Critical Review of the Kinetics of Calcite ... - ACS Publications

25 Critical Review of the Kinetics of Calcite Dissolution and Precipitation L. N. PLUMMER and D. L. PARKHURST U.S. Geological Survey, Reston, VA 22092

Downloaded by MICHIGAN STATE UNIV on November 29, 2013 | http://pubs.acs.org Publication Date: March 19, 1979 | doi: 10.1021/bk-1979-0093.ch025

T. M. L. WIGLEY University of East Anglia, Norwich NR47TJ, England

The r a t e of c a l c i t e d i s s o l u t i o n i s known to depend on the hydrodynamic c o n d i t i o n s o f the environment and on the rate of heterogeneous r e a c t i o n at the mineral s u r f a c e . Numerous l a b o r a t o r y s t u d i e s demonstrate t r a n s p o r t and s u r f a c e - c o n t r o l l e d aspects of c a l c i t e r e a c t i o n s i n aqueous s o l u t i o n s , but u n t i l r e c e n t l y , no study has been comprehensive enough to enable comparison of k i n e t i c r e s u l t s among d i f f e r i n g hydro-chemical systems. We have s t u d i e d the d i s s o l u t i o n k i n e t i c s of c a l c i t e i n s t i r r ed C 0 - water systems a t C 0 p a r t i a l pressures between 0.0003 and 0.97 atm and between 5° and 6 0 ° C , using pH-stat and f r e e d r i f t methods 0 1 ) · Our r e s u l t s suggest a mechanistic model f o r reac t i o n s at the calcite-aqueous s o l u t i o n i n t e r f a c e that has broad i m p l i c a t i o n s t o the c o n t r o l s on c a l c i t e d i s s o l u t i o n and p r e c i p i t a t i o n under d i v e r s e chemical and hydrodynamic c o n d i t i o n s . This paper reviews the subject of the k i n e t i c s of c a l c i t e d i s s o l u t i o n and p r e c i p i t a t i o n by comparing p r e d i c t i o n s made by our mechanistic model w i t h published l a b o r a t o r y r e s u l t s . 2

2

Summary of the R e s u l t s of Plummer et a l . ( l ) Experimental. We s t u d i e d the d i s s o l u t i o n of semi-opticâl grade c r y s t a l s of Iceland spar (44.5 cm g"" and 96.5 c m ^ " ) i n d i l u t e s o l u t i o n s as a f u n c t i o n of pH, PCO2 and temperature. The "pH-stat" method was used to i d e n t i f y forward r e a c t i o n s f a r from e q u i l i b r i u m ( i n the near absence of backward r e a c t i o n ) . The "free d r i f t " method was used to study the r e a c t i o n near e q u i l i b r i u m where both forward and backward r a t e s must be considered. Details of the experimental procedures are given elsewhere (_1)» Figure 1 summarizes our pH-stat r e s u l t s f o r three C 0 p a r t i a l pressures at 25°C as a f u n c t i o n of pH. In g e n e r a l , the p a t t e r n shown i n Figure 1 demonstrates three c o n t r o l s on the forward r a t e . 1) At low pH, d i s s o l u t i o n r a t e shows l i t t l e dependence on P C 0 . The slope o f the l o g r a t e vs pH p l o t i s approximately - 1 . 0 and r a t e i s p r o p o r t i o n a l t o the bulk f l u i d a c t i v i t y of H . 2) At intermediate pH, forward r a t e depends on PC0 and pH and the slope 2

1

1

2

2

+

2

0-8412-0479-9/79/47-093-537$09.25/0 This chapter not subject to U.S. copyright Published 1979 American Chemical Society In Chemical Modeling in Aqueous Systems; Jenne, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

CHEMICAL MODELING IN AQUEOUS SYSTEMS


538

-3.0 25°C

-4.0

Γ

SX

-5.0!

ο Ε

~

-6.0!

χ

-3(e)

+ HCO'

— 3 3 ( e ) 2

3

CaCO

H+ + CO " (s) 3(s) +

H

ts)

( 4 b )

In Chemical Modeling in Aqueous Systems; Jenne, E.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

25.

PLUMMER ET

|Ca

2 +

Calcite Dissolution and Precipitation

AL.

+

- HC(T| , , 3 (o)

+ HCO"

, 3(s)

+

CaCO

545

+ H C0° , 2 3(s)

3

(5b)

and ka

- HCO~| , + 0H~ (o) (s)

2 +

+

s

3

+

x

CaCO„ + H O 3

, 2 (s)

(6b)

x

where HCO3 on the surface maintains e q u i l i b r i u m w i t h the surface species and the n o t a t i o n | C a - H C O 3 | (o) p o i n t s to our uncer t a i n t y as to the p h y s i c a l nature of the C a - HC0 association during backward r e a c t i o n . R e c a l l i n g our assumption that the surface species are i n e q u i l i b r i u m w i t h c a l c i t e , forward and backward r a t e terms f o r surface species have a net r a t e of zero, and thus c a n c e l . The r a t e s of r e a c t i o n s 4 , 5 , 6 are then g i v e n by: 2 +

2 +


3

1

R

4

Rt; "5

=

k

1

+

2+ — " 4 Ca(o)- HCO^( )

a

l H

a

k

( o )

a

/, *2 άH πC ρ0 ( ) " k*4

— _

ko

a

Λ

Λ Λ / 3 o

2

u pCn0^3/( )\ C a, ( N) -» Hu Cr n0 o3/( o \) ' H

a 3-n„

x

6

=

k

3 H 0( )

"

a

2

o

k

4

,a

aa

a

s

o

1 , 1 R

( 7 )

0

a

2+ — — Ca(o) HC03(o)* 0H( ) e a

a

>

s

( 9 )

and the net r a t e of d i s s o l u t i o n i s given by R = R

+ R

4

(10)

+ R.

5

6

F l u x c a l c u l a t i o n s (4) show that boundary l a y e r a c t i v i t i e s are approximately equal to bulk f l u i d a c t i v i t i e s f o r a l l species other than HT; thus k aH C0°(o) i s replaced by k a H C 0 ( B ) and k3aH 0(o) becomes k a H 0 ( B ) . Because the forward r a t e dependence of r e a c t i o n 4 i s t r a n s p o r t - c o n t r o l l e d , 2

2

2

R

4,f

=

k

( a

2

2

3

2

3

a

l H(B) " H(o)^

k

l

a

H(B)

at low pH. At higher pH, the forward r a t e of 4 i s more d i f f i c u l t to describe but i s always small r e l a t i v e to the other terms i n 10 and can be neglected. Equation 10 i s then i d e n t i c a l w i t h the e m p i r i c a l equation 3 , and defines ki+ as I f I III k = k + k a + k a . (12) 4

4

4

H C 0

( s )

4

0 H ( g )

From the p r i n c i p l e of microscopic r e v e r s i b i l i t y , forward


and

546

CHEMICAL MODELING IN AQUEOUS

SYSTEMS

backward r a t e s of a l l r e a c t i o n s must balance a t e q u i l i b r i u m , and thus, equations 7 - 9 g i v e t k

ι 4

k1K2 >

=

K

1 1 k

k2K2 , and k

4 = K

c

1 1 1

k3K2

4

K

K

c l

K

c w

where K K , Κ , and K are e q u i l i b r i u m const; tants f o r H C0? = H + H C O 3 , HCOI = H + C O 3 " , CaCO3 ( c a l c i t e ) = C a + CO , and H 0 = Η + OH . S u b s t i t u t i o n i n t o equation 12 ao l9

2

w

+

2

+

2 +


2-

UCX-LUCO

2

k

4

7

=

Wl

K

+

1

c

I"

k

- T ~ H ) a

H 0( )l

a a

2 H C03(s)

+

k

2

3

2

( s

s

'

J

4

(13)

>

By r e p l a c i n g k j i n 13 w i t h the e x p e r i m e n t a l l y determined values of k , we can compare the t h e o r e t i c a l dependence of k4 on PC0 and temperature w i t h the observed PC0 and temperature de pendence ( F i g u r e 4 ) . Because k j > k , the computed values of k should show a systematic b i a s ( w i t h the computed values below the experimental v a l u e s ) . However, the PC0 dependence should remain u n a l t e r e d by u s i n g ki i n s t e a d of k j , and, i f the k j term i s r e l a t i v e l y s m a l l , the temperature dependence w i l l a l s o be l a r g e l y unchanged. F i g u r e 4 shows that the PC0 and temperature trends i n com puted and observed values of k are s i m i l a r . Computed values are below the experimental values as expected, i m p l y i n g a k value some ten t o twenty times k . This q u a l i t a t i v e and q u a n t i t a t i v e agreement between theory and experiment gives f u r t h e r support f o r our mechanistic model. In terms of the s a t u r a t i o n r a t i o , Ω (Ω = IAP/K , where IAP i s the i o n a c t i v i t y product of c a l c i t e i n s o l u t i o n ; Ω i s 1 during p r e c i p i t a t i o n , and Ω = 1 a t e q u i l i b r i u m ) , equations 3 and 13 define r a t e as x

2

2

x

4

2

2

4

x

x

C

a

H

+

a

H (s)

R = ot+e-(a+

g ) Ω

(14)

+

+

where α = k i a H , and 3 = k aH C03 + k a H 0 . At low PC0 (

'

( 1 5 )

H

I t i s apparent that i n order to use our r a t e model, a thermo dynamic e v a l u a t i o n of the bulk f l u i d and surface s p e c i a t i o n i s


25.

P L U M MER

ET AL.


547

r e q u i r e d . Thermodynamic s p e c i a t i o n i n the bulk f l u i d can be c a l c u l a t e d through the use of thermodynamic models of the aqueous phase, such as the computer program WATEQF ( 5 ) . A parameter more d i f f i c u l t to assess i n our r a t e model i s the surface a c t i v i t y of H . At r e l a t i v e l y high C 0 p a r t i a l pressures, as i n our e x p e r i ments (1), we have concluded that surface PC0 and aH 0 are near the bulk f l u i d values and surface pH i s then determined by c a l c i t e e q u i l i b r i u m owing t o the r a p i d r e a c t i o n w i t h H . But as shown i n a l a t e r s e c t i o n of t h i s paper, t h i s c o n c l u s i o n ( t h a t surface PC0 = bulk f l u i d PC0 ) may be only approximately true i n our own experiments, and i t becomes c r u c i a l to any a n a l y s i s of c a l c i t e k i n e t i c s a t low C 0 p a r t i a l pressures. +

2

2


2

2

2

2

Comparison With Other Studies For purposes of d i s c u s s i o n , r e l e v a n t s t u d i e s i n the pub l i s h e d l i t e r a t u r e can be grouped under four t o p i c s : 1) d i s s o l u t i o n i n a c i d s , 2) C02-dependence, 3) e f f e c t of i m p u r i t i e s and 4) p r e c i p i t a t i o n . These t o p i c s cover a diverse l i t e r a t u r e i n methods and c o n d i t i o n s of experimental study, and no s i n g l e set of r a t e measurements i s complete enough f o r d i r e c t comparison w i t h a l l other s t u d i e s . In a d d i t i o n , r a t e equations derived from experiments are u s u a l l y of l i m i t e d a p p l i c a b i l i t y beyond the experimental r e s u l t s . To date, only the t h e o r e t i c a l model of Plummer et_ a l . (1) described above i s comprehensive enough t o a l l o w p r e d i c t i o n s covering the range of experimental r e s u l t s i n the l i t e r a t u r e . In some cases we are unable to make d i r e c t com parisons of observed r a t e s . But where s u f f i c i e n t data are not a v a i l a b l e f o r d i r e c t comparison, we have e i t h e r attempted to cast the r e s u l t s of others i n t o the framework of our model, or we have compared observations w i t h p r e d i c t i o n s based on our model. Our a n a l y s i s of the l i t e r a t u r e i s not exhaustive and i s i n part l i m i t e d to r e p o r t s g i v i n g s u f f i c i e n t data to enable d i r e c t or i n d i r e c t comparison. In order t o cast r e s u l t s of other s t u d i e s i n terms of our model, some t r a n s f o r m a t i o n of data has been necessary. In some cases we have had to estimate a c t i v i t y c o e f f i c i e n t s i n s o l u t i o n s , and t h i s has been done v i a the Davies equation ( 6 ) , log γ. =

-AZ 1

2

[ \ 1+

-0.31 ) 1*

(16)

J

where A i s a constant dependent on temperature, z i s i o n charge, and I i s i o n i c s t r e n g t h ( I = 1/2 Ζ m±z±> where mi i s m o l a l i t y o f the ith i o n ) . I n other cases we nave r e l i e d on an aqueous model and our r a t e model t o p r e d i c t rates under experimental c o n d i t i o n s , or we have used our r a t e equation t o p r e d i c t concentra t i o n - t i m e curves f o r comparison w i t h o b s e r v a t i o n s . The aqueous model used t o make p r e d i c t i o n s i s s i m i l a r t o that of MIX2 (7) f o r the chemical system Ca0-Mg0-K 0-Na 0-HCl-H S0i -H C0 -H 0. The 2

2

2

f

2

3

2


CHEMICAL MODELING IN

548

AQUEOUS SYSTEMS


aqueous model i n c l u d e s 23 i o n p a i r s i n a d d i t i o n to the major species and uses the c o n s t r a i n t s of mass a c t i o n , mass balance and charge balance i n s o l u t i o n . Using a computer program, RATECALC, r e a c t i o n progress and r a t e are f o l l o w e d as a f u n c t i o n of time by way of equations 3 and 13. D i s s o l u t i o n i n A c i d s . Most k i n e t i c work w i t h c a l c i t e has dealt w i t h d i s s o l u t i o n i n a c i d s . King and L i u (8) measured the i n i t i a l r a t e of s o l u t i o n of r o t a t e d marble c y l i n d e r s i n d i l u t e a c i d s between 15° and 35°C. They found that r a t e of d i s s o l u t i o n increased w i t h i n c r e a s e d a c i d c o n c e n t r a t i o n , increased speed of r o t a t i o n and i n c r e a s e d temperature. Rate was i n v e r s e l y r e l a t e d to v i s c o s i t y , supporting t h e i r c o n c l u s i o n of a t r a n s p o r t - c o n t r o l l e d r e a c t i o n . Figure 5 shows some of t h e i r r e s u l t s i n d i l u t e HC1 s o l u t i o n s at 4000 rpm. King and L i u s r a t e s can be described by a l i n e a r r e l a t i o n i n the a c t i v i t y of H (Figure 5), where the slope i s .022, .032, and .042 at 15°, 25°, and 35°C, r e s p e c t i v e l y , and comparable to our k , which i s 0.051 at 25°C 01) f o r suspended p a r t i c l e s s t i r r e d at 1800-2300 rpm. The data of King and L i u (8) give an a c t i v a t i o n energy of 5.6 k c a l / m o l , which i s n e a r l y three times our value (2.0 k c a l / m o l ) . We do not expect c l o s e agree ment i n experimental values of k j , owing to l a r g e d i f f e r e n c e s i n hydrodynamic c o n d i t i o n s between experimental methods. F i g u r e 6 compares l o g r a t e as a f u n c t i o n of pH from v a r i o u s sources. The slope of a best f i t l i n e between pH 2 and 5.5 i s -0.95 c o n f i r m i n g the f i r s t order r e a c t i o n i n air". The data of King and L i u (8) and Plummer et a l . CO i n d i l u t e HC1 s o l u t i o n s , and Berner and Morse (3) i n a r t i f i c i a l sea water s o l u t i o n s at low pH show c l o s e agreement. Table I summarizes experimental methods used by v a r i o u s workers l e a d i n g to the r a t e s given i n Figure 6, and compares our estimates of k i from these data w i t h the temper ature dependence of ki· C l e a r l y , there are r e a l d i f f e r e n c e s i n k i between e x p e r i ments. The highest value of k i i s estimated from the data of Weyl (9), who d i r e c t e d a j e t of C O 2 - s a t u r a t e d water (pH -3.9) onto the surface of c a l c i t e . Weyl found that the r a t e of s o l u t i o n v a r i e d w i t h the j e t v e l o c i t y . His r a t e s imply that k j v a r i e s from 0.11 to 0.23 when v e l o c i t y of the j e t increases from 18 to 35 m sec · The s m a l l e s t value of k (.0073) i s derived from the data of Tominaga et a l . (10). These authors r o t a t e d a d i s k of marble i n HC1 s o l u t i o n s (0.1750 - 0.5317N) at 485 rpm. Rate of d i s s o l u t i o n was f o l l o w e d by the volume of C0 evolved. A f t e r an i n i t i a l p e r i o d f o r s a t u r a t i o n of the a c i d w i t h C0 , r a t e of gas evolved becomes l i n e a r i n the cumulative amount of C0 produced. Because the a c i d c o n c e n t r a t i o n decreased as c a l c i t e d i s s o l v e d , we e x t r a p o l a t e d the observed l i n e a r r e l a t i o n i n C0 production back to the i n i t i a l c o n d i t i o n to estimate i n i t i a l r a t e s under known a c i d c o n c e n t r a t i o n s . C o r r e c t i o n to pH v i a the Davies equation leads to the r a t e s shown f o r these authors i n Figure 6. Most of the v a r i a t i o n i n k i (Table I ) i s probably due to f

+

x

1

x

2

2

2

2



25.

PLUMMER E T AL.


D.O

0.002

0.004 0.006 0.008 0.010 0.012 MOLARITY OF HCI

0.0

0.002

0.004 0.006 0.008 ACTIVITY OF H

549

0.010 0.012

+

Figure 5. Dissolution of rotated marble cylinders in dilute HCI solutions be tween 15° and 35°C at 4000 rpm. Rate is shown as a function of concentration (upper) and activity of H (lower), k, is defined by slope on plots of rate vs. aH\ +

ο King and Liu (fi) ® Tominaga et aj. (10) I Weyl (9) ο Wentzler (39) ° Berner and Morse (3) Lund et al. (13) —

Barton and Vatanatham (38) Δ Plummer et aj. (1)

No

3

0 Sjoberg (14)

PH

4

Figure 6. Summary of log rate as function of pH in acids at 25°C. All data are far from equilibrium and independent of Pco . The slope is —0.95 and rate may be assumed, within the uncertainties of the data, to befirstorder in aH . %

+



) o|


Pry

SYSTEMS

T3 s C CO CO Xi

4J CO 05 TJ

3 -H g CJ CO — iI

0) 4-1

4J h CO 3 T3 4J CO

χ; α;

* i* 4-1 0)

Ο ι—I • υ Ο PC

525

u



25.

PLUMMER E T A L .


551

d i f f e r e n c e s i n hydrodynamic c o n d i t i o n s of the experiment, being the lowest under the approximately laminar boundary l a y e r c o n d i t i o n s a t the surface of a slowly r o t a t i n g disk (10), and highest at the impact of a high v e l o c i t y j e t on the c a l c i t e surface (_9). Transport dependence of the r e a c t i o n i n HCI s o l u t i o n s i s a l s o documented by the work o f Kaye (LI) and Nierode e t a l . (12)« The temperature dependence of k j shows considerable v a r i a t i o n (2.0 - 5.6 kcal/mole), and may a l s o be a f u n c t i o n of the hydrodynamic c o n d i t i o n s of the experiment. Lund e t a l . (13) obtained an a c t i v a t i o n energy of 15 kcal/mol between -15.6 and +1.0°C under c o n d i t i o n s where they concluded both surface reac t i o n and transport processes i n f l u e n c e d the r a t e . They found r a t e p r o p o r t i o n a l t o the 0.63 power of rather than the f i r s t order r e a c t i o n observed f o r c o n d i t i o n s of transport c o n t r o l . The data shown i n Figure 6 give the v a r i a t i o n i n l o g r a t e as a f u n c t i o n of pH f a r from e q u i l i b r i u m . We have shown that be low pH 4, C0 p a r t i a l pressures between 0 and 1.0 atm do not i n f l u e n c e the rate s i g n i f i c a n t l y . Above pH 4, a l l data shown i n Figure 6 are a t C 0 p a r t i a l pressures l e s s than 10"" atm and can thus be compared. Only the data o f Plummer et_ a l . (1) and Sjoberg (14) are a t pH greater than 5.5 f a r from e q u i l i b r i u m , and both confirm a plateau i n rate as a f u n c t i o n of pH (Figures 1 and 6). We have concluded that t h i s plateau defines the rate of the forward r e a c t i o n i n the near absence of both C 0 and H and i s c o n t r o l l e d by r e a c t i o n with H 0 (1). I t i s not understood, how ever, why S j o b e r g s r a t e s are approximately 2.8 times greater than our rates f a r from e q u i l i b r i u m i n the near absence of H and C0 , and are s i g n i f i c a n t l y lower than most observed rates at pH l e s s than 5.0 (Figure 6). The rates f a r from e q u i l i b r i u m i n Figure 6 were obtained i n a v a r i e t y of aqueous s o l u t i o n s i n c l u d i n g HCI, H N O 3 , H S0if, NaClC a C l and KC1 t o 0.7 molar a t 25°C, and suggest that a t l e a s t f o r these c o n d i t i o n s , the forward rate i s not s i g n i f i c a n t l y dependent upon the presence of these c o n s t i t u e n t s i n s o l u t i o n . 2

1,5

2

2

2

1

2

2

2

C0 -dependence. There are r e l a t i v e l y few i n v e s t i g a t i o n s that deal w i t h the e f f e c t s of C0 -dependence on r a t e of d i s s o l u t i o n . Erga and Terjesen (15) followed c a l c i t e d i s s o l u t i o n by the f r e e d r i f t method t o near e q u i l i b r i u m i n C0 -water s o l u t i o n s a t 25°C by measurement of d i s s o l v e d calcium as a f u n c t i o n of time. PC0 was maintained constant by bubbling gas mixtures. The c a l c i t e used was of " n a t u r a l o r i g i n " and surface area estimated from p a r t i c l e s i z e was 125 cm g~ . Experiments a t .95 - .97 atm C0 showed that r a t e was d i r e c t l y p r o p o r t i o n a l t o surface area of the p a r t i c l e s , but independent of gas v e l o c i t y , l e a d i n g t o t h e i r c o n c l u s i o n that the r e a c t i o n rate i s independent of 1) the t r a n s f e r of carbon d i o x i d e from the gas to l i q u i d phase, and 2) chemi c a l r e a c t i o n i n the bulk f l u i d . Rate of d i s s o l u t i o n was propor t i o n a l t o s t i r r i n g rate t o the power ( s t i r r i n g c o e f f i c i e n t ) 0.22 (between 280 and 555 rpm). Because s t i r r i n g c o e f f i c i e n t s of .5 t o 2

2

2

2

2

1

2


552


1.0 are expected i n t r a n s p o r t - c o n t r o l l e d r e a c t i o n s ( 1 6 ) , the low s t i r r i n g c o e f f i c i e n t of Erga and Terjesen (15) f u r t h e r supports t h e i r c o n c l u s i o n t h a t f o r t h e i r experimental c o n d i t i o n s , "the r a t e determining steps are l o c a l i z e d a t the s o l i d - l i q u i d i n t e r face or i n the l i q u i d f i l m i n immediate contact w i t h i t " . Erga and Terjesen (15) p u b l i s h e d two s e t s of data that we can use f o r comparison w i t h our r a t e model. The f i r s t i s a p l o t of d i s s o l v e d Ca vs time i n a f r e e d r i f t run a t 0.954 atm C 0 , and the second i s a p l o t of d i s s o l u t i o n r a t e vs t o t a l calcium i n the s o l u t i o n f o r f o u r f r e e d r i f t runs a t C0 p a r t i a l pressures of 0.135, 0.392, 0.664 and 0.952 atm ( 1 5 ) . Figure 7 compares two concentration-time curves c a l c u l a t e d from equation 3 ( u s i n g the program RATECALC mentioned e a r l i e r ) w i t h that observed by Erga and Terjesen. The dashed curve ( F i g ure 7^ i s c a l c u l a t e d u s i n g the r e p o r t e d surface area (1250. cm 1" ) and the s o l i d curve i s a s i m u l a t i o n of t h e i r experiment assuming t h e i r s u r f a c e area was 1/2 the r e p o r t e d v a l u e . F i g u r e 7 shows that the r e s u l t s of Erga and Terjesen (15) d i f f e r from ours by a constant f a c t o r of two. That i s , the form of our r a t e equa t i o n p r e d i c t s the observed shape o f the concentration-time curve w i t h an u n c e r t a i n t y of a f a c t o r of two i n the r a t e c o n s t a n t s . This u n c e r t a i n t y i s s i m i l a r t o the u n c e r t a i n t y i n the measurement of k.3(_l). Surface area adjustments w i t h i n a f a c t o r of two may a l s o r e f l e c t u n c e r t a i n t i e s i n e s t i m a t i o n of area based on p a r t i c l e s i z e , and ( o r ) d i f f e r e n c e s i n r e a c t i o n s i t e d e n s i t y among d i f f e r i n g m a t e r i a l . What i s important i s that the shape of the f r e e d r i f t data of Erga and Terjesen (15) i s c l o s e l y matched by the form of our r a t e equation ( F i g u r e 7 ) . The match may be even c l o s e r i f one c o n s i d e r s the expected ( s m a l l ) decrease i n surface area during r e a c t i o n , which was not accounted f o r i n the computer s i m u l a t i o n . Erga and Terjesen used 100g o f c a l c i t e i n 10 l i t e r s of d i s t i l l e d water, so that a t 0.95 atm C 0 , n e a r l y 10 percent of the weight of t h e i r s t a r t i n g m a t e r i a l was d i s s o l v e d by the end of t h e i r run. Using the surface area c o r r e c t i o n of 1/2, we a l s o c l o s e l y match concentration-time curves f o r s i m i l a r experiments r e p o r t e d by these authors i n subsequent p u b l i c a t i o n s (17, 18) as shown f o r the r e s u l t s o f Terjesen et al - (17) i n F i g u r e 8. Figure 9 shows that i f we use the surface area c o r r e c t i o n of 1/2, our r a t e equation a l s o c l o s e l y simulates the observed r a t e s of Erga and Terjesen (15) a t other CO^ p a r t i a l pressures. Be cause i t i s necessary t o consider both forward and backward r e a c t i o n i n a n a l y s i s of the r e s u l t s of Erga and Terjesen ( 1 5 ) , we have made the c a l c u l a t i o n s of Figure 9 assuming s u r f a c e PC0 i s equal t o the bulk f l u i d value and the surface pH i s determined by c a l c i t e e q u i l i b r i u m , i d e n t i c a l t o the c a l c u l a t i o n s o f Plummer et_ a l . ( 1 ) . As b e f o r e , we have not c o r r e c t e d f o r expected decreases i n s u r f a c e area during t h e i r experiments. But even without t h i s c o r r e c t i o n the match i n computed and observed r a t e s s t r o n g l y sup ports the PC0 dependence of forward and backward r a t e p r e d i c t e d 2


2

2

2

2


25.

PLUMMER


ET AL.

-r io

553

r

Ε £

6

L

Ψ. Downloaded by MICHIGAN STATE UNIV on November 29, 2013 | http://pubs.acs.org Publication Date: March 19, 1979 | doi: 10.1021/bk-1979-0093.ch025

50

Erga and Terjesen (15) •Calculated using reported surface area Calculated using corrected surface area 100

150 200 250 TIME (Minutes)

300

350

400

Figure 7. Comparison of observed calcium in solution (15) during free drift experiment at 0.954 atm C0 and 25°C with simulated reaction. The dashed line is calculated using the reported surface area^and the solid line is calculated assuming the area is half the reported value. 2

TIME (Minutes)

Figure 8. Comparison of simulated and observed calcium-time curve of Terjesen et al. (17) in a free drift run at 0.97 atm C0 and 25°C. The solid line represents the simulated reaction using the same surface area correction as found for the free drift experiments of Erga and Terjesen (15). 2

2.5^

-

DISSOLVED CALCIUM (mmoles liter" ) 1

Figure 9. Comparison of observed and simulated rate for four C0 partial pres sures at 25°C in the free drift experiments of Erga and Terjesen (15). The varia tion in rate as a function of Pco is closely predicted by the rate model of Plummer et al. (1). 2

2



554

SYSTEMS

by Plummer e_t a l . Q ) . Figure 10 compares the C0 and H dependence of d i s s o l u t i o n r a t e observed by Berner and Morse (3) f a r from e q u i l i b r i u m i n pseudo-sea water (a CaCl2 - NaCl s o l u t i o n of the i o n i c s t r e n g t h and t o t a l calcium content of sea water) w i t h the PC0 - a H de pendence given by equation 1. We have found that the r a t e of d i s s o l u t i o n f a r from e q u i l i b r i u m becomes independent of PC0 be low approximately 1 0 ' atm. Most of Berner and Morse's r a t e s f a r from e q u i l i b r i u m are at C0 p a r t i a l pressures equal to or below 1 0 ~ atm, and as expected, show l i t t l e or no C0 depend ence f a r from e q u i l i b r i u m (Figure 10)· According to equation 1, the d i f f e r e n c e i n forward r a t e at constant pH between 0 and 1 atm C0 should be approximately 1.2 χ 10" mmol cm" s e c " , but the one value of Berner and Morse (3) a t 1 atm C0 that can be p l o t ted on Figure 10 shows no C0 dependence. Although most of the r a t e s of Berner and Morse (_3) shown i n Figure 10 are w i t h i n a f a c t o r of two of our r a t e s , the expected r e l a t i o n of increased r a t e with increased PC0 i s even reversed i n some of t h e i r low PCO2 data (Figure 10). Because most of the r a t e s of Berner and Morse (_3) f a r from e q u i l i b r i u m are a t low PC0 , t h e i r data do not provide an adequate t e s t of PC0 dependence. Almost a l l of the data of Sjoberg (14) are f o r very low C0 p a r t i a l pressures. However, two r a t e s f a r from e q u i l i b r i u m a t 0.97 atm CO2 ( i n 0.7M KC1 a t pH4.4 and 5.0) are approximately twice the measured values at 1 0 " atm C0 ( 1 4 ) . Below pH 4, S j o b e r g s r a t e s f a r from e q u i l i b r i u m are dominated by r e a c t i o n w i t h H and become independent of PC0 , as we have found (1)· Although there are s i g n i f i c a n t d i f f e r e n c e s between the a b s o l u t e values of S j o b e r g s r a t e s and ours (Figure 6 ) , the PC0 depend ence observed by Sjoberg agrees reasonably w e l l w i t h that observ ed i n our experiments. +

2

+

2

2

- 1

5

2

1 , 5


2

6

2

1

2

2

2

2

2

2

2

2 , 5

2

1

2

1

2

E f f e c t of I m p u r i t i e s . In the previous s e c t i o n s we have con s i d e r e d c a l c i t e d i s s o l u t i o n 1) f a r from e q u i l i b r i u m i n v a r i o u s s o l u t i o n s , and 2) both f a r from and near e q u i l i b r i u m but only i n pure C0 -water s o l u t i o n s . We now i n v e s t i g a t e c a l c i t e d i s s o l u t i o n i n s o l u t i o n s where backward r e a c t i o n must be considered i n the presence of i m p u r i t i e s . I m p u r i t i e s can be defined as c o n s t i t u e n t s present i n the aqueous phase that are not part of the o r i g i n a l s t o i c h i o m e t r i c composition of the reactant ( 2 ) . The presence of i m p u r i t i e s can have a profound e f f e c t on the r a t e of d i s s o l u t i o n or p r e c i p i t a t i o n , b u t , u n f o r t u n a t e l y , there i s no simple way of p r e d i c t i n g , a p r i o r i , the t o t a l e f f e c t that an impurity or com b i n a t i o n of i m p u r i t i e s can have on the r a t e of r e a c t i o n . The e f f e c t of i m p u r i t i e s can be p a r t i a l l y evaluated through thermodynamic a n a l y s i s . C e r t a i n l y , there are many other ways that i m p u r i t i e s may a f f e c t the r a t e of r e a c t i o n ( 2 ) , and by a c counting f o r the thermodynamic e f f e c t of i m p u r i t i e s , other e f f e c t s may be i d e n t i f i e d . Two c l a s s e s of thermodynamic problems are evident. 2



25.

PLUMMER E T AL.


555

The f i r s t i s concerned w i t h what thermodynamic changes w i l l take place i n a heterogeneous system upon a d d i t i o n of an impu r i t y . This problem can be described i n terms of changes i n mineral s o l u b i l i t y . I f an impurity contains a c o n s t i t u e n t that i s present i n the reactant (common i o n e f f e c t ) , the s o l u b i l i t y of the reactant i s u s u a l l y decreased and p r e c i p i t a t i o n may occur. Impurities may a l s o cause changes i n a c t i v i t y c o e f f i c i e n t s . De c r e a s i n g a c t i v i t y c o e f f i c i e n t s cause s o l u b i l i t y t o increase ( s a l t i n g - i n ) . Increasing a c t i v i t y c o e f f i c i e n t s can cause p r e c i p i t a t i o n ( s a l t i n g - o u t ) . These and other thermodynamic e f f e c t s of i m p u r i t i e s on s o l u b i l i t y are discussed elsewhere (_2, 19_, 20). The second type of thermodynamic problem i s concerned w i t h comparing p a r a l l e l r e a c t i o n s i n pure and impure systems. In the case of c a l c i t e d i s s o l u t i o n we ask, how w i l l r a t e change a t con stant pH and PCO2 owing to the presence or absence of an impu r i t y ? Equation 14 shows that thermodynamic e f f e c t s of i m p u r i t i e s on the r a t e of c a l c i t e d i s s o l u t i o n are accounted f o r by c a l c u l a t i o n of the bulk f l u i d s a t u r a t i o n (Ω) and the e q u i l i b r i u m a c t i v i t y of H i n the a d s o r p t i o n l a y e r ( a H ( s ) ) . The f o l l o w i n g ex ample demonstrates one p o s s i b i l i t y . Consider the d i s s o l u t i o n of c a l c i t e a t 25°C and 0.95 atm C 0 i n separate s t a r t i n g s o l u t i o n s of pure water and 0.2 M C a C l s o l u t i o n . Thermodynamic c a l c u l a t i o n s i n d i c a t e that the surface e q u i l i b r i u m pH (assuming surface PC0 i s equal t o the bulk f l u i d value) i s lower i n the C a C l s o l u t i o n (5.51) than i n the pure s o l u t i o n (6.02). A f t e r some i n i t i a l d i s s o l u t i o n , pH 5.36 i s reached, a t d i f f e r e n t times, i n both s o l u t i o n s . In the pure s o l u t i o n Ω i s lower (0.025) and the r a t i o , a H / a H ( s ) , i s higher (4.57) than comparable values i n the 0.2 M C a C l s o l u t i o n , 0.479 and 1.41, r e s p e c t i v e l y . The increase i n Ω from the pure s o l u t i o n t o the C a C l 2 s o l u t i o n i s nearly 6 times l a r g e r than the accompanying decrease i n a H / a H ( s ) r a t i o . Equation 14 then shows that r a t e of c a l c i t e d i s s o l u t i o n a t constant pH and PCO2 should be slower i n the CaCl2 s o l u t i o n s than i n pure s o l u t i o n s . These thermodynamic e f f e c t s are complex and almost every impurity i s a s p e c i a l case. R e s o l u t i o n of the thermodynamic e f f e c t s of i m p u r i t i e s u s u a l l y r e q u i r e s a computer program, such as RATECALC mentioned e a r l i e r . One can only properly address the question as to what other e f f e c t s i m p u r i t i e s may have on rate of r e a c t i o n , a f t e r the thermodynamic e f f e c t s of i m p u r i t i e s have been evaluated. This i s the approach we have f o l l o w e d i n our e v a l u a t i o n of the data o f Berner and Morse ( 3 ) , Morse (21) and Sjoberg (14) i n v a r i o u s s a l t s o l u t i o n s of the i o n i c s t r e n g t h of sea water ( I = 0.7). No attempt has been made to t r e a t rate data of Berner and Morse (3) or others f o r which trace i m p u r i t i e s (such as PO^) cause l a r g e changes i n r a t e without s i g n i f i c a n t l y a l t e r i n g the thermodynamic p r o p e r t i e s of the system. C l e a r l y , other mecha nisms must be considered i n i n t e r p r e t i n g these r e s u l t s . Table I I summarizes our c a l c u l a t i o n s of d i s s o l u t i o n r a t e i n pseudo-sea water and sea water f o r comparison w i t h the pH-stat +

+

2

2

2

2

+

+

2

+

+


CHEMICAL MODELING

556

IN AQUEOUS

SYSTEMS

measurements o f Berner and Morse (3)· Berner and Morse t a b u l a t e measured pH, PC0 and r a t e . Because many of these data depend s i g n i f i c a n t l y on backward r e a c t i o n , our c a l c u l a t i o n s of the r a t e s expected i n t h e i r experiments have employed a thermodynamic model f o r t h e i r aqueous s o l u t i o n s . We have had t o c o r r e c t t h e i r meas ured pH values f o r the e f f e c t s o f r e s i d u a l l i q u i d j u n c t i o n po t e n t i a l . The r e s i d u a l l i q u i d j u n c t i o n p o t e n t i a l i n sea water has been estimated by Hawley and Pytkowicz (22) to be -3.2 mv, or +.054 pH (added t o the measured v a l u e ) . As Berner and Morse r e port measured pH t o two decimal p l a c e s , we have added 0.05 pH t o t h e i r measured values i n making our thermodynamic c a l c u l a t i o n s . For comparison, dual c a l c u l a t i o n s are presented i n Table I I f o r uncorrected and c o r r e c t e d pH. I n order t o o b t a i n d i f f e r e n t pH values i n pseudo-sea water and a r t i f i c i a l sea water a t constant PC0 , Berner and Morse added various amounts of HCI o r NaOH t o t h e i r s t a r t i n g s o l u t i o n s . Because the amounts of these a d d i t i o n s are not given i n t h e i r paper, we have c a l c u l a t e d them using the reported pH, PC0 , composition of the i n i t i a l s o l u t i o n (pseudosea water or a r t i f i c i a l sea w a t e r ) , and the charge balance c r i t e r i a f o r the aqueous model i n RATECALC. Our estimates of the amounts of these a d d i t i o n s of HCI and NaOH have been considered i n c a l c u l a t i o n of r a t e and are shown i n Table I I . Table I I a l s o gives the c a l c u l a t e d surface e q u i l i b r i u m pH (assuming surface PC0 = bulk f l u i d P C 0 ) , bulk f l u i d s a t u r a t i o n index ( S I = l o g Ω) and p r e d i c t e d r a t e . Far from e q u i l i b r i u m the c o r r e c t i o n f o r r e s i d u a l l i q u i d j u n c t i o n p o t e n t i a l i s not s i g n i f i c a n t , but the r e s i d u a l l i q u i d j u n c t i o n p o t e n t i a l becomes extremely important c l o s e t o e q u i l i b rium ( s p e c i f i c a l l y f o r r a t e s l e s s than approximately 100 mg cm y r " ) . Figure 11 shows a c l o s e c o r r e l a t i o n between c a l c u l a t e d r a t e s based on the j u n c t i o n p o t e n t i a l c o r r e c t e d pH and the ob served r a t e a t various C 0 p a r t i a l pressures. Most of our c a l c u l a t e d r a t e s are w i t h i n a f a c t o r of two of the observed. Some of the data (Figure 11) show a trend w i t h the computed rates l a r g e r than the observed as r a t e decreases. This trend i n departure of computed and observed r a t e s i s not understood. Sources of un c e r t a i n t y i n c l u d e the f o l l o w i n g : 1) u n c e r t a i n t y i n the (thermo dynamic) pH of the bulk f l u i d , 2) u n c e r t a i n t y i n the surface e q u i l i b r i u m pH due t o some u n c e r t a i n t y i n surface PC0 , 3) p o s s i b l e i n h i b i t i n g e f f e c t s i n t h e i r s o l u t i o n s , and 4) one must be aware o f the p o s s i b i l i t y o f other r e a c t i o n mechanisms o c c u r r i n g which are p r e s e n t l y u n i d e n t i f i e d . I f higher pH values are not due e n t i r e l y t o the a d d i t i o n of NaOH, but due, i n p a r t , t o the d i s s o l u t i o n of small amounts of CaC03, the bulk f l u i d s a t u r a t i o n w i t h respect t o c a l c i t e would be higher than that given i n Table I I and the c a l c u l a t e d r a t e would be slower. One r a t e near e q u i l i b rium a t one atmosphere C 0 (pH 6.00, Table I I ) i s c a l c u l a t e d t o be 15 times f a s t e r than the observed value. This d i f f e r e n c e could be accounted f o r by accompanying d i s s o l u t i o n of a small amount of CaC0 .


2

2

2

2

2

2

1

2

2

2

3


25.

P L U M M E R E T AL.


557

Figure 10. Dissolution rates from pHstat experiments of Berner and Morse (3) in pseudo-sea water at 25°C. No Pco dependence is observed at C0 partial pressures < 10' - atm, as expected. Range of rates observed by Plummer et al. (1) in dilute solutions shows that most rates at low Pco far from equilibrium agree with our rate model. One rate measurement of Berner and Morse (3) at 1 atm C0 shows little or no Pco dependence.


2

2

1

5

2

2

2

Figure 11. Comparison of observed rates of Berner and Morse (3) in pseudo-sea water and sea water at 25°C with the predicted rates. Most rates are within a factor of two of the observed.



-0 18 -0 18 -0 18 -0 18 -0 18 -1 5 -1 5 -1 5 -1 5 -1 5 -1 5 -2 0 -2 0 -2 .0 -2 0 -2 0

6.00 5.96 5.93 5.87 5.79 6.80 6.71 6.70 6.68 6.42 6.12 7.11 7.09 7.04 6.99 6.95

2

018 5 5 5 5 5 5 5 5 5 5 5

C0

-0 -1 -1 -2 -2 -2 -2 -2 -2 -3 -3 -3

ρ

Log

5.08 3.92 4.42 3.94 4.55 4.80 4.82 4.95 5.23 4.44 4.80 5.19

PH

OBSERVED

75. 318. 920. 1240. 1280. 18.8 96. 360. 430. 740. 950. 0.85 2.9 49. 71. 220.

1479. 12023. 5623. 35481. 3311. 1238. 1738. 1479. 1072. 6026. 1380. 759.

Rate -2 -1 mg cm yr

-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-

-00.153 0.028 0.152 0.034 0.016 0.013 0.007 -00.048 0.021 0.007

HCI

]

25 23 22 19 15 5 4 4 4 2 1 3 3 2 2 2

957 661 074 214 969 409 390 289 095 244 122 518 357 987 659 422

3 095 0•0000000.007 000-

NaOH

Computed adjust ments to i n i t i a l solution i n mmole/kg IL^O

6 091 6 079 6 071 6 058 6 042 6 867 6 858 6 857 6 856 6 841 6 832 7 123 7 .122 7 .118 7 .115 7 .113

bea Water 11 5 987 6 823 91 6 824 91 87 7 353 65 7 354 7 354 15 05 7 354 85 7 355 7 355 29 87 7 866 15 7 866 37 7 866

-0 29 -0 37 -0 42 -0 54 -0 70 -0 15 -0 33 -0 35 -0 39 -0 91 -1 51 -0 03 -0 .07 -0 .17 -0 .27 -0 .35

-2 -5 -4 -6 -5 -5 -5 -4 -4 -6 -6 -5 j

Log Ω

Equil ibrium pH

COMPUTED USING UNCORRECTED pH

1513. 1807. 2005. 2354. 2743. 93. 183. 191. 209. 381. 526. 15. 35. 80. 121. 150.

5031. 19892. 6621. 18914. 4930. 2937. 2658. 2189. 1327 . 6230. 2927 . 1410.

Rate -2 -1 mg cm yr

-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-

-00.135 0.020 0.135 0.030 0.013 0.010 0.005 -00.043 0.018 0.006

HCI

j

29.144 26.565 24.782 21.569 17.926 6.075 4.930 4.817 4.598 2.519 1.259 3.954 3.773 2.597 3.357 2.987

3.475 -0-0-0-0-0-0-00.009 -0-0-0-

NaOH

-0.19 -0.27 -0.33 -0.44 -0.60 -0.05 -0.23 -0.25 -0.29 -0.81 -1.41 +0.07 +0.03 -0.07 -0.17 -0.25

-2.01 -5.81 -4.81 -6.77 -5.55 -5.05 -4.95 -4.75 -4.19 -6.77 -6.05 -5.27

Log Ω

6 108 6 094 6 085 6.069 6 051 6 872 6 863 6 862 6 860 6.843 6.833 7.127 7 .126 7.115 7.122 7 .118

5 989 6.823 6.824 7.353 7.354 7.354 7.354 7.355 7.355 7.866 7.866 7 866

Equil ibrium pH

COMPUTED USING CORRECTED pH

Computed adjust ments to i n i t i a l solution i n mmole/kg H2O

Table II. Calculation of the Rates of Berner and Morse (3_)


m

2

1089. 1439. 1665. 2067. 2509. 34. 135. 145. 164. 353. 503. -39. -17. 35. 80. 113.

4854. 17780. 5952. 16897. 4434. 2658. 2410. 1992. 1224. 5592. 2649. 1297.

cm" -1 yr

Rate


-2. -2. -2, -2, -2. -2, -2, -2, -2, -2, -2

7.37 7.32 7.28 7.24 7.22 7.16 7.08 6.96 6.71 6.65 6.51

.6 .6 .6 .6 .6 .6 .6 .6 .6 .6 .6

-2.0 -2.0 -2.0 -2.0 -2.0 -2.0 -2.5 -2.5 -2.5 -2.5

6.93 6.35 6.82 6.57 6.45 6.19 7.30 7.22 6.87 6.58

6.7 27. 51. 68. 76. 176. 242. 336. 530. 610. 675.

245. 360. 380. 600. 710. 950. 20. 135. 540. 840.

-0-0-0-0-0-0-0-0-0-0-0-

-0-0-0-0-0-0-0-0-00.156

1. .801 1. .600 1. .456 1. .325 1. .264 1. .098 0, .910 0. .687 0. .381 0. .334 0, .242

2.312 1.920 1.791 1.003 0.760 0.416 1.665 1.439 0.145 -0-

-0.16 -0.26 -0.34 -0.42 -0.46 -0.57 -0.73 -0.97 -1.48 -1.59 -1.87

-Sea

-0.39 -0.55 -0.61 -1.11 -1..35 -1.87 -0.15 -0.31 -1.01 -1.59

164. 213. 229. 337. 378. 463. 64. 121. 283. 362.

7,.444 7,.442 7,.441 7,.440 7,.439 7 .438 7 .436 7 .434 7 .433 7 .431 7 .430 67. 103. 130. 154. 165. 196. 231. 275. 342. 356. 386.

W a t e r , Near E q u i l i b r i u m

7..112 7,.109 7..108 7..101 7,.099 7,.096 7,.371 7,.368 7..360 7,.357

-0-0-0-0-0-0-0-0-0-0-0-

-0-0-0-0-0-0-0-0-00.116

2. .029 1. .801 1. .635 1, .491 1. .422 1, .234 1, .023 0, .773 0, .432 0, .376 0, .271

2.721 2.156 2.011 1.126 0.853 0.468 1.618 1.880 0.222 -0-


-0. -0, -0, -0, -0. -0, -0, -0, -1, -1, -1

-0, -0. -0, -1, -1, -1, -0, -0. -0, -1,

.06 .16 .24 .32 .36 .48 .63 .87 .37 .49 .77

.29 .45 .51 .01 .25 .77 .21 .05 .91 .49

7,.447 7,.444 7..443 7 .441 , 7,.441 7 .439 , 7 .437 , 7,.435 7,.432 7..431 7 .430

7,.116 7..111 7,.110 7,.102 7,.100 7,.096 7..369 7,.373 7,.361 7,.358

25 67 96 123 136 170 210 258 330 335 375

183 201 319 362 446 86 22 266 350

128

ZD

οι οι

ο

"2.

ο!.

S"

OK

η

N>

to

οι


560

SYSTEMS

F i g u r e 11 shows that our r a t e equation, w i t h a p p r o p r i a t e thermodynamic c o r r e c t i o n s , s a t i s f a c t o r i l y p r e d i c t s observed r a t e i n sea water over a wide range of pH and PC0 f o r values of Ω between 0.0 and 0.6. Nearer e q u i l i b r i u m , u n c e r t a i n t i e s i n the c a l c u l a t i o n s and the experimental data (3) are too l a r g e f o r a r e l i a b l e t e s t of our model. We have a great deal more d i f f i c u l t y i n i n t e r p r e t i n g the r e s u l t s of Sjoberg (23, 1 4 ) . Most of our problems stem from S j o b e r g s experimental design which i n v o l v e d d i s s o l u t i o n i n 0.7 M KC1 s o l u t i o n u s i n g both pH-stat and f r e e d r i f t methods. Except f o r a few pH-stat measurements at 0.97 atm, most measurements were made a t very low PCO2. U n f o r t u n a t e l y , PCO2 was not a c t u a l l y c o n t r o l l e d and we only know that PCO2 was low owing t o bubbling of "C02-free" n i t r o g e n . Although there was probably very l i t t l e t r a n s f e r of C 0 from the r e a c t i o n system, and thus the r e a c t i o n was e s s e n t i a l l y c l o s e d t o C 0 as Sjoberg assumed, the a c t u a l PC0 i n s o l u t i o n depends on a number of f a c t o r s i n c l u d i n g bubbling r a t e and d i s s o l u t i o n r a t e . Our k i n e t i c r e s u l t s show that s u r face PC0 i s extremely important i n c o n t r o l l i n g r a t e because C 0 e q u i l i b r i u m w i t h c a l c i t e determines surface pH. Although Sjoberg was c o r r e c t i n assuming a r e a c t i o n system c l o s e d to C 0 and i n assuming PC0 was very low, s u r f a c e PC0 may have v a r i e d s i g n i f i c a n t l y . Our c a l c u l a t i o n s show that i f surface PC0 v a r i e d by an order of magnitude i n S j o b e r g s f r e e d r i f t experiments, surface e q u i l i b r i u m pH would vary by 0.66 pH. Sjoberg found that r a t e i n 0.7 M KC1 s o l u t i o n s was described 2


1

2

2

2

2

2

2

2

2

2

1

(17) where the brackets denote c o n c e n t r a t i o n , k i s a r a t e constant, A i s surface area, and C i s the value of f C a ] [CO ] at e q u i l i b r i u m . Taking values of k and C from Sjoberg (23), equation 17 becomes, a t 20°C, 2+

R = 1.60 χ 1 0 "

6

(1 -

1/2)

2

- 1

where R i s i n mmol cm" s e c . At low equation (equation 14) reduces t o

PCO2

2-

(18) and h i g h pH, our r a t e

a+ R

R = 1.14 χ 1 0 "

7

(1

) a

(19)

+

H (s)

at 20°C. I g n o r i n g , f o r the moment, the obvious d i f f e r e n c e i n r a t e constants, we f i r s t compare the form of equations 18 and 19 c o r r e l a t i n g çfc w i t h ( a H / a H ( s ) ) . Using RATECALC, we reconstructed a f r e e d r i f t d i s s o l u t i o n run i n 0.7 M KC1 i n a c l o s e d system a t 25°C. Figure 12 shows that these two terms behave s i m i l a r l y , but that 1/2 i s s l i g h t l y l a r g e r than the term +

+


25.

PLUMMER +

ET AL.

561


+

( a H / a H ( s ) )Ω . I n our c a l c u l a t i o n , though, we assumed a c l o s e d system and that surface PCO2 was equal t o the bulk f l u i d v a l u e , which i s c a l c u l a t e d near 1 0 ~ * atm. Bubbling of pure N gas w i l l lower t h i s value i n the bulk f l u i d and thus lower^ the s u r face PC0 . For example, r e f e r r i n g t o Figure 12, a t Ω^ = 0.5, our c a l c u l a t i o n s show that Ω^ and our term (aH /aH (s))Ω are i d e n t i c a l i f surface PC0 i s 10"" rather than 1 0 " . Thus, c o n s i d e r i n g the u n c e r t a i n t i e s i n S j o b e r g s PC0 and the problems a s s o c i a t e d with determining low values of surface PCO2, there may be no fundamental d i f f e r e n c e between the form of S j o b e r g s r a t e equation and ours under comparable experimental c o n d i t i o n s . Comparing r a t e constants i n equations 18 and 19 shows that S j o b e r g s i n i t i a l rates i n f r e e d r i f t experiments are 14 times f a s t e r than ours. There may be considerable u n c e r t a i n t y i n S j o b e r g s i n i t i a l free d r i f t rates as they are based on slopes of calcium vs time curves c a l c u l a t e d from the measured pH. We found i n our free d r i f t experiments (1) that rate was u n r e l i a b l e f o r the f i r s t s e v e r a l hours of r e a c t i o n a t a PC0 of 1 0 ~ ' owing t o non-equilibrium of the C0 -water system. Furthermore, S j o b e r g s f r e e d r i f t r a t e f a r from e q u i l i b r i u m i s 3.2 times f a s t e r than h i s i n i t i a l rate determined by pH-stat. Sjoberg (23, 14) a l s o shows that i n i t i a l r a t e decreases i n a supposedly C 0 - f r e e system by a d d i t i o n of C a C l . According t o our r a t e equation, added calcium should have l i t t l e e f f e c t on r a t e f o r a C 0 - f r e e system. The decrease i n rate observed by Sjoberg f o r a d d i t i o n of calcium may point t o the presence of small amounts of C0 i n h i s s t a r t i n g s o l u t i o n s . Despite problems i n i n t e r p r e t i n g S j o b e r g s r e s u l t s , there are s e v e r a l points of general agreement. Sjoberg's pH and PC0 dependence f a r from e q u i l i b r i u m i s s i m i l a r t o ours, as shown e a r l i e r . Forward rate i n the near absence of C 0 and H appears constant (Figure 6) which a l s o agrees w i t h the form of our f o r ward r a t e . We a l s o f i n d a s i m i l a r temperature dependence i n acids (Table I ) , and a t low PC0 and high pH, Sjoberg s (14·) r a t e constant has a temperature dependence of 6.8-8.4 kcal/mol which compares w i t h 7.9 kcal/mol measured by us. Because of our un c e r t a i n t i e s i n e s t i m a t i n g PC0 i n Sjoberg's experiments, f u r t h e r s p e c u l a t i o n regarding the c o m p a t i b i l i t y of h i s r e s u l t s and ours i s not warranted. Morse (21) r e c e n t l y reported n e a r - e q u i l i b r i u m pH-stat rates i n sea water a t 25°C and 1 0 ~ * atm C 0 . His r a t e s are a l l l e s s than 8 mg c m y r " . Table I I I compares our c a l c u l a t i o n s (using equation 15 and assuming surface PC0 i s equal t o the bulk f l u i d value) of a s e t of Morse's rates near e q u i l i b r i u m , and shows gen e r a l l y poor agreement. In c a l c u l a t i o n of Ω and aH ( s ) , no c o r r e c t i o n f o r l i q u i d j u n c t i o n p o t e n t i a l e r r o r i n measured pH was necessary, as i n our e a r l i e r c a l c u l a t i o n s f o r pseudo-sea water. In sea water one can use the apparent constant approach t o solve thermodynamic problems i n the carbonate system d i r e c t l y . We have c a l c u l a t e d surface e q u i l i b r i u m pH using the C 0 s o l u b i l i t y data 6

2

2

2

+

+

6 m h

6 , 2

2

1

2


1

1

1

2

5

2

1

2

2

2

2

2

1

2

+

2

1

2

2

2

5 3

2

-2

1

2

+

2



2

7.9 6.8 4.7 3.7 1.4 0.79 0.12 0.049 0.017

Rate mg cm y r

1

1

4

2

7.418 7.419 7.419 7.419 7.420 7.420 7.421 7.422 7.422

81.5 74.3 67.4 60.4 52.8 45.6 35.2 24.8 17.0

_ 1

7.518 7.510 7.502 7.493 7.486 7.477 7.465 7.452 7.442

Implied pH(s)

Calculated pH(s) Rate (open system) mg c m " y r

3

5

7.509 7.501 7.493 7.484 7.476 7.468 7.457 7.447 7.439

PCO2

(open system) .

— T h e o r e t i c a l c a l c i t e e q u i l i b r i u m pH i n a sea water system c l o s e d t o CO2.

6/

— Value o f pH(s) i m p l i e d by the observed r a t e and equation 15.

5/

— C a l c u l a t e d u s i n g equation 15 and the open system e q u i l i b r i u m pH.

— T h e o r e t i c a l c a l c i t e e q u i l i b r i u m pH a t b u l k f l u i d

3 /

6

.

pH(s) ( c l o s e d system)

— R e c a l c u l a t e d t o show t h i r d s i g n i f i c a n t f i g u r e using the apparent constants o f Weiss (24), Lyman (25), I n g l e et a l . ( 2 6 ) , and the measured pH and reported PCO2

2/

^ M o r s e (21).

0.620 0.649 0.680 0.712 0.745 0.780 0.828 0.876 0.917

7.32 7.33 7.34 7.35 7.36 7.37 7.383 7.395 7.405

2

Ω

PH

Observed

Table I I I .


25.

PLUMMER

E T AL.


563

of Weiss (24), the apparent constants of Lyman (25), and the ap parent c a l c i t e s o l u b i l i t y constant o f Ingle e t a l . (26). Also shown i n Table I I I are values of surface pH necessary f o r our r a t e equation t o reproduce Morse's r a t e s . The i m p l i e d surface pH i s 0.10 t o 0.02 higher than the c a l c u l a t e d e q u i l i b r i u m value at 1 0 - · atm C 0 ( open system e q u i l i b r i u m ) . This d i f f e r e n c e i n pH i m p l i e s a surface PCO2 s l i g h t l y lower than the bulk f l u i d v a l u e , i . e . , 10"" · t o 1 0 " · during Morse's pH-stat rate meas urements. The surface e q u i l i b r i u m pH values i m p l i e d by our rate equa t i o n and Morse's rates are a l l w i t h i n 0.01 pH of the t h e o r e t i c a l pH f o r c a l c i t e e q u i l i b r i u m i n sea water closed t o CO2 (Table I I I ) . In a c l o s e d system, c a l c i t e e q u i l i b r i u m determines both surface pH and PCO2, and r a t e depends, i n p a r t , on the f l u x of CO2 t o the s u r f a c e . Sjoberg (2^3) noted a s t i r r i n g dependence of rate a t pH 8 and very low C 0 p a r t i a l pressures, where c a l c i t e d i s s o l u t i o n has p r e v i o u s l y been a t t r i b u t e d t o surface r e a c t i o n a l o n e . The m a t e r i a l used by Morse was "whole Indian Ocean sediment" which i s l a r g e l y of biogenic o r i g i n . I t i s expected that the r e a c t i n g surface area i s considerably l e s s than the BET surface area used by Morse t o normalize r a t e . This may a l s o e x p l a i n some of the d i s p a r i t y between c a l c u l a t e d and observed rates (Table III). C a l c u l a t i o n of d i s s o l u t i o n r a t e using equations 14 and 15 becomes extremely s e n s i t i v e t o values of Ω and pH as e q u i l i b r i u m i s approached. C a l c u l a t e d rates l e s s than 100 mg c m y r " must be open t o considerable u n c e r t a i n t y owing t o the d i f f i c u l t y i n e s t i mating Ω and surface pH with s u f f i c i e n t accuracy. 2

5 3

2


2

68

2

5 6

2

-2

1

P r e c i p i t a t i o n . The rate model o f Plummer eit_ a l . (_1 ), a l though derived from d i s s o l u t i o n experiments, accounts f o r both forward and backward r e a c t i o n . I f no other mechanisms occur, t h i s r a t e model should a l s o describe the k i n e t i c s of c r y s t a l growth of c a l c i t e . There are s e v e r a l studies of the c r y s t a l growth of c a l c i t e (27 - J34 ), a l l using the seeded growth t e c h nique of Reddy and Nancollas (_27, 28). By t h i s method, w e l l c h a r a c t e r i z e d seed c r y s t a l s are introduced i n t o a s t a b l e super saturated s o l u t i o n o f NaHC0 -CaCl2. C r y s t a l growth begins imme d i a t e l y and i s f o l l o w e d by measurement of pH and t o t a l d i s s o l v e d calcium. The p a r t i a l pressure of CO2 i s not c o n t r o l l e d and tends to increase i n s o l u t i o n as c r y s t a l l i z a t i o n proceeds. Our c a l c u l a t i o n s show that some CO2 i s a l s o outgassed from s o l u t i o n during c r y s t a l growth. Most c r y s t a l growth experiments have been con ducted between pH 8 and 10, and a t CO2 p a r t i a l pressures between 10~ and 10"~ atm, the only exception being the work of Nancollas et a l . (34) which i s near pH 6 and 1.7 atm CO2. At low PC0 , Reddy and Nancollas (_27, .28) found that the r a t e of c r y s t a l growth was described by an equation of the form 3

3

5

2



564


SYSTEMS

Figure 12. Correlation of Ω with the term aH /aH+(s) Ω showing similarity of the terms, indicating that the form of Sjoberg's rate equation (14, 23) is similar to ours +

1/2

Figure 13. Typical variations in cal cium, pH, log Pco , and calcite satura tion (Ω) during crystal growth experi ments of Reddy (30, 35) in dilute NaHC0 -CaCl solutions

Ω '

2

3

2

0, Ό

1

20

*

α

Equilibrium

!

1

40 60 80 TIME (Minutes)


100

25.

PLUMMER E T AL.

R


k

565

}

= ~G Karoos" ~

( 2 0 )

2

Y±

where 1 · H+(s) +

(

2 2

)

+

C a l c u l a t i o n of the term a H / a H ( s ) i n s e v e r a l low PC0 c r y s t a l growth experiments gives values near 0.93 i n i t i a l l y and i n c r e a s ing t o 0.97 a t the t e r m i n a t i o n of the growth experiments. Thus the_ form of equations 21 and 22 i s s i m i l a r because the term i s n e a r l y constant and near u n i t y . More r e c e n t l y a rate equation which i s second order i n the instantaneous calcium y i e l d has been proposed (29) and a p p l i e d t o low PC0 c r y s t a l growth data (30, 32, 33.)· These s t u d i e s de s c r i b e r a t e of c r y s t a l growth by an equation of the form 2

2

R = k (C - C )

2

(23)

g

where R i s r a t e of c r y s t a l growth, k i s a c r y s t a l growth r a t e constant, C i s the c o n c e n t r a t i o n of d i s s o l v e d calcium i n s o l u t i o n as a f u n c t i o n of time and C i s the e q u i l i b r i u m calcium concen t r a t i o n a t that time. As a means of t e s t i n g our r a t e model during c r y s t a l growth, we examined d e t a i l s of t o t a l calcium and pH during four comparable c r y s t a l growth experiments (30, 35). Figure 13 compares t o t a l c a l c i u m , pH, l o g PC0 and c a l c i t e s a t u r a t i o n (Ω) i n the bulk f l u i d during a t y p i c a l run. Rate of c r y s t a l growth was c a l c u l a t e d using the d i f f e r e n c e i n successive calcium measurements, and v a r i e s from about 80 t o 2 χ 10~ mmol cm" s e c i n the four s e l e c t e d c r y s t a l growth experiments. When we assume that surface PC0 i s equal t o that c a l c u l a t e d i n the bulk f l u i d , and assume that c a l c i t e e q u i l i b r i u m determines surface pH, the c a l c u l a t e d r a t e s of c r y s t a l growth vary from 4 to 68 times f a s t e r than the observed v a l u e s , and g e n e r a l l y average ten to twenty times f a s t e r than the observed. These d i f f e r e n c e s between computed and observed rates are 2

9

2

- 1

2


566


s i g n i f i c a n t and i n d i c a t e e i t h e r that our model i s wrong, or that surface PCO2 values d i f f e r from those i n the bulk f l u i d . We have used these d i f f e r e n c e s to p r e d i c t the chemical p r o p e r t i e s of the surface during Reddy s c r y s t a l growth experiments (30, 35) assum ing our r e a c t i o n mechanism model describes the r e a c t i o n . Figure 14 shows the r a t i o of the i m p l i e d surface PC0 to the bulk f l u i d value as a f u n c t i o n of r e a c t i o n progress (Ω). E a r l y i n the r e a c t i o n , when c r y s t a l growth i s most r a p i d , our r a t e model and the data of Reddy (30, 35) imply that surface PCO2 i s approximately 5 times l a r g e r than the bulk f l u i d v a l u e . This r a t i o decreases as the r a t e of c r y s t a l growth decreases, w i t h the i m p l i e d surface PC0 n e a r l y twice the bulk f l u i d value a t the t e r m i n a t i o n of the run (which i s s t i l l q u i t e f a r from e q u i l i b r i u m ) . In Figure 15 we compare the t h e o r e t i c a l open system e q u i l i b r i u m surface pH (assuming surface PC0 = bulk f l u i d PC0 ) w i t h the surface pH i m p l i e d by the PC0 imbalance shown i n Figure 14. If our r e a c t i o n mechanisms can be a p p l i e d to c r y s t a l growth, our r a t e model p r e d i c t s that surface pH i s i n i t i a l l y 0.6 pH l e s s than the t h e o r e t i c a l open system e q u i l i b r i u m value and the d i f f e r e n c e decreases to about 0.3 pH a t t e r m i n a t i o n of the experiment. These d i f f e r e n c e s d i m i n i s h as the r e a c t i o n approaches e q u i l i b r i u m . These c a l c u l a t i o n s n e i t h e r prove nor disprove our mechanism model, s i n c e the i m p l i e d PCO2 (and pH) d i f f e r e n c e s are q u a l i t a t i v e l y c o n s i s t e n t . That i s , during the c r y s t a l growth e x p e r i ments, CO2 produced by CaC03 p r e c i p i t a t i o n increases i n the bulk f l u i d and some i s l o s t to the atmosphere. This net f l u x of CO2 i s c o n s i s t e n t w i t h the c a l c u l a t e d higher surface CO2 p a r t i a l pressures. We have made a p a r a l l e l c a l c u l a t i o n , s i m i l a r t o that given above f o r c r y s t a l growth a t low PC0 , using c r y s t a l growth data (34) near pH 6 and 1.7 atm. C0 . During t h i s experiment, of 110 minutes d u r a t i o n , most of the c r y s t a l growth occurred i n the f i r s t 40 minutes, during which Ω v a r i e d from 17.3 ( i n i t i a l l y ) t o 7.4 ( a t 40 minutes), w i t h the f i n a l value of Ω near 5.8 i n the bulk f l u i d . C a l c u l a t e d r a t e s (assuming surface PC0 i s equal t o the bulk f l u i d v a l u e s , and that c a l c i t e e q u i l i b r i u m then d e t e r mines surface pH) a r e a l l somewhat f a s t e r than the observed r a t e s , but during the f i r s t 40 minutes of r e a c t i o n , computed and observed r a t e s d i f f e r by only a f a c t o r of two or l e s s . A f t e r 40 minutes, the observed r a t e s decrease f a s t e r than the c a l c u l a t e d r a t e s ; the f i n a l c a l c u l a t e d r a t e being approximately 12.4 times f a s t e r than the observed. I t i s apparent from our c a l c u l a t i o n s of the r a t e of c a l c i t e c r y s t a l growth that the agreement i n computed and observed r a t e i s f a r more s a t i s f a c t o r y at higher PC0 than low PC0 . 1


2

2

2

2

2

2

2

2

2

2

Summary and D i s c u s s i o n This review has been l i m i t e d to s t u d i e s i n which s o l i d s u r face areas were reported. We have not considered s p e c i f i c exper-


P L U M M E R E T AL.


o

567

Reddy (30)


S1 Reddy (35)

/Equilibrium 0

1

2

3

Ω

4

5

6

7

Figure 14. Ratio of surface"Pco to bulk fluid Pco during crystal growth ex periments of Reddy (30, 35), as implied by the observed rates and the rate model of Plummer et al. (1) 2

2

9.0 8.8

Open System Equilibrium pH

8.6 h 8.4

Implied Surface pH Δ

On

Λ Λ

^

Ο •

8.2 8.0 0

3

4 Ω

Figure 15. Comparison of calculated pH in equilibrium with calcite at the bulk fluid Pco during crystal growth experiments of Reddy (30, 35) with the surface pH implied by our rate model and the observed rate as a function of calcite satu ration (Ω ) 2


568


iments i n v o l v i n g i n h i b i t i o n . From the remaining k i n e t i c s t u d i e s w i t h c a l c i t e , r a t e s range from -1 χ 10" mmol cm" s e c " ( p r e c i p i t a t i o n ) to about +1 χ 10"~ mmol cm s e c , while the r e s u l t s of v a r i o u s workers represent a range i n pH of about 0 to 10, PCO2 from 0.000001 to 1.7 atm, and temperature between -15 and 60°C. S o l u t i o n compositions vary from the r e l a t i v e l y simple CO2 - H 0 system to the C0 - sea water system. Hydrodynamic c o n d i t i o n s range from s t i r r e d batch experiments to experiments w i t h r o t a t i n g d i s k s and c y l i n d e r s and s o l u t i o n " d r i l l i n g " experiments w i t h h i g h velocity jets. Most r a t e s p r e d i c t e d using equations 3 and 13, or 14 and 15 are w i t h i n a f a c t o r of 20 of the observed and many are w i t h i n a f a c t o r of 2 or b e t t e r . The form of the forward r a t e as a func t i o n of PC0 and pH seems to agree w i t h that observed by us. In a d d i t i o n , the shape of c o n c e n t r a t i o n - time curves p r e d i c t e d by equations 3 and 13 are s i m i l a r to those observed i n f r e e d r i f t d i s s o l u t i o n experiments. U n c e r t a i n t i e s greater than a f a c t o r of 2 are probably s i g n i f i c a n t and point to three problem areas: 1) At low pH, r a t e depends s i g n i f i c a n t l y on the hydrodynamic t r a n s p o r t constant f o r H which i s not w e l l d e f i n e d . For example, at 25°C, our c a l c u l a t i o n s from observed r a t e s show that k j may vary from ^0.007 cm s e c under approximately laminar boundary l a y e r c o n d i t i o n s at the end of a r o t a t i n g d i s k (10) to about 0.23 cm s e c " at the impact of a j e t (at ^35 m sec ) on the c a l c i t e surface (9). Under the t u r b u l e n t c o n d i t i o n s of the s t i r r e d batch experiments of Plummer e_t a_l. ( 1 ) , k i i s near 0.05 cm s e c " . 2) Accurate comparison of r e s u l t s r e q u i r e s knowledge of r e a c t i o n s i t e d e n s i t y per u n i t surface area. C a l c i t e m a t e r i a l s used f o r k i n e t i c study have i n c l u d e d n a t u r a l marbles, limestones, hydrothermal c r y s t a l s of Iceland spar, t e s t s of calcareous organisms and l a b o r a t o r y and commercial p r e c i p i t a t e s . Surface areas, es timated by BET methods and g r a p h i c a l methods (based on p a r t i c l e s i z e d i s t r i b u t i o n ) range from about 0.005 to 2 m g . There are apparent d i s c r e p a n c i e s between g r a p h i c a l and BET surface areas and the question i s r a i s e d as to which type of surface area es timate i s most r e p r e s e n t a t i v e of the r e a c t i n g surface area. One could argue that BET surface areas overestimate the r e a c t i n g surface area. The r e a c t i n g surface area may c o i n c i d e w i t h a smoothed aqueous f i l m on the surface which can have much l e s s surface area than that determined by BET methods. The surface area of i n t e r s t i c e s may be e s s e n t i a l l y non-reactive owing to con t a c t w i t h s o l u t i o n s which are nearer to e q u i l i b r i u m . The uncer t a i n t y i n r e a c t i n g surface area i s most s i g n i f i c a n t i n r e a c t i o n s w i t h biogenic m a t e r i a l , (36, 21). Even i f the r e a c t i n g surface area can be d e f i n e d , i t i s s t i l l necessary to determine the num ber of r e a c t i o n s i t e s per u n i t r e a c t i n g area. The number of r e a c t i o n s i t e s may depend on the number of imperfections i n the c r y s t a l s t r u c t u r e , so that l e s s p e r f e c t c r y s t a l s may d i s s o l v e f a s t e r than more p e r f e c t c r y s t a l s under otherwise i d e n t i c a l con d i t i o n s . C l e a r l y , an i n t e r c a l i b r a t i o n i s r e q u i r e d where r a t e s 5

2

-2

2

1

- 1

2


2

2

+

- 1

1

1

1

2

_1


25.

PLUMMER E T AL.


are measured f o r d i f f e r i n g m a t e r i a l of known BET surface area under i d e n t i c a l hydrochemical c o n d i t i o n s . 3) The t h i r d general area of u n c e r t a i n t y concerns the c o n t r o l s of surface pH. We have shown (1) that a t r e l a t i v e l y high bulk f l u i d PC0 (>0.03 atm), surface PC0 and aH 0 are near the bulk f l u i d values and surface pH i s c o n t r o l l e d by c a l c i t e e q u i l i b r i u m at the bulk f l u i d PC0 and aH 0. C a l c i t e e q u i l i b r i u m a t the bulk f l u i d PC0 c o n t r o l s surface pH throughout most of our d i s s o l u t i o n experiments, and accounts f o r our c l o s e agreement w i t h the r e s u l t s of Erga and Terjesen (15) (PC0 = 0.135 - 0.952) and Terjesen (17) (PC0 = 0.97 atm). When we assume surface PCO2 i s equal t o bulk f l u i d PC0 during c a l c i t e d i s s o l u t i o n i n sea water, c a l c u l a t e d r a t e s greater than 100 mg/cm /yr are w i t h i n a f a c t o r of two of those observed by Berner and Morse ( 3 ) . Even c a l c u l a t e d r a t e s of c a l c i t e c r y s t a l growth a t high PCO2 are w i t h i n a f a c t o r of two o f the observed ( 3 4 ) . At low PCO2 and nearer e q u i l i b r i u m , however, d i s c r e p a n c i e s i n c a l c u l a t e d r a t e s of d i s s o l u t i o n and p r e c i p i t a t i o n become s i g n i f i c a n t , w i t h c a l c u l a t e d r a t e s , based on the assumption of s u r face PC0 = bulk f l u i d PC0 , g e n e r a l l y f a s t e r than the observed r a t e . C a l c u l a t i o n s show that near e q u i l i b r i u m , c a l c u l a t e d r a t e s of d i s s o l u t i o n and p r e c i p i t a t i o n are extremely s e n s i t i v e to s u r face pH. I t seems l i k e l y that our e a r l i e r p r e d i c t i o n that s u r face PC0 i s equal t o the bulk f l u i d value (1) i s only v a l i d a t r e l a t i v e l y high PC0 (PC0 >0.03 atm). Surface PC0 depends i n part on the f l u x of CO2 t o the s u r face during d i s s o l u t i o n and from the surface during p r e c i p i t a t i o n . P o s s i b l e k i n e t i c problems r e l a t e d t o the CO2 f l u x are discussed elsewhere (37, 4·). During d i s s o l u t i o n , surface PCO2 i s expected to be s l i g h t l y l e s s than the bulk f l u i d v a l u e , and during p r e c i p i t a t i o n , surface PC0 should be greater than the bulk f l u i d v a l u e . This e f f e c t i s most n o t i c a b l e when PC0 of the bulk f l u i d i s low (

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