Techniques of Estimating Thermodynamic Properties for Some

18 Techniques of Estimating Thermodynamic Properties for Some Aqueous Complexes of Geochemical Interest DONALD LANGMUIR

1

Downloaded by FUDAN UNIV on December 27, 2016 | http://pubs.acs.org Publication Date: March 19, 1979 | doi: 10.1021/bk-1979-0093.ch018

Department of Geosciences, Pennsylvania State University, University Park, PA 16802

A host of v a r i a b l e s can i n f l u e n c e the s t a b i l i t y of an aqueous complex r e l a t i v e to i t s uncomplexed addends. Among these a r e : (a) the valences of the addends; (b) t h e i r d i s t a n c e of approach i n the complex; (c) the degree of cdvalency of t h e i r bonding; (d) the number of l i g a n d s c o o r d i n a t i n g the c a t i o n or c a t i o n s i n the complex; (e) the packing arrangement of c a t i o n s and l i g a n d s i n the complex; and more s u b t l e c o n s i d e r a t i o n s , i n c l u d i n g ( f ) the p o l a r i z a b i l i t y or d e f o r m a b i l i t y of the e l e c t r o n cloud surrounding the addends; and (g) l i g a n d f i e l d e f f e c t s f o r t r a n s i t i o n metal complexes i n p a r t i c u l a r (5, 6.). Of these, the most important v a r i a b l e s are the valences of the addends and t h e i r s e p a r a t i o n d i s t a n c e i n the complex. As a r u l e , the s t a b i l i t y of complexes formed w i t h a given l i g a n d i n c r e a s e s w i t h c a t i o n valence and decreases w i t h c a t i o n r a d i u s . This i s expected, based s t r i c t l y on Coulombic arguments. Equations to p r e d i c t the thermodynamic p r o p e r t i e s of complexes as f u n c t i o n s of valence of addends and the r e c i p r o c a l of t h e i r r a d i i or s e p a r a t i o n d i s t a n c e abound i n the l i t e r a t u r e . The best known of these are the simple Coulombic expression of Denison and Ramsey (7) and the equations of Bjerrum and of G i l k e r s o n and Fuoss (8^, 9) . As the covalency and p o l a r i z a b i l i t y (etc.) of a s s o c i a t i n g addends i n c r e a s e s , however, the simple Coulombic models tend to f a i l . They do, n e v e r t h e l e s s s t i l l suggest l i m i t i n g values f o r the thermodynamic p r o p e r t i e s of comp l e x a t i o n . Because of t h e i r convenience and general u t i l i t y , the simple charge-distance equations are discussed a t some l e n g t h i n t h i s paper i n connection w i t h f r e e energy and entropy data f o r s u l f a t e , f l u o r i d e , and phosphate complexes. P r e d i c t i n g the s t a b i l i t y of complexes which owe t h e i r exi s t a n c e to important non-Coulombic c o n t r i b u t i o n s can be d i f f i c u l t . Where increased covalent bonding between c a t i o n s and a given l i g a n d i s i n v o l v e d , p l o t s of s t a b i l i t y versus i o n i z a t i o n p o t e n t i a l or e l e c t r o n e g a t i v i t y (EN) of the c a t i o n are sometimes u s e f u l (5^, 10). In any case, the best general approach i s to compare the Current address: Department of Chemistry and Geochemistry, Mines, Golden, C O 80401 1

Colorado School of

0-8412-0479-9/79/47-093-353$08.25/0 © 1979 American Chemical Society Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

354

CHEMICAL MODELING IN AQUEOUS SYSTEMS

s t a b i l i t i e s of complexes formed w i t h a common l i g a n d where the c a t i o n s considered e x h i b i t s i m i l a r or s y s t e m a t i c a l l y t r e n d i n g behavior i n complexation. Here, c l a s s i f i c a t i o n s d i s t i n g u i s h i n g c a t i o n s and l i g a n d s are u s e f u l . These i n c l u d e the c l a s s A, B, and C c a t i o n groupings of Schwarzenbach ( 2 ) , and the hard and s o f t a c i d and base designations of Pearson C D and Ahrland (A.) . A v a r i e t y of e s t i m a t i o n and c o r r e l a t i o n techniques are pre sented i n t h i s paper. They i n c l u d e p l o t s i n v o l v i n g the thermo dynamic p r o p e r t i e s of_metal complexes w i t h the l i g a n d s HCO3 , ~_ C O 3 " , SO^-, OH , SH , the halogens ( e s p e c i a l l y F ), and H P04 (n = 0-3), p l o t t e d a g a i n s t , f o r example: (a) the v a l u e of η i n H P 0 4 " ; (b) the EN of the c a t i o n or EN order of l i g a n d s ; (c) the l i g a n d number ( f o r complexes of U and Th); and (d) z+z_/d, where z+ and z_ are the valences of the c a t i o n and l i g a n d , r e s p e c t i v e l y , and d t h e i r d i s t a n c e of s e p a r a t i o n i n the complex. The thermodynamic data p l o t t e d i n the f i g u r e s or discussed i n the t e x t have been obtained from references i n c l u d i n g Y a t s i m i r s k i i and V a s i l ' e v ( I T ) , Ringbom (123, S i l l en and M a r t e l l (12_, 2A), Christensen et a l . (15), and Smith and M a r t e l l (16). Other sources have included Wagman et a l . (17) f o r thorium complexes, and Langmuir (18) f o r uranium complexes. Whenever p o s s i b l e , the thermodynamic data are f o r 25°C and zero i o n i c s t r e n g t h ( I = 0 ) . When s t a b i l i t y constants were reported f o r higher i o n i c strengths but could be corrected to I = 0, t h i s has been done, using the extended Debye-Huckel equation or mean s a l t c a l c u l a t i o n s (10. _1£) · 2


n

n

3

n

n

Complexes Formed by H y d r o l y s i s of

Cations

An a p p r e c i a t i o n of the nature and s t a b i l i t y of complexes formed by h y d r o l y s i s of c a t i o n s i s important because: 1) such complexes are the predominant forms of occurrence and t r a n s p o r t of many c a t i o n s i n n a t u r a l waters; and 2) the occurrence of impor tant amounts of other types of complexes i n v o l v i n g the same c a t i o n r e q u i r e s that t h e i r l i g a n d s compete e f f e c t i v e l y w i t h the l i g a n d s formed by h y d r o l y s i s of the c a t i o n . In general, hydro l y s i s of monovalent and d i v a l e n t c a t i o n s produces H20-cation complexes or aquo-cations. In c o n t r a s t , smaller c a t i o n s of v a l ence 3+ to 6+ u s u a l l y e x i s t as OH-or O^ - c a t i o n complexes i n water. The l a r g e r monovalent a l k a l i metals Rb and Cs ( 6 - f o l d c r y s t a l l o g r a p h i c r a d i i of 1.47 and 1.67 A, r e s p e c t i v e l y ) are thought to be e s s e n t i a l l y unassociated w i t h water molecules ( 1 ) . However, the smaller monovalent and most d i v a l e n t c a t i o n s form strong aquo-complexes. Thus, the r e a c t i o n -

+

Mg

2 +

+ nH 0 = M g ( H 0 ) 2

2

+

2 + n

has a Gibbs f r e e energy (AG°) of about -460 kcal/mol. (Here, η corresponds to the number of water molecules i n two l a y e r s of

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

18.

LANGMUiR

Aqueous

Complexes

of Geochemical

Interest

355

c o o r d i n a t i n g water ( 1 ) ) . For most c a t i o n s , the immediate hydra t i o n envelope around the c a t i o n contains s i x water molecules (20). In t h i s f i r s t envelope, the water d i p o l e s are o r i e n t e d w i t h t h e i r oxygens towards the c a t i o n and protons away (21). Second and t h i r d l a y e r s of water may a l s o be s i g n i f i c a n t l y a s s o c i a t e d w i t h the c a t i o n , although these are more l o o s e l y held. The strength o f bonding between the inner sphere o f water d i p o l e s and a p o s i t i v e l y charged core i o n increases q u a l i t a t i v e l y as the charge d e n s i t y of the core i o n i n c r e a s e s . The d i r e c t dependence o f charge d e n s i t y on the valence ( z ) and i t s i n v e r s e dependence on i o n i c r a d i u s ( r , i n Angstroms) has l e d t o the concept of i o n i c p o t e n t i a l (Ip) which i s defined as z+/r. The valence of most geochemically important c a t i o n s o r c a t i o n s i n t h e i r oxy- and hydroxy-complexes i s p l o t t e d against the c a t i o n r a d i i i n Figure 1. Most o f the r a d i i are from Shannon and P r e w i t t (22) and, when the data e x i s t , are f o r the c a t i o n s a t t h e i r appropriate c o o r d i n a t i o n numbers w i t h oxygen o r h y d r o x y l . The p l o t shows, i n general, that a t pH values between 2 and 12 and a t 25°C, the l a r g e r monovalent and d i v a l e n t c a t i o n s occur as simple c a t i o n s o r aquo-ions. I f we d e f i n e a hydroxycation as a c a t i o n whose f i r s t . OH complex pre dominates over the unhydrolyzed c a t i o n a t some pH below 7, then Be, Cu, Sn, Hg, and Pb are a l l hydroxycations (23). 2_ With i n c r e a s i n g i o n i c p o t e n t i a l of the c a t i o n , OH and then 0 -bonding o f the core c a t i o n becomes important. The OH and 0 ~-bonded c a t i o n s become predominant forms even i n very a c i d waters. For the oxycations (e.g., U02 , V0 ) and oxyanions (e.g., SO^ ", PO4 ", 0 0 ~ ) , the cation-oxygen bond i s a strong covalent one, so that these complexes p e r s i s t as such i n most r e a c t i o n s that form l a r g e r complexes. However, f o r d i - and t r i v a l e n t c a t i o n s , the hydroxy complexes may be l e s s s t a b l e than complexes formed w i t h other l i g a n d s . The dashed l i n e s i n Figure 1 are drawn t o roughly separate groups o f c a t i o n s by t h e i r ten dency towards formation o f 0H~ and 0 complexes i n water. These l i n e s c l e a r l y do not y i e l d groupings based simply on i o n i c poten t i a l , which would p l o t as s t r a i g h t l i n e s passing through zero f o r both v a r i a b l e s i n Figure 1. The s t o i c h i o m e t r i e s o f known o r presumed complexes formed by h y d r o l y s i s of c a t i o n s have been l i s t e d i n Table I . The best d i s c u s s i o n o f the s t a b i l i t i e s and behavior o f most o f these species i s given by Baes and Mesmer (23).


+

2

2+

2

3

2+

2

3

Inner and Outer Sphere Complexes As noted above, most metal c a t i o n s i n pure water are complex ed w i t h H2O, OH , or 0 ~. Formation of a complex w i t h another l i g a n d then may i n v o l v e d i s p l a c i n g one o r more water molecules from the c o o r d i n a t i o n sheath of the c a t i o n by the l i g a n d . Thus, 2

M(H 0) + L = M(H 0) ,L + H O ζ η ζ η—1 ζ 9

o

When one or more h y d r a t i o n spheres remain a f t e r complexation, then



356


I

-> x

.

υ

_|

"

1

S

C r

Ν

1—VI

1

Se Mnj.

Ρ

As

Mo\ _> %Te W

j

w

I

oxyanions

'

— ^

U

I

^

F e , V , ^ p f C u o ^ e / t

0

Βοβ

/ C o \ Z n

1

8

^

Cd

M n

Ca

^Rb

BO

#

Ra

Sn

Na cations

1

Γ

hydroxyanions

^

-1

•

1

V Sn Pb JMO.AU

M

σ

'

1

hydroxycations Sb

/Te

^

1

1

U

'

"5

1

j

ο

ο

1

I

I

I

I 0.5

I

8 I

hydroxycations I

Ionic Radii

I

I 1.0

. 1.5

(Â)

Figure 1. Valence of core cations in their aquo-complexes plotted against crystal radii of the cations. The radii are mostly from Shannon and Prewitt (22). (%) Cations; (O) hydroxycations and hydroxyanions; (χ) oxycations; ( Q ) oxyanions. See caption to Table I.


18.

LANGMUiR


Table. I.

Aqueous

Complexes

of Geochemical

Interest

Species formed by h y d r o l y s i s of cations i n water at 25°C, and pH 2-12. Only species which may exceed 10% of the t o t a l core c a t i o n concentration are l i s t e d . Cations are w r i t t e n as f r e e species i f they occur c h i e f l y as such i n the pH range 2-12. When a c a t i o n i s l e s s s t a b l e than i t s hydroxy or oxy-complex at a pH below 7, the hydroxy or oxy-complex i s l i s t e d instead of the f r e e c a t i o n . Most of the f r e e c a t i o n s occur as H^O-complexes. Elements such as C u ( I I ) , F e ( I I I ) and Th(IV) which form polymers, are assumed to occur at Sb(OH)5-n ] +.

2

5

ΝΟ" ~>

u0

n

2

n

2

n

2

11

H C r O " [ 0 , l ] , H Mo0 " [0-2], H S 0 " [ 0 , l ] , H SeO " η 4 η 4 η 4 η 4 [0,11 H W O [ 0 - 2 ] , MnO ", TeO ( O H ) " " [nm = 06, ' η 4 4 n m 15, 24], ( U 0 ) ^ ( 0 H ) " [nm = 10, 11, 22, 35], 2 n ~ 'm W..Ο " 12~39' 2_n

2

2 n

o

y

6

2 n

m

m

v

6


n

358


the complex i s c a l l e d outer sphere o r an i o n p a i r . Bonding i s c h i e f l y l o n g range and e l e c t r o s t a t i c . The i o n p a i r may p e r s i s t through a number o f c o l l i s i o n s w i t h water molecules. Examples of i o n p a i r s are most monovalent and d i v a l e n t oxyanion complexes formed w i t h a l k a l i metals and a l k a l i earths ( f o r example, NaHC03 , SrC03°, CaNÛ3 , and MgHP04°). The l i s t a l s o i n c l u d e s most monov a l e n t and d i v a l e n t metal s u l f a t e and c h l o r i d e complexes. A v a i l able data suggest the f o l l o w i n g l o g K values f o r i o n p a i r s : ML p a i r s ^ 0 - 1 ; ML2 o r M2L p a i r s ^.7 - 1.3, and M2L2 p a i r s 2.3 - 3 . 2 . For i o n p a i r s , K values tend t o be roughly constant f o r a given l i g a n d w i t h metal c a t i o n s o f i d e n t i c a l valence and roughly the same s i z e . For example, the d i v a l e n t metal s u l f a t e i o n p a i r s formed w i t h Ca, Mg, N i , Zn, Cu, Co, Cd, Mn, Fe, and Cu have l o g K values from 2.28 t o 2.35 (see F i g u r e 2 ) . T h i s behavior r e f l e c t s the l a r g e l y e l e c t r o s t a t i c a t t r a c t i o n between the i o n s , n e a r l y independent o f the d e t a i l e d e l e c t r o n c o n f i g u r a t i o n of the c a t i o n ( 1 ) . When complexation i n v o l v e s displacement by the l i g a n d o f water molecules immediately adjacent t o the c a t i o n so t h a t the l i g a n d contacts the c a t i o n , the complex i s c a l l e d i n n e r sphere. Such complexes are g e n e r a l l y more s t a b l e than outer sphere complexes o r i o n p a i r s . A c t u a l l y , there are no pure " i n n e r " o r "outer" sphere complexes. For example, even i n SO4 complexes o f Be, Mg, Zn, N i , Co, and Mn, about 10% of the bonding i s inner and 90% outer sphere. For C r - s u l f a t e , the p r o p o r t i o n s become more than 70% inner and 30% outer sphere ( 1 ) . +

a s s o c


a s s o c

a s s o c

3 +

Electronegativity P a u l i n g (24) has defined e l e c t r o n e g a t i v i t y (EN) as the power of an atom to a t t r a c t e l e c t r o n s . The concept i s u s e f u l i n comp a r i n g s t a b i l i t i e s of i n n e r sphere complexes when t h e i r bonding i s s i g n i f i c a n t l y c o v a l e n t . The degree o f covalency (as opposed to i o n i c i t y ) o f bonding i n the complex i n c r e a s e s as the d i f f e r ence i n EN (ΔΕΝ) o f the c a t i o n and l i g a n d approaches zero. Based on bonds i n c r y s t a l s , P a u l i n g computes t h a t roughly when ΔΕΝ 1.5. Based on the r e l a t i v e s o l u b i l i t i e s o f t h e i r s a l t s , EN values f o r CO 2~\ -

2

2

2


18.

Aqueous Complexes of Geochemical Interest

LANGMUiR


7.0

6.0

• so|"

Δ

ε ο ο Ξ

7 /

ο CO* x ΗΡ0|' HCO;

CO'

5.0

ο

V

/

4.0 ΗΡ0

χ/

Δ

3.0 n — •

— —-

u

π

2- •

S0 -Έ-° 4

D

α

π

-

π

—* τ -

2.0 HCO;

i.oh Βα

I Sr

Ca

Mg

111 I

II

in

Be I P b I Cd |UCv>|Co| Ni 'ode Mn Zn VO Fe Cu Hg

I

_J

2.0

I.0 I.5 Electronegativity of Cation

Figure 2. Stabilities of some 1:1 oxyanion complexes plotted against the electro negativity of the cation. Literature data have been corrected to I = 0 when necessary. Lines through the data for HCOf and SO ' complexes are for mean values. Curves drawn through the ΗΡΟ/' and CO/' data have no statistical significance. 2

/f


359


360

HP04 ~,

and SO^^ should decrease from near 4 to about 3 i n the order SO^ > HPO4 "" > C O 3 " . Thus, covalency of bonding should be l e a s t f o r the s u l f a t e complexes and greatest f o r the carbonate complexes, which are apparently f o r the most p a r t of inner sphere character f o r c a t i o n EN values above 1.5. For the a l k a l i n e e a r t h s , bonding w i t h a l l four l i g a n d s shown i n Figure 2 i s l a r g e l y i o n i c ( i . e . , independent of EN) be cause of t h e i r predominantly outer sphere c h a r a c t e r . The s l i g h t decrease i n s t a b i l i t y of these complexes g e n e r a l l y , from Ba through Be, may r e f l e c t the l i g a n d s c l o s e r approach to the r e l a t i v e l y unhydrated Ba i o n (Ip = 1.5), a p r o x i m i t y not p o s s i b l e i n the case of Mg (Ip = 3 . 0 ) or Be (Ip = 5.7). These s m a l l e r ions s t r o n g l y r e t a i n t h e i r waters of h y d r a t i o n i n complex form ation. -

Z

2-

2

2


1

Schwarzenbach's and Pearson's C l a s s i f i c a t i o n s There are no simple r u l e s i n v o l v i n g addend s i z e , valence, Ip, or EN that can e x p l a i n a l l the observed s t a b i l i t i e s of com p l e x e s . However, f u r t h e r i n s i g h t s are provided through approaches suggested by Schwarzenbach ( 2 ) , and Pearson (3) and Ahrland (4). Pearson and Ahrland c l a s s i f y c a t i o n s and l i g a n d s as 'hard or s o f t a c i d s or bases. Soft i n f e r s the s p e c i e s ' e l e c t r o n cloud i s deformable or p o l a r i z a b l e and may enter i n t o e l e c t r o n i c a l l y unique s t a t e s i n complexation. Hard addends are comparatively r i g i d and non-deformable and show an absence of e l e c t r o n i c i n t e r a c t i o n s i n complexation. Schwarzenbach (2) (see a l s o P h i l l i p s and W i l l i a m s ( 3 Q ) ; N a n c o l l a s , (1)) d e f i n e s three c l a s s e s of complexes. Class A i n c l u d e s metal c a t i o n s which have noble gas c o n f i g u r a t i o n s . These are l i s t e d below. 1

!

T

Cation ( i n c r e a s i n g covalency Be +

Na , K', Rb"*

Mg , A l 2+

3 +

Sc , 2 +

3+

cs

3 +

Sr , Y ,

Ti

4 +

Zr

4 +

•HCO cd

ω

u

g

•H

Cs

Ba

Atomic C o n f i g u r a t i o n He

2+

Ca

> )

2+

, La

>·> Ο β CD

Ne

> Ο

Kr

Ar

u

Xe

Class A c a t i o n s have s p h e r i c a l symmetry and low p o l a r i z a b i l i t y and thus are 'hard spheres' (31). Pearson's hard a c i d s i n c l u d e the above, but a l s o M n , U O ^ , V0 , C r , F e , C o , G a , S i , U^ , and T h . These c a t i o n s tend to form l a r g e l y e l e c t r o s t a t i c bonds w i t h l i g a n d s , e s p e c i a l l y when the l i g a n d s are hard (have low 2+

+

2+

3 +

3 +

3 +

3 +

4 +


4 +

18.

361

Aqueous Complexes of Geochemical Interest

LANGMUiR

p o l a r i z a b i l i t y ) and the c a t i o n s monovalent or d i v a l e n t . Important complexes are formed with hard l i g a n d s F , H2O, and 0H~. Carbon ate and bicarbonate complexes are a l s o important but only f o r the monovalent and e s p e c i a l l y d i v a l e n t c a t i o n s . The s t a b i l i t y of_ complexes i s g e n e r a l l y i n the order OH~>F , C 0 3 ~ > H P 0 4 " » N 0 3 and P 0 ^ 3 " » H P 0 4 ~ > S 0 4 ~ . Complexes are u s u a l l y not formed with S, N, C, CI , Br , or Γ , because these species cannot compete with H2O or OH . Complexes probably increase g e n e r a l l y i n s t a b i l i t y i n the order I

Techniques of Estimating Thermodynamic Properties for Some

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