations which are common to all solubility investigations may be illustrated by taking zinc carbonate as an example (see Table III). Determining [ Z n ] presents no difficulties if the solubility is not too small. As shown in Table II, [ Z n ] oc P [ H C ( V ] " oc [CO3 ]" . Moreover, in calculating [ Z n ] , it should be kept in mind that analytical data yield: 2+

2+

C 0 2

2

2

1

2+

W

-

[ Z n ] + ^jn 2+

[Zn (OH)„^-"> ] + J j P m

+

[Zn (C0 )/ "-' p

3

(

/,+

]

Therefore, it seems favorable to operate under experimental conditions such that [ C 0 ] , [HCO3-], and [ O H ] are small. 3

2 _

In Equilibrium Concepts in Natural Water Systems; Stumm, W.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

200

E Q U I L I B R I U M CONCEPTS I N N A T U R A L W A T E R SYSTEMS

Table II.

Equilibrium Constants in Ternary Systems M e - H 0 - C ( > 2 z+

2

Homogeneous Equilibria H 0 and {Zn +}, {HCO3-} or [Zn +], [ H C O r ]

or *Ks

2

0

2

P 02 and {Zn +}, {H+} or [Zn +], [H+] C

2

2


9.

SCHINDLER

Heterogeneous

201

Equilibria

The concentrations of HCO3" and CO3 " may be obtained from acidimétrie titrations. It is sometimes best to avoid this procedure, however, since the presence of hydroxo or carbonato complexes may cause serious difficulties. We conclude that determining *Ks is most convenient since P o be fixed and [H ] is available from measurements with a glass electrode. We may now summarize some details of a recent experimental approach (46). Z n C 0 was equilibrated with an aqueous phase of the original composition: 2

0

C

2

c

a

n

+


3

[CIO4] = 0 . 0 2 0 0 M [H ] = HM +

[Na ] — ( 0 . 2 0 0 +

_1

1.0

H)M

I

I

1.5

2.0

Figure 1. Solubility of ZnC0 . The straight line was calculated with log *Ks = 8.17 (25°C, I = 0.2M NaClOJ 3

0


202

EQUILIBRIUM CONCEPTS I N N A T U R A L W A T E R SYSTEMS

and a number of different gaseous mixtures covering a range of known Pco values. T o maintain a constant ionic strength, H was always small and never exceeded 0.01M. The composition of the equilibrated solution was: 2

[CIO4-]

0.200M

—

[ Z n ] = bM 2+

[ H ] — hM Downloaded by UNIV ILLINOIS URBANA on May 31, 2013 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/ba-1967-0067.ch009

+

[HCO3] —Kpa -

Fco * h- = tM 1

2

x

[ N a ] — (0.200 + t - h -

2b)M

+

If the analytically determined concentration of zinc is equal to b> we obtain: (I = 02 NaC10 )

*Ks = bh- P 2

0

4

C02

In varying H and P o over a broad range, it was possible to check the validity of this relationship. Figure 1 shows a plot of log h vs. i log C

2

(WWThis procedure enables us to determine the stoichiometric solubility constant. W i t h a little additional information we can calculate the corresponding thermodynamic constant. F o r this purpose we shall consider a simple cycle: Zn + ,, . 2

(

0

+ C0 (g) + H O

2 )

2

2

. ) ^ Z n C O ( s ) + 2H+ AG, = RT\n*Ks

( / = 0

2

3

0

0

Zn(s) + 2H+(, .2> ^ Zn +< .2> + H,(g) 2

= 0

7=0

AG

2

= 2F£°(/_o.2>

C(s) + 0 ( g ) ^ C 0 ( g ) 2

2

H (g) + ^ 0 ( g ) ^ H 0(g) 2

2

2

H 0 ( g ) ^ H O(/_ .2) 2

2

2

3

AG

4

A G = RT\nP 6

0

Zn(s) + C(s) + 3/20 (g) ^ Z n C 0 ( s )

AG

AG = AG, + AG + AG, + A G + AG A G = -i?rinP (/=o)

3

6

2

4

H 0(/=o) ^ H 0 ( g ) 2

2

2

2

2

-AG,

Zn +c/ ) + H ( g ) ^ Zn(s) + 2H+cr_ > Zn +, AG 2

=0

/=0 9

2

H20

—AG4

2

C 0 ( g ) ^ C(s) + 0 ( g ) 2

5

7

H 0(g) ^ H (g) + i o ( g ) 2

Ki0

AG = -2F£°c, >

0

8

=0

) + C 0 (g) + H O > ^ Z n C 0 ( s ) + 2H+ r= > A G , = A G , + A G + AGs + A G , + A G = RTln *Ks„ 2

2

2

( r = 0

3

(

8

0

T


9.

SCHINDLER

203

Heterogeneous Equilibria

or RT\n**Ks

= RT\n*Ks

'° - ' ^H2O(I=0) + 2F(£ (/ o.2) - £°)(or*Ks(d~ )) 0

0

+ log Kso(»)(or *Ks (s)) = log Ks ( >(or o

0

s==0

Heterogeneous Equilibria Involving Oxides, Hydroxides, Carbonates

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