Chemical Modeling in Aqueous Systems - American Chemical Society

22 Dissolution Kinetics of Silicate Rocks—Application to

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Solute Modeling ART

F. WHITE and HANS C. CLAASSEN

U.S. Geological Survey, Denver, CO 80225

S i l i c a t e minerals comprise more than 75 percent of the rocks with which ground water comes i n contact (1). Quantitative knowledge of the weathering rates of these minerals could provide an important means of estimating the t o t a l residence time a water has been i n contact with a given s i l i c a t e rock, the effective surface area of the aquifer, and other information pertinent i n defining a given hydrogeologic system (for a specific example, see Claassen and White's report i n these proceedings). Since the work of Daubreé i n 1867 (2), workers have experimented to define the dissolution rates of s i l i c a t e minerals. This paper will b r i e f l y review the types of reaction rates that have been observed, followed by more detailed discussion concerning the dependence of these rates on constituents i n the aqueous media, and the implications for solute modeling. The Rate Expression S i l i c a t e dissolution can generally be described by one of two rate expressions (3,4): Q = Q01 + k ,

(1)

l t

5

or

Q = Q0p + k t , (2) Ρ Ρ where Q (mol/cm ) i s the mass transfer of a species into the aqueous solution per unit surface area of the s o l i d , Qi and Q (mol/cm-) are the linear and parabolic mass transfers extrapo lated to time t, equal to zero, and kj (mol/cm sec) and k (mol/cm sec ) are the respective linear and parabolic rate constants. Figures 1 and 2, respectively, show the mass transfer of sodium, Q , plotted against time (sees), and the square root of time (sees ), for dissolution experiments involving laboradori t e , a plagioclase feldspar, and obsidian^ a volcanic glass. Both 2

2

2

2

2

Na

2

0-8412-0479-9/79/47-093-447$06.75/0 This chapter not subject to U.S. copyright Published 1979 American Chemical Society


448

CHEMICAL

M O D E L I N G IN AQUEOUS

0.5

1.0 3

Time ( s e c ^ χ 1 0 " ) *

Figure 1.

SYSTEMS

5

Mass transfer rates of sodium from a plagioclase feldspar into solution at pH 6.0 and 25°C


22. WHITE AND CLAASSEN Dissolution Kinetics of Silicate Rocks 449


450

CHEMICAL MODELING IN

AQUEOUS SYSTEMS

experiments were conducted under a n i t r o g e n atmosphere at 25°C + 0.1 using a Metrohm pH s t a t t i t r a t o r and .01 Ν HC1. The s o l i d l i n e s through the data are l i n e a r r e g r e s s i o n f i t s f o r the l i n e a r r a t e expression (equation 1), and the dashed l i n e s r e g r e s s i o n f i t s for the p a r a b o l i c r a t e (equation 2). Data p o i n t s at short r e a c t i o n times which represent n e i t h e r l i n e a r nor p a r a b o l i c rates are excluded from the s t a t i s t i c a l f i t . Based on the r e g r e s s i o n c o e f f i c i e n t , r , the l i n e a r r a t e best describes p l a g i o c l a s e d i s s o l u t i o n , and the p a r a b o l i c r a t e best describes glass d i s s o l u t i o n . The d i f f e r ence i n r a t e expression under i d e n t i c a l experimental c o n d i t i o n s emphasizes the r o l e of s i l i c a t e s t r u c t u r e and composition i n determining the d i s s o l u t i o n mechanism. Figures 1 and 2 show that the i n t e r c e p t s Q0 and Q at t = 0 are not zero. Rapid i n i t i a l mass t r a n s f e r i n t o s o l u t i B n at short times i s a t t r i b u t e d to exchange between aqueous hydrogen ions and c a t i o n s s i t u a t e d at or near the f r e s h s i l i c a t e surface. Tamm (5) and G a r r e l s and Howard (6) have demonstrated the r e v e r s i b i l i t y of such surface exchange between hydrogen and potassium ions i n potassium f e l d s p a r s . However, i n the case of magnesium s i l i c a t e s , Luce and others (4) showed that such exchange was not s t o i c h i o m e t r i c , owing to establishment of surface charge and the e l e c t r i c double l a y e r . Three b a s i c r e a c t i o n mechanisms have been invoked by v a r i o u s workers to e x p l a i n the long-term r a t e expressions (equations 1,2): I. The d i s s o l u t i o n r a t e i s c o n t r o l l e d by r e a c t i o n of the unaltered s i l i c a t e w i t h aqueous hydrogen ions at the i n t e r f a c e between the two phases (7, 8, 9). I I . The d i s s o l u t i o n r a t e i s c o n t r o l l e d by i n t e r d i f f u s i o n of hydrogen or hydronium ions and species contained i n l a t t i c e s i t e s w i t h i n the i n t e r i o r of the s i l i c a t e phase. This process r e s u l t s i n a leached l a y e r c o n s i s t i n g mainly of s i l i c a and alumina. Such a l a y e r may r e t a i n the o r i g i n a l s i l i c a t e s t r u c t u r e (10, 11) or may represent a c o l l a p s e d or hydrated l a y e r (12, 13). I I I . The d i s s o l u t i o n r a t e i s c o n t r o l l e d by d i f f u s i o n through a continuously growing p r e c i p i t a t e l a y e r that forms on the s i l i c a t e surface. Such a p r o t e c t i v e b a r r i e r has been p o s t u l a t e d to c o n s i s t of an amorphous a l u m i n o - s i l i c a phase (14) or a mono- or multi-phase c r y s t a l l i n e a l u m i n o - s i l i c a t e assemblage (15). Assuming a constant surface area, d i s s o l u t i o n at a s o l u t i o n s o l i d i n t e r f a c e (Case I) r e s u l t s i n l i n e a r k i n e t i c s i n which the r a t e of mass t r a n s f e r i s constant w i t h time (equation 1 ) . A n a l y t i c a l s o l u t i o n s to the d i f f u s i o n equation r e s u l t i n p a r a b o l i c r a t e s of mass t r a n s f e r (4, 16) (equation 2 ) , This r e s u l t i s obtained whether the boundary c o n d i t i o n s are defined so d i f f u s i o n occurs across a p r o g r e s s i v e l y t h i c k e n i n g , leached l a y e r w i t h i n the s i l i c a t e phase (Case I I ) , or across a growing p r e c i p i t a t e l a y e r forming on the s i l i c a t e surface (Case I I I ) . Another case of l i n e a r k i n e t i c s (equation 1) may occur when the r a t e of formation of a metastable product or leached l a y e r at the f r e s h s i l i c a t e surface becomes equal to the r a t e at which t h i s l a y e r i s destroyed at the aqueous 2


22.

WHITE AND CLAASSEN

Dissolution Kinetics of Silicate Rocks

451

i n t e r f a c e (4, 11, 17); that i s , such steady s t a t e d i f f u s i o n across a l a y e r of constant thickness r e s u l t s i n a l i n e a r mass t r a n s f e r r a t e (equation 1 ) . The above hypotheses are based p r i n c i p a l l y on r a t e expres sions d e s c r i b i n g changes i n experimental aqueous compositions such as those shown on Figures 1 and 2. As i n d i c a t e d , more than one r e a c t i o n mechanism can be invoked to e x p l a i n the observed r a t e expressions. S u b s t a n t i a t i n g evidence, p a r t i c u l a r l y regarding the c o n d i t i o n of the s o l i d s t a t e during d i s s o l u t i o n , i s meager. The e x i s t e n c e of d i f f u s i o n i n leached l a y e r s of a r t i f i c i a l s i l i c a t e glass has been confirmed by step-wise d i s s o l u t i o n of the g l a s s w i t h h y d r o f l u o r i c a c i d (JL2, 13, 18). The extent of the s t r u c t u r a l c o l l a p s e of t h i s l a y e r was dependent on the s i z e r a t i o of the sub s t i t u t i n g ions and cations o r i g i n a l l y contained i n the s i l i c a t e s t r u c t u r e . The occurrence of l i t h i u m d i f f u s i o n through the leached l a y e r of an a r t i f i c i a l s i l i c a t e glass was confirmed using an i o n - s p u t t e r i n g technique (19). The occurrence of a p r e c i p i t a t e l a y e r c o n t r o l l i n g the r a t e of d i f f u s i o n i s more tenuous. Various amorphous p r e c i p i t a t e s , i n ad d i t i o n t o c r y s t a l l i n e phases, i n c l u d i n g boehmite, k a o l i n i t e , and h a l l o y s i t e , have been shown t o form on s i l i c a t e surfaces during d i s s o l u t i o n (20, 21, 22, 23). However, based on a summary of sur face c h a r a c t e r i s t i c s , P e t r o v i c (24) concluded that such phases g e n e r a l l y occur as i n d i v i d u a l p a r t i c l e s on the s i l i c a t e s u r f a c e , and not as l a y e r s coating the surface. The r e s u l t i n g high p o r o s i t y would tend t o exclude such m a t e r i a l as a d i f f u s i o n - l i m i t i n g medium. P e t r o v i c and others (25), using X-ray photoelectron spectros copy, f a i l e d t o detect the presence of e i t h e r a leached or p r e c i p i t a t e d l a y e r on a l k a l i f e l d s p a r s reacted a t 82 C. The d e r i v a t i v e of mass t r a n s f e r w i t h respect t o time f o r equations 1 and 2 i s , r e s p e c t i v e l y 3Q/3t = k

l 5

(3)

and 3Q/3t = ^k t " ^ . (4) Ρ The r a t e of mass t r a n s f e r w i l l be constant with time f o r the l i n e a r r a t e and w i l l c o n t i n u a l l y decrease f o r the p a r a b o l i c r a t e . For long times, such as those encountered i n hydrogeologic e n v i ronments, the l i n e a r rates of mass t r a n s f e r may be expected t o dominate over the p a r a b o l i c r a t e s . Although the d u r a t i o n of exper imental r e a c t i o n s i s short compared t o such times, evidence e x i s t s that a s h i f t from p a r a b o l i c t o l i n e a r rates does occur. I n an a r t i f i c i a l s i l i c a t e glass a t elevated temperatures (60-100 C ) , Rana and Douglas (3) found that change from p a r a b o l i c t o l i n e a r k i n e t i c s occurred between 6 minutes and 66 hours, depending on the glass composition. Busenberg and Clemency (26) noted that changeover


452


AQUEOUS SYSTEMS

during the r e a c t i o n of p l a g i o c l a s e f e l d s p a r at 25°C occurred a f t e r approximately 20 days (26). One of the problems i n p o s t u l a t i n g l i n e a r r e a c t i o n s f o r a l l n a t u r a l long-term processes l i e s i n the problem of congruency. Almost a l l experimental r e a c t i o n s , whether p a r a b o l i c or l i n e a r , are incongruent; that i s , the r a t i o s of mass t r a n s f e r s of chemical species i n t o s o l u t i o n are not d i r e c t l y prop o r t i o n a l to the molecular composition of the d i s s o l v i n g phase(14). Incongruent mass t r a n s f e r i n the case of p a r a b o l i c k i n e t i c s based on d i f f u s i o n c o n t r o l can be r e a d i l y explained by d i f f e r e n c e s i n the d i f f u s i o n c o e f f i c i e n t s of chemical species. However, the proposed mechanisms invoked to e x p l a i n l i n e a r k i n e t i c s i n v o l v e the d i s s o l u t i o n of the bulk s i l i c a t e phase, which, over extended p e r i o d s , should r e s u l t i n the chemical components being t r a n s f e r r e d to s o l u t i o n from the s i l i c a t e i n t h e i r s t o i c h i o m e t r i c r a t i o s (25). However, many f i e l d s t u d i e s have shown that s i l i cates weather incongruently i n nature (27). This i s supported by our s t u d i e s of ground waters a s s o c i a t e d w i t h v i t r i c r h y o l i t e tuffs. E f f e c t of S p e c i f i c Aqueous Ions on the Rate

Expression

One parameter necessary f o r modeling s i l i c a t e d i s s o l u t i o n k i n e t i c s i s the i n f l u e n c e of aqueous chemistry on the r a t e express i o n . Lagache and others (7) found that f o r K-feldspar d i s s o l u t i o n at 200 C, the r a t e of r e l e a s e of s i l i c a and alumina was i n v e r s e l y p r o p o r t i o n a l to t h e i r r e s p e c t i v e concentrations i n aqueous s o l u t i o n . On the other hand, Wollast (28) found that the r e l e a s e of s i l i c a and alumina from K-feldspar at room temperature was independent of aqueous concentrations. Wollast suggested that the r e a c t i o n r a t e i s i n f l u e n c e d by aqueous concentrations only when those concentrations approach s a t u r a t i o n w i t h respect to a product phase. However, extensive data c o l l e c t e d by the authors (29) on v i t r i c t u f f s and o b s i d i a n showed that the r e s u l t i n g p a r a b o l i c r a t e expressions f o r c a t i o n s , f a r from e q u i l i b r i u m w i t h a product phase, are s t r o n g l y dependent on the concentrations of c e r t a i n c a t i o n s i n c o e x i s t i n g aqueous s o l u t i o n . The aqueous-dissolution experiments were performed i n the f o l l o w i n g manner. I n d i v i d u a l 25-, 50-, 100-, and 200-g p o r t i o n s of glass were added to 2-L volumes of deionized water i n p o l y e t h ylene Erlenmeyer f l a s k s . The f l a s k s were placed i n constanttemperature water baths. The mixtures were a g i t a t e d by s t i r r i n g paddles at a r a t e j u s t s u f f i c i e n t to keep the g l a s s i n suspension. Surface area determinations before and a f t e r i n d i v i d u a l e x p e r i ments i n d i c a t e d no surface area change due to abrasion during agitation. Commercial grade CO2 and compressed a i r , c o n t r o l l e d by flow meters, were c o n t i n u a l l y mixed p r i o r to being bubbled through the s o l u t i o n s . The r e s u l t i n g p a r t i a l pressures of CO2, which e q u i l i brated w i t h the water, determined the pH ranges of the experiments.


22.

WHITE AND CLAASSEN

453


E q u i l i b r a t i o n of the s o l u t i o n s was accomplished p r i o r t o a d d i t i o n of s o l i d and v e r i f i e d by pH measurements. Immediately a f t e r a d d i t i o n of the g l a s s phase, the pH of the system i n c r e a s e d , i n d i c a t i n g r a p i d hydrogen i o n consumption. A f t e r approximately 24 hours, the r a t e of consumption decreased. This e f f e c t , coupled w i t h the b u f f e r i n g e f f e c t of i n c r e a s i n g bicarbonate c o n c e n t r a t i o n s , confined subsequent pH increases t o an average of about 0.3 u n i t s f o r the remainder of a given experiment. Twenty 5-ml a l i q u o t s of the homogenized suspension were withdrawn w i t h a p l a s t i c s y r i n g e at appropriate time i n t e r v a l s . Samples were f i l t e r e d through 0.45-ym membrane f i l t e r s and analyzed f o r major d i s s o l v e d c o n s t i t uents . F i g u r e 3 shows a p l o t of the mass t r a n s f e r data f o r sodium from v i t r i c R a i n i e r Mesa t u f f p l o t t e d against the square root of time i n seconds f o r four d i f f e r e n t surface-to-volume r a t i o s a t 25 C and an average pH o f 4.75. Experimental data are presented i n Table I . The s o l i d l i n e s represent the l i n e a r r e g r e s s i o n f i t s to the data. Because the p a r a b o l i c mass t r a n s f e r i s normalized per u n i t surface area, the r e a c t i o n r a t e , k, i d e a l l y should be independent of the t o t a l surface area used i n a given experiment. However, F i g u r e 3 c l e a r l y shows that the r e a c t i o n r a t e s are lower f o r experiments i n v o l v i n g greater t o t a l surface areas. A greater surface area produces a l a r g e r t o t a l mass t r a n s f e r , and, f o r a f i x e d s o l u t i o n volume, a greater aqueous c o n c e n t r a t i o n . This i n creased c o n c e n t r a t i o n apparently i n h i b i t s the r e l e a s e r a t e of sodium from the g l a s s , as shown on Figure 3. The i n h i b i t i o n of the r e l e a s e of sodium can be demonstrated more d i r e c t l y by a d d i t i o n of sodium c h l o r i d e t o the aqueous s o l u t i o n s , p r i o r t o i n t r o d u c t i o n of the v i t r i c t u f f . In Figure 4, data l a b e l e d C, c o n t a i n i n g no sodium c h l o r i d e , cover the same experiment shown on F i g u r e 3. Data l a b e l e d Ε and F are, respec t i v e l y , f o r experiments i n which 1.5 χ 10"^ and 3.0 χ 10~ mol/Ι οί NaCl were added t o s o l u t i o n . Experimental data are presented i n Table II· The data show only the sodium mass t r a n s f e r from the g l a s s and not sodium introduced as NaCl. The s o l i d l i n e s represent l i n e a r r e g r e s s i o n f i t s t o the data. As shown i n Figure 4, i n c r e a s i n g a d d i t i o n s of NaCl p r o g r e s s i v e l y decrease the slope of the r e g r e s s i o n l i n e , and, consequently, the p a r a b o l i c r a t e constant. F i g u r e 5 shows calcium data f o r experiments C, G, and H, i n which, r e s p e c t i v e l y , no calcium c h l o r i d e , 1.5 χ 10"" , mol/L C a C l 2 , and 3.0 χ 10" mol/L C a C l 2 were i n i t i a l l y added to s o l u t i o n . Decreases i n calcium r a t e constants w i t h increases i n C a C l 2 are smaller than the decreases i n the sodium r a t e constants w i t h comparable a d d i t i o n s of NaCl (Figure 4). Note, however, the s t r o n g i n h i b i t i o n of added calcium on the i n i t i a l - e x c h a n g e p a r t of the r e a c t i o n . Figure 5 shows t h a t , a t short times, experiments G and H produced a net-negative mass t r a n s f e r i n which calcium ions were sorbed from s o l u t i o n onto the g l a s s s u r f a c e . Experiments on the v i t r i c t u f f showed that the r a t e of mass t r a n s f e r of an i o n from the g l a s s was i n h i b i t e d s p e c i f i c a l l y by 4

4

4


454

CHEMICAL MODELING IN AQUEOUS

SYSTEMS

Fi gure 3. Effect of surface to volume ratios on inhibition of sodium mass transfer from a rhyolitic tuff at an average pH of 4.83 and 25°C. Solid lines are statistical fits to data points. Dashed lines predict inhibition based on diffusion model.

*

A

0.0078 .024 .055 .094 .138 .294 .415 .495 .702 .825 .921 1.09 1.21 1.30 1.37 1.44 1.52 1.63 1.71

t

Na

6

0.61 .75 .93 1.15 1.12 1.25 1.33 1.33 1.52 1.57 1.57 1.68 1.71 1.76 1.87 1.84 1.89 1.95 1.95

Q

(0.38 Χ 1 0

Data not a v a i l a b l e .

Sample No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

S o l i d surface area - s o l u t i o n volume r a t i o

Experiment

1 0

4.23 4.38 4.37 4.39 4.40 4.46 4.46 4.43 4.53 4.47 4.51 4.54 4.49 4.54 4.54 4.60 4.59 4.60 4.54

pH

2

cm /L) 6

2

0.0078 .025 .052 .095 .127 .289 .412 .522 .722 .842 .937 1.10 1.22 1.35 1.38 1.44 1.53 1.64 1.72

t Na

0.56 .72 .85 .88 .93 1.15 1.20 1.25 1.28 1.39 1.41 1.47 1.49 1.52 1.55 1.60 1.60 1.63 1.68

Q

4.38 4.44 4.49 4.53 4.49 4.57 4.61 4.60 4.63 4.65 4.67 4.68 4.65 4.72 4.71 4.70 4.70 4.70 4.75

pH

(0.75 X 1 0 cm /L)

Β

0.0078 .025 .052 .084 .118 .285 .409 .517 .722 .842 .937 1.10 1.22 1.32 1.39 1.44 1.55 1.64 1.72

t Na

6

0.61 .69 .77 .88 .91 1.01 1.11 1.14 1.19 1.19 1.25 1.30 1.33 1.35 1.35 1.38 1.38 1.41 1.41

Q

(1.5 X 10

C

PH

4.51 4.58 4.59 4.64 4.64 4.73 4.73 4.74 4.79 4.78 4.82 4.85 4.81 4.85 4.84 4.82 4.86 4.92 4.84

2

cm /L)

D

0.0078 .024 .051 * .103 .278 .404 .516 .727 .842 .937 1.10 1.22 1.32 1.38 1.45 1.53 1.64 1.71

t

Q

6

2

4.77 4.84 4.96 * 5.22 4.87 4.93 4.92 4.83 4.96 4.99 5.02 5.00 5.02 5.01 4.99 4.99 5.07 5.00

pH

cm / L )

0.54 .59 .69 * .74 .87 .94 1.00 1.04 1.07 1.09 1.11 1.11 1.13 1.15 1.17 1.17 1.20 1.20

Na

(3.0 X 10

(mol/cm Χ 1 0 ) , And pH, For Experiments Of D i f f e r e n t T o t a l Surface Areas

2

Table I . — E x p e r i m e n t a l Data L i s t e d As Time, t (s^.10 ) , Mass T r a n s f e r Of Sodium, Q.

3


Sample No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Experiment

10

r

m

3

0.0078 .030 .052 .120 .281 .400 .509 .712 .835 .885 1.05 1.17 1.31 1.37 1.44 1.55 1.63 1.73 1.80

t Na

0.48 .53 .73 .80 .94 1.09 1.19 1.23 1.27 1.27 1.27 1.34 1.34 1.38 1.34 1.38 1.45 1.45 1.49

Q

4

0.29 .33 .41 .47 .54 .63 .70 .77 .76 .76 .83 .83 .89 .92 .88 .90 .94 (*) (*)

^Ca 4.46 4.51 (*) 4.61 4.75 4.73 4.80 4.76 4.81 4.81 4.85 4.90 4.90 4.83 4.86 4.83 4.93 5.02 5.07

pH

(1.5 X 10- N NaCl added)

2

2

0.0078 .030 .052 .106 .276 .391 .509 .710 .840 .871 1.05 1.17 1.34 1.37 1.44 1.54 1.63 1.74 1.80

t Na

0.31 .57 .61 .79 .79 .88 .92 1.00 1.07 1.07 1.09 1.09 1.14 1.09 1.14 1.14 1.14 1.18 1.22

Q

0.30 .33 .39 .48 .61 .63 .70 .74 .77 .77 .82 .86 .90 .94 .92 a±r and i s defined as


1

D

N a

C

D

Na+,H+

=

D

Na+ *

Na+

+

V C

D

Na+ Na+

+

°H+

H

5

(7) W

where I> + and are the constant s e l f - d i f f u s i o n c o e f f i c i e n t s of sodium and hydrogen i o n s , and v j + and C + are the c o n c e n t r a t i o n of d i f f u s i b l e sodium and hydrogen i o n s . As i n d i c a t e d by H e l f f e r i c h (32), the i n t e r d i f f u s i o n c o e f f i c i e n t i s g e n e r a l l y not a constant but v a r i e s continuously w i t h changing concentrations of the i n t e r d i f f u s i n g species. Equation 7 i s s t r i c t l y true only i f sodium i s the s o l e species d i f f u s i n g from the s i l i c a t e . In the case of the v i t r i c t u f f p r e v i o u s l y modeled, the d i f f u s i o n of sodium i s a l s o r e l a t e d to other c a t i o n s d i f f u s i n g from the glass by the common f l u x of hydrogen i o n s . The use of such an i n t e r d i f f u s i o n c o e f f i c i e n t r e s u l t s i n an exceedingly complex s o l u t i o n to equation 5. A s i m p l i f i e d s o l u t i o n was e s t a b l i s h e d which permits the apparent sodium d i f f u s i o n c o e f f i c i e n t to be an e m p i r i c a l f u n c t i o n of pH. Figure 10 shows four experiments conducted at an average pH of 7.13 and 25 C . Table I I I l i s t s the experimental data. The s o l i d l i n e s represent the l i n e a r r e g r e s s i o n f i t to the data. Although the surface-to-volume r a t i o s are i d e n t i c a l to data i n Figure 3 (pH 4.75), the r e l a t i v e slopes are much g e n t l e r , i n d i c a t i n g a decrease i n the p a r a b o l i c r a t e s w i t h i n c r e a s i n g pH. The two v a r i a b l e s i n the numerical s o l u t i o n which define the rates of mass t r a n s f e r i n experiments of equal surface-to-volume r a t i o s are the s u r f a c e adsorption isotherm and the apparent d i f f u s i o n c o e f f i c i e n t . Exchange experiments were conducted i n which glasses reacted w i t h aqueous s o l u t i o n s at pH 6.0 and 7.0 f o r s e v e r a l weeks were r a p i d l y Na

C

a

R


22.

WHITE AND CLAASSEN

Figure

9.


Effect of pH on the parabolic reaction coefficients for species of different valency during dissolution of a rhyolitic tuff at 25°C

467


468

CHEMICAL MODELING IN AQUEOUS

SYSTEMS

Figure 10. Effect of surface-to-volume ratios on inhibition of sodium mass transfer from a rhyolitic tuff at an average pH of 7.13 and 25°C. Solid lines are statistical fits to data points. Dashed lines predict inhibition based on diffusion model.

*

I

1.05 1.09 1.09 1.15

1.57 1.62 1.64 1.79

Na

0.59 .60 .64 * * .83 .85 .88 .88 .88 * .96 1.01 1.01

Q

6

0.0078 .030 .052 .124 .292 .407 .502 .715 .785 .926 1.10 1.18 1.32 1.41

t

(0.38 X 1 0

Data not a v a i l a b l e .

Sample No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Solid surface area - s o l u t i o n volume r a t i o

Experiment

1 0

6.79 * 6.85 6.89

6.35 6.62 6.49 6.77 6.80 6.70 6.69 6.73 6.70 6.60 6.61 6.80 6.70 6.70

PH

2

cm /L) 6

2

0.024 .051 .094 .130 .291 .420 .526 .732 .879 .939 1.06 1.17 1.22 1.32 1.39 1.44 1.53 1.71 1.74

t Na

0.43 .49 .60 .55 .63 .67 Λ .72 .77 .84 .81 .81 .85 .85 .84 .87 .93 .89 .92

Q

6.52 6.67 * 6.63 6.69 6.74 6.75 6.80 7.01 7.10 6.91 7.00 7.07 6.91 6.91 6.91 6.82 6.95 6.96

PH

(0.75 Χ ΙΟ cm /L)

J

0.025 .052 .088 .120 .286 .416 .523 .730 .887 .937 1.06 1.17 1.22 1.32 1.38 1.44 1.53 1.71 1.74

t

0.25 .35 .37 .41 .47 * .52 .57 .60 .60 .60 .63 .65 .66 .65 .66 .68 .69 .70

%a

(1.5 Χ 1 0

Κ 6

6.85 6.77 6.85 6.79 7.01 7.00 6.98 7.15 7.20 7.22 7.20 7.18 7.20 7.25 7.12 7.11 7.06 7.13 7.06

PH

2

cm /L)

]

L 5

2

.109 .281 .411 .523 .730 .877 .939 1.07 1.17 1.22 1.32 1.38 1.44 1.53 1.71 1.74

.025 .052

t

.48 .50 .54 .55 .57 .57 .58 .57 .57 .59 .61 .62 .63

•k

Na

0.26 .29 * .39 .46

Q

7.42 7.50 7.28 * 7.00 7.29 7.28

6.95 7.16 6.90 7.32 7.48 7.44 7.42 7.54

7.08 7.00

PH

(3.0 Χ ΙΟ ιcm /L)

(mol/cm Χ 1 0 ) , And pH, For Experiments Of D i f f e r e n t T o t a l Surface Areas

6

Table I I I . — E x p e r i m e n t a l Data L i s t e d As Time, t ( s ^ . H T ) , Mass Transfer Of Sodium, Q

3



470


AQUEOUS SYSTEMS

t i t r a t e d to pH 4.0. The l a c k of sodium r e l e a s e i n t o s o l u t i o n s t r o n g l y suggested that the surface sodium concentration was unaf f e c t e d by aqueous hydrogen concentrations. A match to the data (Figure 10) was sought assuming an i d e n t i c a l isotherm to that which defined the surface sodium concentrations at pH 4.75. A new pH-dependent apparent d i f f u s i o n was then c a l c u l a t e d . The dashed l i n e s i n F i g u r e 10 are the s o l u t i o n s generated by the model. Com p a r i s o n i s good between r a t e constants based on the l i n e a r regres s i o n f i t of the data and those based on the numerical model, using 22

2

an apparent d i f f u s i o n c o e f f i c i e n t of 1.7 χ 1 0 ~ cm /s. As ex pected f o r an i n t e r d i f f u s i o n process i n v o l v i n g a v a i l a b l e hydrogen i o n s , the apparent sodium d i f f u s i o n c o e f f i c i e n t decreases w i t h i n c r e a s i n g pH. Conclusions Although simple r a t e expressions can be u t i l i z e d to e x p l a i n s h o r t term, l a b o r a t o r y - c o n t r o l l e d d i s s o l u t i o n of many s i l i c a t e phases, t h e i r a p p l i c a t i o n to modeling n a t u r a l weathering processes i s much more d i f f i c u l t . As i n d i c a t e d , the form of the r a t e ex p r e s s i o n , whether l i n e a r or p a r a b o l i c , can depend on the type of s i l i c a t e s t r u c t u r e , the pH of r e a c t i o n , and the time span of the weathering process i t s e l f . Perhaps the best method of deter mining the type of r a t e expression a p p l i c a b l e to a s p e c i f i c n a t u r a l s i t u a t i o n i s to compare n a t u r a l water compositions to those p r e d i c t e d by l a b o r a t o r y - d e r i v e d r a t e constants. In the case of long-term p a r a b o l i c k i n e t i c s , the r a t i o of d i s s o l v e d c o n s t i t uents should be d i r e c t l y p r o p o r t i o n a l to the r a t i o s of the para b o l i c r a t e constants. In the case of l i n e a r k i n e t i c s , the r a t i o of c o n s t i t u e n t s should be s t o i c h i o m e t r i c a l l y equal to the compo s i t i o n of the d i s s o l v i n g phase. In the case of a system i n which more than one s i l i c a t e phase i s d i s s o l v i n g , the r a t i o of the con s t i t u e n t s w i l l r e f l e c t the r e l a t i v e r e a c t i o n r a t e s of i n d i v i d u a l phases, whether they are l i n e a r or p a r a b o l i c . The above scheme a p p l i e s only to those c o n s t i t u e n t s which are s u b s t i t u t i o n a l compo nents of major d i s s o l v i n g mineral phases, and which are conserved i n the aqueous s o l u t i o n . In a d d i t i o n to the form of the r a t e expression, the magnitude of the r a t e constant must be a s c e r t a i n e d . As i n d i c a t e d i n the d i s c u s s i o n , the composition of the aqueous media can exert a s t r o n g c o n t r o l on the r a t e constant. Modeling of k i n e t i c r a t e s , t h e r e f o r e , can be considerably complicated, as i n closed ground water recharge systems where the aqueous composition would be expected to c o n t i n u a l l y vary along the flow path. In the case of the simple R a i n i e r Mesa a q u i f e r system, a q u a n t i t a t i v e model can be derived to e x p l a i n such v a r i a t i o n s . As i n d i c a t e d i n the case of sodium, the r a t e of mass t r a n s f e r can, at any p o i n t i n the r e a c t i o n path, be r e l a t e d to the aqueous sodium concentration by use of an adsorption isotherm. This


22.

WHITE AND CLAASSEN


471

isotherm appears to be a separable v a r i a b l e independent of other aqueous c o n s t i t u e n t s over the range of s o l u t i o n composition i n v e s t i g a t e d by the authors. The r a t e of mass t r a n s f e r can a l s o be independently r e l a t e d to the aqueous pH by use of an apparent s o d i u m - d i f f u s i o n c o e f f i c i e n t which i s e m p i r i c a l l y determined and which allows f o r the c o d i f f u s i o n of hydrogen i o n s . Thus, the r e a c t i o n r a t e f o r sodium d i s s o l u t i o n f o r the v i t r i c t u f f can be modeled i n a c l o s e d system w i t h a v a r i a b l e pH and d i s s o l v e d Na aqueous composition, by summing the r e s u l t s of s m a l l r e a c t i o n increments, assuming constant source-rock composition. An example of t h i s method i s presented elsewhere i n t h i s volume. Abstract Experimentally determined dissolution kinetics are applicable to natural weathering processes of s i l i c a t e rocks. Mass transfer from the mineral to the aqueous phase was determined to be incon gruent under a range of experimental conditions. Transfer rates of individual species (Q) at times (t) can usually be described by one of two rate expressions; Q = Q + k t or Q = Qo + o

1

1/2

kt p

where k i s a linear rate constant, k i s a parabolic rate constant, and Q i s the mass transferred during an i n i t i a l surface exchange with hydrogen ions. The linear rate constant, k , represents continued surface exchange coupled to incongruent dissolution of the s i l i c a t e framework whereas the parabolic rate constant, k , represents cation diffusion through a relatively undisturbed s i l i c a t e framework. Detailed investigation of dissolution of a v i t r i c tuff indicates that the rate of mass transfer of a species is described by a parabolic expression and i s inversely dependent on the concentration of that species in aqueous solution. A numerical solution to the one-dimensional diffusion equation i s presented using a Freundlich isotherm to relate the aqueous ion concentration and the ion density on the surfaces of the v i t r i c tuff. This ion density on the surface in turn determines the con centration gradient within the glass. Results indicate that the apparent diffusion coefficient for sodium decreases from 1.3 x 10 at pH 4.8 to 1.7 x 10 at pH 7.0 and that the surface isotherm remains constant. 1

p

o

1

p

-21

-22

Literature Cited 1. 2.

Garrels, R. Μ., and Mackenzie, F. T. "Evolution of Sedimen tary Rocks," 397 p. W. A. Norton and Co., New York, 1971. Daubreé, A. Experiences sus des les decomposition chimiques provoquies par les action mecaniques dans divers mineraux tels que le feldspart, Compt. Rend., 339-345 (1867).

472

3.

4.


5.

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CHEMICAL

MODELING IN AQUEOUS

Rana, Μ. Α., and Douglas, R. W. The reaction between glass and water Part 2. Discussion of the results, Phys. Chem. Glasses 2, 196-205 (1961). Luce, R. W., Bartlett, R. W., and Parks, G. A. Dissolution kinetics of magnesium s i l i c a t e s , Geochim. Cosmochim. Acta 30, 35-50 (1972). Tamm, Olof Expermentelle studien über die verwitterung und tonbildung von feldspäten, Chemie der Erde 4, 420-430 (1930). Garrels, R. M. and Howard, P. Reactions of feldspar and mica with water at low temperature and pressure, Clays Clay Min. 6, 68-88 (1957). Lagache, Μ., Wyart, J., and Sabatier, G. Dissolution des feldspaths alcalins dan l'eau pure ou chargee de CO a 200ºC, C. R. Acad. Sci. Paris, 253, 2019 (1961). Lagache, M. Contribution à l'etude de l'altération des feldspaths den l'eau 100 et 200°C sous diverses pressions de CO et application à l a synthese des minéraux argileax, Bull. Soc. Fr. Minerai. Cust. 88, 223-253 (1965). Aagaard, P., and Helgeson, H. C. Thermodynamic and kinetic constraints on the dissolution of feldspars, Geol. Soc. Amer. Abstr. 9 (7), 873, 1977. Marshall, C. E. Reactions of feldspars and micas with aqueous solutions, Econ. Geol. 57, 1219-1227 (1962). Paces, T. Steady-state kinetics and equilibrium between ground water and granitic rock, Geochim. Cosmochim. Acta 37, 2641-2663 (1973). Boksay, Ζ., Bouquet, G., and Dobos, S. Diffusion processes in the surface layer of glass, Phys. Chem. Glasses 8, 140-144 (1967). Boksay, Ζ., and Bouquet, G. On the reaction of water molecules with the s i l i c a t e network in the glass phase, Phys. Chem. Glasses 16, 81-83 (1975). Correns, C. W., and van Engelhardt, W. Neue untersuchungen über die verwitterung des kalifeldspates, Chem. Erde 12, 1-22 (1938). Helgeson, H. C. Kinetics of mass transfer among s i l i c a t e s and aqueous solutions, Geochim. Cosmochim. Acta 35, 421-469 (1971). Crank, J. "The Mathematics of Diffusion," 347 p. Oxford Press, London, 1955. Correns, C. The experimental chemical weathering of s i l i c a t e s , Clay Mineral. Bull. 4, 249-265 (1961). Csakvari, Β., Boksay, Ζ., and Bouquet, G. Investigation of surface layers on electrode glass for pH measurement, Anal. Chim. Acta 56, 279-284 (1971). Baucke, F. Investigation of surface layers, formed on glass electrode membranes in aqueous solutions, by means of an ion sputtering method, Jour. Non-Crystalline Solids 14, 13-31 (1974). 2

8.

2

9.

10. 11.

12.

13.

14.

15.

16. 17. 18.

19.

SYSTEMS

22.

20.


21.

22.

23.

24.

25.

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473

Tchoubar, C., and Oberlin, A. Altération de l'albite par action d'eau. Etude en microscopie et microdiffraction électroniques de l a precipitation et de l'evolution des fibres de boehmite formée, Jour. Microsc. 2, 415-432 (1963). Tchoubar, C. Formation de l a kaolinite à partier d'albite por l'eau à 200ºC. Etude en microscopie et diffraction électroniques, Bull. Soc. Fr. Mineral. Crist. 88, 483-518 (1965). Parham, W. E. Formation of halloysite from feldspar: low temperature a r t i f i c i a l weathering versus natural weathering, Clays Clay Min. 17, 13-22 (1969). LaIglesia, A., Martin-Caballero, J. L., and Martin-Vivaldi, J. L. Formation de kaolinite par precipitation hologene à temperature ambiante, Emploi de feldspaths potassiques, Compt. Rend. D279, 1143-1145 (1974). Petrović, R. Rate control in feldspar dissolution-II. The protective effect of precipitate, Geochim. Cosmochim. Acta 40, 1509-1521 (1976). Petrović, R., Berner, R. Α., and Goldhaber, M. B. Rate control i n dissolution of a l k a l i feldspars I. Study of residual grains by X-ray photoelectron spectroscopy, Geochim. Cosmochim. Acta 40, 537-548 (1976). Busenberg, Ε., and Clemency, C. V. The dissolution kinetics of feldspars at 25ºC and 1 atm-C0 partial pressure, Geochim. Cosmochim. Acta 40, 41-49 (1976). Loughnan, F. "Chemical Weathering of Silicate Minerals", 155 p. Elsevier, Amsterdam, 1969. Wollast, R. Kinetics of the alteration of Κ feldspar i n buffered solutions at low temperature, Geochim. Cosmochim. Acta 31, 635-648 (1967). White, A. F., and Claassen, H. C. Kinetic model for the dissolution of a rhyolitic glass, Geol. Soc. Am. Abst. 9, 1223 (1977). Halsey, G., and Taylor, H. S. The adsorption of hydrogen on tungsten powder, Jour. Chem. Physics 15, 624-630 (1947). Crank, J., and Nicolson, P. A practical method for numerical evaluation of solutions of partial differential equations of the heat type, Proc. Cambridge Phil. Soc. 43, 50-67 (1947). Helfferich, F. "Ion Exchange", 327 p. McGraw-Hill, New York, 1962. 2

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32.

Disclaimer: The reviews expressed and/ or the products mentioned in this article repre sent the opinions of the author(s) only and do not necessarily represent the opinions of the U.S. Geological Survey. RECEIVED November16,1978.

Chemical Modeling in Aqueous Systems - American Chemical Society

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