Chemical Modeling in Aqueous Systems - American Chemical Society

28 Relationships of Activities ofMetal-LigandSpecies to Aquatic Toxicity

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V. R. MAGNUSON, D. K. HARRISS, M. S. SUN, and D. K. TAYLOR Department of Chemistry, University of Minnesota, Duluth, Duluth, MN 55812 G. E. GLASS U.S. Environmental Protection Agency, Environmental Research Laboratory, 6201 Congdon Boulevard, Duluth, MN 55804 Much has been p u b l i s h e d concerning t o x i c i t y of metals t o aquatic l i f e although o n l y during the past decade have there been i n t e r p r e t a t i o n s o f the t o x i c i t y data i n terms of the r e l a t i v e t o x i c i t y o f p a r t i c u l a r s p e c i a t i o n forms, e.g., C u , CuOH , CuCCL 3 (l-7). The s p e c i f i c o b j e c t i v e of t h i s paper i s t o i l l u s t r a t e the use o f Factor A n a l y s i s i n d i s c r i m i n a t i n g between t o x i c and nont o x i c s p e c i e s . The procedure t o be f o l l o w e d i s : determination of e q u i l i b r i u m aqueous s p e c i a t i o n , c a l c u l a t i o n of a p p r o p r i a t e factors, correlation of t o x i c i t y with these f a c t o r s , and i n t e r p r e t a t i o n of the c o r r e l a t i o n a n a l y s i s i n terms o f p a r t i c u l a r species activities. The a n a l y s i s o f t o x i c i t y data i n terms of s p e c i a t i o n products i s a d i f f i c u l t task s i n c e the v a r i a b l e s , species a c t i v i t i e s , u s u a l l y are numerous and o f t e n are i n t e r r e l a t e d . F a c t o r A n a l y s i s a l l o w s one t o determine a s m a l l number o f s t a t i s t i c a l l y independent, l i n e a r combinations o f a c t i v i t i e s ( f a c t o r s ) . C o r r e l a t i o n of these combinations ( f a c t o r s ) w i t h t o x i c i t y allows d i s c r i m i n a t i o n to be made between t o x i c and non-toxic s p e c i e s . Conclusions drawn from a s t a t i s t i c a l study o f t h i s type are o n l y as v a l i d as the data upon which the study i s based. The p u b l i s h e d t o x i c i t y study (Andrew, B i e s i n g e r , and Glass (2)) which we use f o r i l l u s t r a t i o n i s s c i e n t i f i c a l l y sound, however, the number o f experimental p o i n t s and l i m i t e d ranges o f some o f the experimental v a r i a b l e s do r e s t r i c t the a b i l i t y t o d i s c r i m i n a t e between s p e c i e s . Andrew et al. (2) s t u d i e d the e f f e c t s of carbonate, o r t h o phosphate, and pyrophosphate on the t o x i c i t y o f c o p p e r ( I I ) t o Vapkvwa magna a t constant pH and t o t a l hardness. They r e p o r t e d m o r t a l i t y r a t e s and r e c i p r o c a l s u r v i v a l times t o be d i r e c t l y c o r r e l a t e d w i t h c u p r i c and copper-hydroxo i o n a c t i v i t i e s as determined by e q u i l i b r i u m c a l c u l a t i o n s . They a l s o found t o x i c i t y t o be n e g a t i v e l y r e l a t e d t o a c t i v i t i e s o f s o l u b l e copper carbonate (CuCCL), and independent o f t o t a l o r d i s s o l v e d copper concentrat i o n . Data f o r t h e i r s e t o f experiments i n v o l v i n g a d d i t i o n o f orthophosphate a r e i n c l u d e d i n Table I but were not used i n some 2 +

0-8412-0479-9/79/47-093-635$05.50/0 © 1979 American Chemical Society Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

o

CHEMICAL

636

M O D E L I N G IN

AQUEOUS

SYSTEMS

of our l a t e r c a l c u l a t i o n s due t o u n c e r t a i n t y as t o the s t a b i l i t y constants f o r phosphate complexes. C a l c u l a t i o n s when a l l p o i n t s were used are r e f e r r e d t o as 30 p o i n t and those i n which the orthophosphate p o i n t s are excluded are r e f e r r e d t o as 26 p o i n t . The c a l c u l a t i o n s described below are of two types; f i r s t , r e c a l c u l a t i o n of m e t a l - l i g a n d s p e c i a t i o n and comparison w i t h previous r e s u l t s , and secondly, i n t e r p r e t a t i o n of the t o x i c i t y data i n terms of s p e c i a t i o n u s i n g f a c t o r a n a l y s i s and m u l t i p l e r e g r e s s i o n . The s p e c i a t i o n c a l c u l a t i o n s were performed u s i n g REDEQL2 (8_) and SPSS (9) was used f o r f a c t o r a n a l y s i s and m u l t i p l e r e g r e s s i o n .


Sources of Data and L i m i t a t i o n s S t a b i l i t y Constants. The choice of e q u i l i b r i a to i n c l u d e and the accuracy of the r e l a t e d s t a b i l i t y constants have, of course, a major e f f e c t upon the p r e d i c t e d s p e c i a t i o n and upon i n f e r e n c e s drawn from c o r r e l a t i o n s of a c t i v i t i e s of the species w i t h t o x i c i t y . A measure of the e f f e c t s o f l i m i t e d accuracy i n the s t a b i l i t y constants on p r e d i c t e d s p e c i a t i o n concentrations can be obtained through r e p e t i t i v e c a l c u l a t i o n s on a system w h i l e a l l o w i n g f o r s m a l l , random v a r i a t i o n s i n the s t a b i l i t y constants. Such c a l c u l a t i o n s have been c a r r i e d out using a three-metal, t h r e e - l i g a n d model ( 31 complexes ) w i t h concentrations ranging from 1 n i t o 0.01 uM. Random v a r i a t i o n s of 0.05 t o -0.05 u n i t s i n the mantis sas of the p K s l e d t o c o n c e n t r a t i o n changes ranging from 6% t o 30$ w i t h a mean change of 14?. I n g e n e r a l , the percentage changes were g r e a t e s t f o r the species whose concentrations were s m a l l f r a c t i o n s of the t o t a l c o n c e n t r a t i o n . Use of s m a l l e r random v a r i a t i o n s of 0.01 t o -0.01 u n i t s produced p r o p o r t i o n a t e l y s m a l l e r changes, about 1/5 as g r e a t . T

T o x i c i t y S t u d i e s . I t i s d i f f i c u l t to f i n d p u b l i s h e d t o x i c i t y s t u d i e s which are w e l l documented and which a l s o c o n t a i n a s u f f i c i e n t number of data p o i n t s t o a l l o w meaningful s t a t i s t i c a l analyses. Minimal necessary documentation r e q u i r e s pH, a l k a l i n i t y , measured concentrations of the p a r t i c u l a r metals or l i g a n d s under study, and a complete a n a l y t i c a l background a n a l y s i s . This pre sumes of course t h a t : e q u i l i b r i a i n v o l v i n g the background species are important and w i l l be considered; t o t a l i n o r g a n i c carbon w i l l be d e r i v e d from a l k a l i n i t y and knowledge of other a c i d s present; and the nominal added metal or l i g a n d does not n e c e s s a r i l y equal the measured d i s s o l v e d metal or l i g a n d . With regard t o i n c l u d i n g a l l e q u i l i b r i a , f o r the e x p e r i m e n t r e f e r r e d t o i n l i n e 7 of Table I , the c a l c u l a t e d a c t i v i t y of CuSO^ i s twice t h a t of C u ^ O H ^ a n d f i v e times t h a t of Cu(0H)". The r e l a t i v e magnitudes of these a c t i v i t i e s l e a d one t o b e l i e v e t h a t the amount of copper combined w i t h s u l f a t e and other l i g a n d s must be taken i n t o account i f c a l c u l a t e d a c t i v i t i e s of species such as — 2+ Cu(0H) and C u ( 0 H ) are to be meaningful. q

p

9

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

28.

MAGNUSON

ET

AL.

M etal-Ligand Species and

Aquatic Toxicity

637

With regard t o c a l c u l a t i o n of t o t a l i n o r g a n i c carbon ( T I C ) , knowledge of the a n a l y t i c a l background and the a l k a l i n i t y a l l o w the c a l c u l a t i o n of i n o r g a n i c carbon from ( f o r a l k a l i n i t y expressed as mg C CaCO^)

T I C

(1+2x10


I 30^00 " ^

-10.33+pH )

1 0

1 0

J '

when other a c i d s are not present, w i t h a p p r o p r i a t e adjustments when other a c i d s are present. E m p i r i c a l equations expressing TIC i n terms of pH and hardness have been used but seem not t o be s a t i s f a c t o r y over a wide range of pH ( 1 0 ) . With regard t o c a l c u l a t e d versus measured amounts of metals , i n the work of Andrew, B i e s i n g e r and Glass (2), the measured d i s s o l v e d copper v a r i e d between 53 and 100? of the nominal copper added t o the system (see Table I ) and t h e i r data i s r e p r e s e n t a t i v e of s e v e r a l other p u b l i s h e d r e p o r t s when l i k e comparisons are made. A n a l y s i s of Data The i s s u e t o be addressed i n a subsequent s e c t i o n i s the a t t r i b u t i o n of the t o x i c i t y of copper i n aquatic systems t g . p a r t i c u l a r s p e c i a t i o n forms, e.g., Cu , CuÔH)^ " , Cu.(CO^)^ A n a l y s i s of p u b l i s h e d experimental data i n t h i s area normally i s d i f f i c u l t f o r s e v e r a l reasons: s t a t i s t i c a l l y s m a l l numbers of data p o i n t s i n r e l a t i o n t o the number of v a r i a b l e s , l a c k of i n d e pendence of the v a r i a b l e s w i t h c o r r e l a t i o n c o e f f i c i e n t s o f t e n of the order of 0.8 or 0.9 (see Table I I ) , and s m a l l ranges and s c a t t e r of p o i n t s due t o the u s u a l experimental p r a c t i c e of v a r y i n g as few parameters as p o s s i b l e i n a p a r t i c u l a r run w i t h the i n t e n t of determining b i v a r i a t e r e l a t i o n s h i p s . In the f i r s t set of experiments of Andrew 2X at. (2), for example, pH, hardness and t o t a l a l k a l i n i t y are h e l d constant w h i l e copper i s added t o s o l u t i o n s w i t h f i x e d added amounts of NaHCO^, or Na^HPO,, or Na^PÔ^, i n a d d i t i o n t o copper added to the back ground, w i t h no subset of experiments i n c l u d i n g more than s i x cases. In our s p e c i a t i o n c a l c u l a t i o n s r e l a t e d t o t h i s set of n i n e t e e n experiments, some t w e n t y - f i v e complexes of copper i n c l u d i n g three w i t h carbonate, two w i t h phosphate, s i x w i t h hydroxide, and s i x w i t h pyrophosphate are i n v o l v e d . I t i s p o s s i b l e t o c r e a t e new v a r i a b l e s , e.g., as l i n e a r combinations of the a c t i v i t i e s , intended t o c h a r a c t e r i z e a p a r t i c u l a r aspect of the system and then i n t e r p r e t the data i n terms of t h i s smaller set of new v a r i a b l e s . One might, f o r example, use 2 +

+

1

the sum of the a c t i v i t i e s of C u , Cu0H and CuÔH)^" " as a v a r i a b l e r a t h e r than the three species s e p a r a t e l y (10)· In t h i s way a l a r g e number of b i v a r i a t e c o r r e l a t i o n s can be made, but



1

Measured Dissolved Cu(uM) "•0.02 0.20 0.33 0.41 0.61 1.02 1.54 ~0.02 0.60 0.98 1.45 ~0.02 0.54 0.76 1.07

Nominal Added Cu(pM) Control 0.20 0.32 0.51 0.80 1.27 2.01 Control 0.80 1.27 2.01 Control 0.80 1.27 2.01

? +

+

CuOH o

?+ Cu (0H£ * * Cu(0H)° *

Cu(QH)

Ρ Cu(OH),

10.06 9.00 8.78 8.69 8.51 8.29 8.11

o

o

Lake Superior Water 0nly,pH 7.85-8.05 9.80 14.57 7.85 12.99 17.84 8.72 12.41 6.75 11.87 16.71 8.50 11.97 6.54 11.65 16.49 16.40 8.41 11.79 6.44 11.56 16.22 8.24 11.44 6.27 11.39 8.01 10.99 6.05 11.16 16.00 7.83 10.64 5.87 10.98 15.82 Lake S u p e r i o r Water + 48 μΜ NaHC0 ,pH 7.85--8.05 10.11 9.83 14.62 7.85 12.97 17.80 8.50 16.26 8.24 11.44 6.28 11.41 8.27 8.02 11.00 6.07 11.21 16.07 8.08 15.92 7.83 10.64 5.90 11.05 Lake Superior Water + 210 μΜ Na HP0.,pH 7.85--8.05 10.12 17.82 9.84 14.64 7.86 * 12.98 8.58 8.30 11.57 6.34 11.46 16.31 8.42 16.16 8.15 11.27 6.19 11.32 8.27 8.00 10.97 6.04 11.17 16.03

Cu

8.71 7.18 7.03 6.88

8.77 7.19 6.97 6.78

8.77 7.69 7.48 7.38 7.21 6.99 6.81

π CuC0°

TABLE I C a l c u l a t e d E q u i l i b r i u m Values f o r A c t i v i t i e s of S e l e c t e d Species Involved i n the Andrew s Values shown are the negative logarithms of the a c t i v i t i e s


10.88 9.35 9.20 9.06

11.01 9.44 9.23 9.06

11.06 9.96 9.74 9.64 9.47 9.25 9.07

p Cu(C0„)f"

Experiments.

C/J

9

en

ιΟ

1s

>

Ο

C

M

§

M

η

GO 00


Cu0H

+ 2

Cu (0H)2

+

Cu( OH )°

Cu(0H) 3

Cu( OH )

6.46

11.86

8.45

8.74

8.55 6.87 6.67

16.06 12.69 12.28

10.85 10.54 9.16 8 . 8 6 8.95 8.65

7.62 7.41 3

9.86

7.07 7.12 7.17 7.29 7.52

9.01 9.21 9.31 9.56 10.02

11.56 11.78 6.12

5.89

11.44

11.35 11.40

5.67 5.72 5.77

16.76 16.80 16.85 16.97 17.20 7

7.89

9.75

XXX XXX

XXX

6.75 6.90 7.03 7.24

xxx xxx xxx 6.96 7.09 7.21 7..40 8.04 9.91 9.76 11.05 14.78

9.39

8.88 9.15

8.38

6.50

5.86

5.59 5.70

5.47

11.07 11.18 11.27 11.42 12.04 13.92

16.48 16.56 16.69 17.30 19.21

7.00 8.80

6.36

5.93

6.06 6.18

16.39

2

9.06 9.67 11.41

8.89

8.67 8.79

7.23

5.47

8.86

8.29 7.99 7.67

6.03 5.78 5.66 5.57

Lake S u p e r i o r Water + (0,2.5,5.0,10.0,50.0,500 μΜ) added N a ^ P 0 , pH 7.4-7.6

6.88 7.01 7.24

6.77 6.83

3.38

3.82 4.13 4.21 4.37

9.66

10.06

7.83

16.78 16.58

11.97 11.76 11.57

16.39

11.74

3

Cu(C0 )

9.51

CuC0°

18.45

?

2

13.64

2

Lake S u p e r i o r Water + 110 μΜ Na P 0 , p H 7.85-8.05

2 +

*** Values3 Assumed To Be 5.

5

5

5 5 5 5 5

~0.02 0.77 1.24 1.95

Control 0.80 1.27 2.01

Cu

TABLE I Cont'd.

Lake S u p e r i o r Water + (0,1*2,4,10 mM) added NaHC0 ,pH 7.3-7.5

Measured Dissolved Cu(yM)

Nominal Added Cu(yM)


2

CD

δ*

ο

8. S"

a,

CO

CTQ

>

M H

Ο

d

ο

I

to

9°

Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979. 2 +

+

0.22

Cu(C0 )^3

0.65

-0.21

Cu(OH)^" CuCO°

0.34

Cu(OH)~

0.94 0.89

+

0.99

2 +

Cu(OH)°

2

Cu (0H)^

CuOH

Cu

Cu

0.17

0.60

-0.13

0.45

0.95

0.96

0.99

Cu0H

+

0.05

0.46

-0.14

0.41

0.91

0.96

0.94

2

Cu (0H)

2 +

0.07

0.47

0.18

0.70

0.91

0.95

0.89

Cu(0H) 2

-0.12

0.06

0.83

0.70

0.41

0.45

0.34

Cu(0H)~

2

-0.21

-0.26

0.83

0.18

-0.14

-0.12

-0.21

Cu(0H ) ~ 4

C o r r e l a t i o n C o e f f i c i e n t s Between the A c t i v i t i e s of Copper Species i n t h e 26 p o i n t C a l c u l a t i o n s

TABLE I I


0.84

-0.26

0.06

0.47

0.46

0.60

0.65

CuC0°

0.84

-0.21

-0.12

0.07

0.05

0.17

0.22

3

2Cu(C0 ) 2

CO H M CO

*

Ε ο

I

>

Ω

g

ο

Ο

4^

as


28.

MAGNUSON

ET

Metal-Ligand Species and

AL.

Aquatic Toxicity

641

d i r e c t comparisons between the new v a r i a b l e s are d i f f i c u l t s i n c e i n t e r r e l a t i o n s h i p s of the new v a r i a b l e s are not c l e a r and they may be c o r r e l a t e d w i t h each other. What i s d e s i r e d i s a l o g i c a l , systematic procedure t o gener ate a s m a l l set of u n c o r r e l a t e d v a r i a b l e s which a l l o w d i r e c t com p a r i s o n , make chemical sense, and are amenable t o easy i n t e r p r e t a t i o n . A mathematical procedure which meets these c r i t e r i a i s the use of f a c t o r a n a l y s i s ( 9 , 11, 12, 13) t o generate s t a t i s t i c a l l y independent new variabTes"XfacTors7 f o l l o w e d by c o r r e l a t i o n of t o x i c i t y w i t h the generated f a c t o r s . Factor a n a l y s i s has two general uses; t o see whether under l y i n g p a t t e r n s o f r e l a t i o n s h i p s e x i s t among s e t s of v a r i a b l e s , and t o rearrange or reduce the data ( v a r i a b l e s ) t o a smaller s e t o f f a c t o r s or components t h a t may be taken as primary or source v a r i a b l e s . One o f t e n i s cautioned about the f i r s t use, employment of f a c t o r a n a l y t i c methods t o determine r e l a t i o n s h i p s among the v a r i a b l e s , i n t h a t spurious p a t t e r n s may be i n d i c a t e d . I n our a p p l i c a t i o n s , however, the d e s i r e d p a t t e r n s , i . e . combinations of a c t i v i t i e s , normally w i l l be known or can be p r e d i c t e d and the use of f a c t o r a n a l y s i s w i l l be t o generate a reduced set of s t a t i s t i c a l l y independent components ( f a c t o r s ) , e.g. three f a c t o r s r e p l a c i n g e i g h t i n d i v i d u a l a c t i v i t i e s . I n cases where the p a t t e r n s are not c l e a r , one r e t a i n s the c r i t e r i o n t h a t the r e s u l t s must be c h e m i c a l l y r a t i o n a l and may r e j e c t those t h a t f a i l t o meet t h i s c r i t e r i o n . These f a c t o r s then are used i n m u l t i p l e r e g r e s s i o n analyses t o attempt t o i d e n t i f y t o x i c s p e c i e s . T o x i c i t y of Copper t o Aquatic Forms General. A v a r i e t y of c o n c l u s i o n s have been p u b l i s h e d recent years on the r e l a t i v e t o x i c i t y of f r e e copper i o n (Cu ), hydroxo copper complexes, (CuOH , Cu(0H)°, Cu(0H) , Cu(OH)77 2\ ο 2CuÔH)^;, and carbanato copper complexes (CuCO^, CuiCO^)^ )· o

The statements have been, i n g e n e r a l , q u a l i t a t i v e i n nature r a t h e r than q u a n t i t a t i v e . Shaw and Brown ( 1 4 ) concluded t h a t CuCO^ i s as 2+ t o x i c as Cu ; Pagenkopf at at. (15) f i n d the major t o x i c species 2+ + to be Cu w i t h a p o s s i b l e c o n t r i b u t i o n from CuOH : Andrew (it at. (2)

s t a t e t h a t copper t o x i c i t y i s d i r e c t l y r e l a t e d o n l y t o the 2 +

+

a c t i v i t i e s of C u , CuOH , and C u ^ O H ) ^ ; Chakoumakos 2 +

at.

+

(16)

r e p o r t C u , CuOH , Cu(0H)° and C u ^ O H ^ t o be t o x i c forms and found CuHCO* CuC0° and Cu(CO ) " n o t t o x i c under t h e i r c o n d i t i o n s ; Hawarth and Sprague (10) found the smoothest response s u r f a c e , of t h o s e t r i e d , f o r conper t o x i c i t y t o be generated by [Cu ] + [CuOH ] + [CuÔH) ]and, on the b a s i s of t h i s , c l a i m these three t o be the t o x i c forms and, on the b a s i s on non-smooth response s u r f a c e s , t h a t Cu(0H) and the carbonato copper species are not toxic. 2

+

2


642

CHEMICAL

MODELING IN AQUEOUS

SYSTEMS

Most o f t h e experiments r e p o r t e d upon i n the above referenced papers i n v o l v e d systems w i t h pH i n range 6.5-8.5, hardnessûp t o 35Qmg JT as CaCCL, i n i t i a l a l k a l i n i t y as h i g h as 30Qmg t as CaCCL, and t o t a l copper up t o 5mg t~ . In the f o l l o w i n g s e c t i o n s , f a c t o r a n a l y s i s and m u l t i p l e r e g r e s s i o n are used i n an attempt t o determine the r e l a t i v e t o x i c i t y of t h e copper species discussed above. The a c t i v i t i e s o f e i g h t 2 +

+

2 +

2

species ( C u , CuOH , C u ( 0 H ) , Cu(0H)°, Cu(0H)~, C u ( 0 H ) J CuCO°, 2


Cu(CO^)

2

) a r e i n c l u d e d i n the c a l c u l a t i o n s .

F a c t o r Determination. One i s s t r o n g l y tempted t o generate " u n i v e r s a l " f a c t o r s f o r the species o f i n t e r e s t , v a l i d over t y p i c a l ranges o f the parameters i n v o l v e d . The problem i s t h a t the p o i n t s f o r a g i v e n experiment are u n l i k e l y t o be r e p r e s e n t a t i v e o f the p o i n t s used t o generate t h e " u n i v e r s a l " f a c t o r s and the f a c t o r s l o s e t h e i r s t a t i s t i c a l independence. One has l i t t l e choice then, when u s i n g p u b l i s h e d data, but t o use t h e experimen t a l p o i n t s d i r e c t l y i n the determination o f the f a c t o r s as w e l l as i n the c o r r e l a t i o n s and we have done so i n the systems r e p o r t e d here although we l a t e r d i s c u s s t h e s t r u c t u r e o f t h e experimental design which would be most u s e f u l t o t h i s type of a n a l y s i s . The q u a l i t y o f species s e p a r a t i o n obtained through use o f p r e v i o u s l y p u b l i s h e d experimental p o i n t s i s good however, s i n c e the parameter s e l e c t i o n s made by the experimenters o f t e n were f o r the purpose o f studying t o x i c i t y as a f u n c t i o n o f s p e c i a t i o n . A comparison o f f a c t o r s determined w i t h 100 random p o i n t s and w i t h 30 and 26 experimental p o i n t s can be made from t h e data shown i n Table I I I . A short d e s c r i p t i o n of t h e data may be u s e f u l t o those u n f a m i l i a r w i t h f a c t o r a n a l y s i s . The values shown a r e " f a c t o r l o a d i n g s " f o r the species on the f a c t o r s , e.g. the t o p l i n e under t h e 100 random p o i n t heading s t a t e s t h a t a c t i v i t y ( C u ) = 0.88xFactor 1 - 0.19xFactor 2 + 0.27xFactor 3 ( 2 ) 2 +

2 +

and the a c t i v i t y o f C u can be c a l c u l a t e d from values o f t h e f a c t o r s . The " f a c t o r l o a d i n g s " a r e c o r r e l a t i o n c o e f f i c i e n t s and the r e l a t i v e importance o f the f a c t o r s i n determining t h e a c t i v i t y of Cu i s given as t h e square o f the c o e f f i c i e n t s , i m p l y i n g t h a t F a c t o r 1 i s s u f f i c i e n t t o e x p l a i n 77$ o f the v a r i a n c e i n t h e a c t i v i t y o f Cu , F a c t o r 2 e x p l a i n s and F a c t o r 3 e x p l a i n s 7%. The f a c t t h a t these add up t o 0.88 r a t h e r than 1.00 s t a t e s t h a t these three f a c t o r s a r e s u f f i c i e n t t o e x p l a i n o n l y 88% o f t h e v a r i a t i o n i n the a c t i v i t y o f Cu i n the 100 p o i n t s . I n compari son, three f a c t o r s a r g s u f f i c i e n t t o e x p l a i n 98% of the v a r i a t i o n of t h e a c t i v i t y o f Cu i n Andrew s 30 p o i n t and 26 p o i n t cases. The a c t u a l a c t i v i t i e s o f t h e species are not used i n t h e determination o f f a c t o r s , b u t i n s t e a d K a i s e r normalized values of the a c t i v i t i e s a r e used, +

f



2+

0.04

:

I

*** Value l e s s than p r e c i s i o n shown

39.0 Percent o f 48.6 12.4 o v e r a l l variance i n the p o i n t s accounted f o r by the 3 f a c t o r s

ι 0.56

27.5

-0.08

14.9

0.95

; 0.70

2

-0.18

Cu(C0 )

3

0.87

-0.07

0.88

0.04

0.38

CuCO

3

-0.13

-0.04

0.92 0.97

0.11

0.36

0.02

0.05

***

' 0.95

0.20

0.24

Factor 3

0.05

0.05

Factor 2

-0.12

-0.01

1.00

Factor 1

Andrew's 30 P o i n t s

2Cu(OH) 4

3

Cu(OH)

-0.03 0.08

0.04

0.96

0.22

0.27

Factor 3

0.73

0.06

0.59_

2 +

-0.19

Factor 2

0.97

0.88

Factor 1

100 Random P o i n t s

Cu(oH)°

2

Cu (0H)

+1 CuOH

Cu

Species

oJi at.

Experiments

I 0.96 |

Factor 1

27.5

-0.08

-0.09

14.9

0.95

0.87

-0.13

-0.04 0.91 0.97

0.11

0.04

0.02 0.35

0.19

0.24

Factor 3

0.05

-0.05

Factor 2

Andrew's 26 P o i n t s

Varimax Rotated F a c t o r M a t r i c e s A f t e r R o t a t i o n w i t h K a i s e r N o r m a l i z a t i o n

Three-Factor Case f o r Random P o i n t s and t h e Andrew

TABLE I I I


644

C H E M I C A L MODELING IN AQUEOUS SYSTEMS

T

where X i s the experimental v a l u e , X i s t h e normalized v a l u e , X the mean of the X and σ the standard d e v i a t i o n of the X, K a i s e r normalized v a r i a b l e s have nominal means o f zero and standard de v i a t i o n s of one. Equation 2 should be w r i t t e n i n s t e a d as T

- 0.19 F

2 +

A ( C u ) = 0.88 ^

+ 0.27

2

(2')

2+ 2+ where A ( C u ) i s the K a i s e r normalized a c t i v i t y of Cu and the f a c t o r s are K a i s e r normalized v a r i a b l e s . From known values of a c t i v i t i e s , one can c a l c u l a t e the value of the f a c t o r ( f a c t o r s c o r e ) VÂJOL f a c t o r score c o e f f i c i e n t s ,


f

F

l

=

C

l l ï X

+

C

12

X ,

2 "-+

+ C

m 'n X

i k )

where t h e c are the f a c t o r score c o e f f i c i e n t s and the X* a r e the normalized ? i l u e s o f the activités. The means and standard d e v i a t i o n s of the a c t i v i t i e s of the s p e c i e s , p l u s the f a c t o r score c o e f f i c i e n t s f o r the 26 p o i n t case are g i v e n i n Table IV. The second f a c t o r would be w r i t t e n F

T

2

2 +

f

+

= -1.09 A ( C u ) + 7.19 A ( C u 0 H ) + ...

(.5)

TABLE IV Means, Standard D e v i a t i o n s , and F a c t o r Score C o e f f i c i e n t s f o r Andrew s 26 P o i n t s w i t h Three F a c t o r s . (Means and Standard Deviation i n Molarities) 1

Species Cu

Mean Activity

2 +

CuOH

+

Cu (0H)

2 +

2

4.28xl0~

8

2.65xl0~

8

1.91xl0"

Standard Deviation

F a c t o r Score C o e f f i c i e n t s Factor 1 Factor 2 Factor 3

6.10x10

-19.55

-1.09

3.11

48.73

7.19

-7.89

0.23

0.29

0.06

3.33xlO" 10

8

3.36xlO"

10

Cu(0H)°

9.39xl0"

-38.18

-14.37

4.95

Cu( OH)"

3.62xl0~

12

2.85xl0~

12

16.76

14.23

-1.05

Cu(OH)^"

3.62xl0"

17

3.8lxl0~

1 7

-5.61

-7.48

-0.09

CuC0°

5.75xl0~

7

9.26xl0"

7

-1.34

-0.01

1.14

4.14xl0"

9

1.20xl0"

8

0.49

0.05

0.18

2

Cu(C0 ) " 3

7

9.03xl0"

7

Using m u l t i p l e r e g r e s s i o n , b i o l o g i c a l response (BR) can then be c o r r e l a t e d w i t h the f a c t o r s ( f a c t o r s c o r e s ) as BR = aF^^ + b F

2

+ c F + ... 3


(6)

28.

MAGNUSON

Metal-Ligand Species and Aquatic Toxicity

ET AL.

645

thereby generating a r e l a t i o n s h i p between b i o l o g i c a l response and a c t i v i t i e s , e.g. Equations 7 and 8. The f a c t o r score c o e f f i c i e n t s ( c ) are not c o r r e l a t i o n c o e f f i c i e n t s f o r independent v a r i a b l e S ^ a n d the concept o f r e l a t i v e weight o f the a c t i v i t i e s o f the species does not h o l d , i . e . t h e squares o f the c o e f f i c i e n t s do not g i v e the r e l a t i v e importance of the a c t i v i t i e s i n the f a c t o r . The q u a l i t y o f species s e p a r a t i o n appears t o be b e t t e r i n the 30 and 26 experimental p o i n t cases, t h a t i s t o say t h a t the l o a d ings g e n e r a l l y are more r e s t r i c t e d t o s i n g l e f a c t o r s , e s p e c i a l l y 2

f o r Cu(0H)° and C u ( C 0 ) ~ although Cu(OH)" and CuC0° are somewhat l e s s w e l l separated (Table I I I ) . The boxes drawn are t o i n d i c a t e the p r i n c i p a l species dominating a f a c t o r , e.g. under Andrew's 30


3

2 +

+

2 +

p o i n t case F a c t o r 1 I s p r i m a r i l y ( C u , CuOH , C u ( 0 H ) , Cu(0H)°) 2

2

w i t h F a c t o r 2 represented w e l l by (Cu(COH)", Cu(OH) ") and F a c t o r 3 by (CuCO^, C u ( C 0 ) " ) . 3

2

Note i n the 100 random p o i n t case t h a t

Cu(0H)° d i s t r i b u t e s 35% on F a c t o r 1 and 53% on F a c t o r 2 and Cu(C0 ) d i s t r i b u t e s A9% on F a c t o r 2 w i t h 31% on Factor 3, r e l a t i v e l y poor s e p a r a t i o n s . An o f t e n used rule-of-thumb i s t h a t l o a d i n g s g r e a t e r than 0.3 should be considered s i g n i f i c a n t (12, p.10). As w i l l be evident from the d i s c u s s i o n below on s e p a r a b i l i t y o f s p e c i e s , the 100 random-point-factors are a more accurate r e p r e s e n t a t i o n o f the behavior o f the hydroxo complexes over a wide pH range than are the 30 and 26 p o i n t f a c t o r s . The e x p e r i ments o f Andrew at at. are r e s t r i c t e d t o three pH values (7.4> 7.5, 7.95) thereby l i m i t i n g the r e l a t i v e v a r i a t i o n o f hydroxo complex a c t i v i t i e s , c r e a t i n g a set o f data more e a s i l y represented by three f a c t o r s and p o s s i b l y g i v i n g the f a l s e impression t h a t t h e separations achieved are b e t t e r . Further a t t e n t i o n has not been given t o f a c t o r s generated from random p o i n t s due t o problems o f s t a t i s t i c a l independence e a r l i e r d i s c u s s e d . Separation o f species by f a c t o r a n a l y s i s i s l i m i t e d i n s e v e r a l ways. I n order o f decreasing importance the s e p a r a b i l i t y i s c o n t r o l l e d by: s p e c i a t i o n behavior over the ranges o f para meters used, experimental p o i n t d i s t r i b u t i o n over the ranges o f parameters, number o f species i n v o l v e d i n the c a l c u l a t i o n , and number o f f a c t o r s determined. With regard t o s p e c i a t i o n behavior: i n F i g u r e 1 are d i s played the s p e c i a t i o n curves f o r the a c t i v i t i e s o f f r e e copper i o n and the hydroxo-complexes o f copper over a range o f pH. Inspec t i o n o f the curves r e v e a l s t h a t CuOH and C u ( 0 H ) have the same p a t t e r n o f behavior^ over the e n t i r e range ana cannot be separated, Cu(0H)^ and Cu(0H) ~ are s i m i l a r enough t h a t s e p a r a t i o n i s not t o be expected, and over the range o f pH values used by Andrew oX at. 7.4-8.0, one should not expect s e p a r a t i o n s other than those ob served. One might, upon f i r s t glance, f e e l t h a t the forms of t h e f a c t o r s are completely described by the c o r r e l a t i o n c o e f f i c i e n t s 2

2

2


CHEMICAL


646

Figure 1.

MODELING IN AQUEOUS

SYSTEMS

Speciation curves for the activities of free copper ion and the hydroxo complexes of copper vs. pH



28.

MAGNUSON E T A L .

Metal-Ligand Species and

Aquatic Toxicity

647

given i n Table I I . The boxes drawn around sets of c o r r e l a t i o n c o e f f i c i e n t s correspond t o the boxes i n Table I I I and indeed, the l a r g e s t c o r r e l a t i o n c o e f f i c i e n t s l i e w i t h i n the boxes although q u i t e s u b s t a n t i a l values do l i e without. No mathematical manipul a t i o n can o b v i a t e the data i n Table I I and of course the f a c t o r s are d e r i v e d from the c o r r e l a t i o n c o e f f i c i e n t s . The u s e f u l n e s s of f a c t o r a n a l y s i s l i e s i n i t s a b i l i t y to determine a s m a l l set of s t a t i s t i c a l l y independant v a r i a b l e s which r e t a i n as much informat i o n as p o s s i b l e about the system. With regard t o p o i n t d i s t r i b u t i o n : i t should be c l e a r from Figure 1 t h a t the pH values must be r e p r e s e n t a t i v e of the range 6.0-8.0 f o r the above d i s c u s s e d s e p a r a t i o n t o be achieved. With regard to the number of s p e c i e s i n v o l v e d : the number of f a c t o r s i s r e s t r i c t e d t o no more than one-half the number of v a r i ables i f convergent, unique values are t o be obtained f o r communa l i t i e s of the v a r i a b l e s (11, p.200), (the communality, of a v a r i a b l e i s the amount of the v a r i a n c e of t h a t v a r i a b l e accounted f o r by the common f a c t o r s ) . Therefore, t o use a f i v e f a c t o r decomposition of a set of species one must have at l e a s t 10 species i n c l u d e d i n the c a l c u l a t i o n . With regard t o the number of f a c t o r s : i t should be obvious t h a t t o o b t a i n a s e p a r a t i o n of the f o u r groups mentioned l a t e r , at l e a s t f o u r f a c t o r s must be used. I f other species which have q u i t e d i f f e r e n t p a t t e r n s of behavior over the set of p o i n t s are i n c l u d e d i n the c a l c u l a t i o n , s u f f i c i e n t a d d i t i o n a l f a c t o r s must be i n c l u d e d to account f o r each s p e c i a t i o n p a t t e r n or the p a t t e r n s w i l l smear over the f a c t o r s . A d d i t i o n of more species or f a c t o r s f o r Andrew s data would not have proven f r u i t f u l due t o the l i m i t e d pH range i n v o l v e d i n the experiment. F i n a l l y , a f t e r a l l of the above have been taken i n t o account, i t i s p o s s i b l e t o " r o t a t e " a set of f a c t o r s w i t h d i f f e r e n t types of r o t a t i o n y i e l d i n g somewhat d i f f e r e n t species l o a d i n g ( 9 ) . I f the s p e c i a t i o n p a t t e r n s f o r the p o i n t s are not d i s t i n c t however, r o t a t i o n of the f a c t o r s cannot achieve a s e p a r a t i o n . We have found Varimax r o t a t i o n , which maximizes the squared l o a d i n g s of v a r i a b l e s i n each f a c t o r w h i l e r e t a i n i n g the o r t h o g o n a l i t y of the f a c t o r s t o be most u s e f u l . 1

Copper T o x i c i t y t o Daphnia Magna Lake S u p e r i o r water was used as the d i l u t i o n water f o r a l l experiments by Andrew (2). A copy of the current a n a l y t i c a l background f o r Lake S u p e r i o r water, Table V, was obtained from the Environmental Research Laboratory-Duluth and was used i n our s p e c i a t i o n c a l c u l a t i o n s . The water has a t o t a l hardness o f -45mg l as CaCO , a l k a l i n i t y of H2mg l as CaCO , and a pH from 7.4 t o 8.2. -1

3

3


648

CHEMICAL

MODELING IN

AQUEOUS

SYSTEMS


TABLE V Concentrations used t o Simulate the A n a l y t i c a l Background of Lake S u p e r i o r Water ( M o l a r i t i e s ) Calcium Magnesium Sodium Potassium Cadmium Chromium Copper Iron Mercury Methyl Mercury Manganese Nickel Lead

3.26x10"^" 1.10x10 \ 5.60x10 \I 1.29x10 1.80x10 Q 3.80x10"^ 1.60x10 * 5.40x10 5.01x10 \

L

5.01X10"Q

5.50x10"^ 3.40xl0"\f 4.84xl0"

n

lu

Zinc Cobalt Barium Strontium Silver

1.10x10 -9 3.40x10 7 1.00x10' 7 1.80x10 -10 1.00x10'

Carbonate Chloride Sulfate Silicate Phosphate Nitrate

8.81x10r 4 3.61x10" 3.65x10^ -5 4.47x10' 3.24x10" 1.66x10"

The pH was adjusted i n each o f t h e i r experiments by r e g u l a t ing C0p-air mixtures bubbled through the s o l u t i o n , e.g. Na^PÔ^ was added t o the s o l u t i o n f o l l o w e d by b u b b l i n g s u f f i c i e n t CO^ through the s o l u t i o n t o b r i n g the pH back t o 7.95. This process i n c r e a s e s the t o t a l i n o r g a n i c carbon. REDEQL2 does a l l o w one t o determine the amount o f 2H + CO ~ necessary t o add t o b r i n g the pH back t o 7 . 9 5 . The t o t a l carbonate c o n c e n t r a t i o n s used i n our c a l c u l a t i o n s are l i s t e d i n Table V I . TABLE V I T o t a l Carbonate Values used i n R e c a l c u l a t i o n of Andrew's Data T o t a l Carbonate Andrew's Table 2

3

4

Experiments 1-7 8-11 12 - 15 16 - 19 1 2 3 4 5 1-4 5 6

0.881 0.929 1.114 0.889 0.935 1.936 2.938 4.932 10.940 0.920 0.931 1.119

S p e c i a t i o n C a l c u l a t i o n s . Although REDEQL2 was used t o determine s p e c i a t i o n i n Andrew's work as w e l l as ours, c o n s i d e r -


28.

MAGNUSON


ET AL.

649


able d i f f e r e n c e s e x i s t i n p r e d i c t e d e q u i l i b r i u m a c t i v i t i e s due t o m o d i f i c a t i o n s which have been made t o the program and the a s s o c i ated data base. The major c o n t r i b u t i o n t o the d i f f e r e n c e s i s the i n c l u s i o n o f more complexes, e.g. Cu(0HL. Complexation by unc h a r a c t e r i z e d o r g a n i c l i g a n d s and a b s o r p t i o n o f s p e c i e s o r sus pended matter were not considered i n these s p e c i a t i o n c a l c u l a t i o n s . (Both organic complexation and a b s o r p t i o n should be l e s s s e r i o u s problems i n t h i s Lake S u p e r i o r study as compared t o a non-laboratory system. ) I n Table V I I some comparative data a r e l i s t e d and i n Table I are shown the c a l c u l a t e d a c t i v i t i e s f o r the f r e e copper i o n p l u s the hydroxo and carbonato complexes. TABLE V I I Comparisons o f Some C a l c u l a t e d Copper Species A c t i v i t i e s from t h i s work (M-G) w i t h t h a t o f Andrew, at at (ABG ) C a l c u l a t e d A c t i v i t y o f Copper Species (μΜ) Measured 2+ Cu' dissolved copper (μΜ) ABG M-G ~0.02 0.20 0.33 0.41 0.61 1.02 1.54

0.001 0.011 0.016 0.020 0.031 0.034 0.076

***

CuOH AbG M-G 0.001 0.009 0.015 0.019 0.028 0.047 0.071

CuCO Cu(QH)° M-G ABG* M-G ABG

***

02 18 30 36 54 89 35

0.014 0.178 0.288 0.363 0.537 0.891 1.349

0.002 0.001 0.003 0.002 0.004 0.002 0.006 0.003 0.005 0.010 0.008 0.015 * Cu(0H)p was not considered i n ABG c a l c u l a t i o n s *** Value l e s s than p r e c i s i o n shown

0.002 0.020 0.033 0.042 0.062 0.102 0.155

S i n g l e Ion C o r r e l a t i o n s w i t h T o x i c i t y . The data g i v e n i n the f i r s t f i f t e e n cases, e x c l u d i n g those w i t h added Na^HPO,, were used t o determine c o r r e l a t i o n s o f ^ j n v e r s e median s u r v i v a l time w i t h species a c t i v i t y f o r f r e e Cu and the seven l i s t e d com p l e x e s . The values f o r r ranged from 0.97 t o ^ 9 8 w i t h s i g n i f i cance 0.00001 f o r a l l species but one, C u ( 0 H ) , which e x h i b i t e d an r o f 0.95. F i v e of the p o i n t s ( 1 , 8, 9, 10, 12 excluding Na HP0. p o i n t s ) are " z e r o - p o i n t s " , i . e . median s u r v i v a l time exceeded the l i f e o f the experiment, and a b e t t e r t e s t o f the hypothesis o f t o x i c i t y due t o copper species r e s u l t s from d i s c a r d i n g the z e r o - p o i n t s . When t h i s i s done, the c o r r e l a t i o n c o e f f i c i e n t s decrease^by 0.01 or l e s s and the l e v e l o f s i g n i f i c a n c e remains a t the 10 level. In F i g u r e 2 a r e ôwn the i n v e r s e median s u r v i v a l time versus a c t i v i t y p l o t s f o r Cu and CuC0~, both f o r the 15 p o i n t cases and the 10 p o i n t cases. +

p

p

2


CHEMICAL

MODELING IN AQUEOUS

SYSTEMS


650

Figure 2. Reciprocal median survival time vs. activity for Cu : (A) 10 point case, (C) 15 point case; for CuC0 °: (B) 10 point case, (D) 15 point case 2+

3


28.

MAGNUSON

ET

651


AL.

F a c t o r A n a l y s i s and M u l t i p l e Regression. F a c t o r scores f o r the 26 and 30 p o i n t cases, generated u s i n g the f a c t o r score c o e f f i c i e n t s i n Table IV, were c o r r e l a t e d w i t h i n v e r s e median s u r v i v a l time, t " . The 26-point case y i e l d e d the f o l l o w i n g r e l a t i o n s h i p i = 0.0046 F

1

+ 0.0027 ?

2

- 0.00013 F' + 0.0061

(7)

2

- 0.00011 F' + 0.0055

(8)

w h i l e the 3 0 - p o i n t case y i e l d e d


i = 0.0051 F

x

+ 0.0024 F

Standard e r r o r s , 95$ confidence i n t e r v a l s , and l e v e l s of s i g n i f i cance are t a b u l a t e d i n Table V I I I f o r the c o e f f i c i e n t s i n Equa t i o n s Τ and 8.

TABLE V I I I Standard E r r o r s , 96% Confidence I n t e r v a l s , L e v e l s o f S i g n i f i c a n c e and Changes i n R f o r the 26-Point and 30-Point Regression Equations 26-Point C o e f f i c i e n t Case χ 10" 4.6

2.7 F Constant

-0.13 6.1

Standard

0

E r r o r χ 10 0.57 0.60 0.62 0.60

3

95% Confidenc I n t e r v a l χ 10" (3.4,5.8) (1.4,3.9) (-1.4,1.2) (4.9,7.4)

L e v e l of Change, Significance i n R

Chemical Modeling in Aqueous Systems - American Chemical Society

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