Complex formation and phosphate-H2O interactions in a concentrated aqueous Mg(H2PO4)2 solution.

Journal of Molecular Liquids, 28 (1984) 191--204

191

Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

COMPLEX F O R M A T I O N AND P H O S P M A T E - H 2 0 INTERACTIONS IN A CONCENTRATED

AQUEOUS Mg(H2P04) 2 SOLUTION.

RUGGER0 CAMINITI Istituto di C h i m i c a Generale, sit~ di Cagllari,

I n o r g a n i c a e Analitica,

Via 0spedale 72, 09100 Cagliari,

Unlver-

(Italy)

(Received 14 F e b r u a r y 1984) ABSTRACT X-ray d i f f r a c t i o n data from a solution of Mg(H2P04) 2 were examined,

the experimental d i s t r i b u t i o n curve shows peaks

at about 2.10,

2.7-2.9, 3.6, 3.9 and 4.25 ~.

The 3.6 A peak

reveals the formation of inner sphere m a g n e s l u m - p h o s p h a t e com+2-z in w h i c h oxygens from phosphate plexes M g ( H 2 0 ) 6 _ z ( H 2 P 0 4 ) z groups substitute z w a t e r m o l e c u l e s of the h y d r a t e d Mg(H20)~+v ions. Least squares refinements of the i(s) curve are consistent with a structural unit in w h i c h the phosphate

tetrahedron sha-

res a corner w i t h one m a g n e s i u m o c t a h e d r o n with Mg-0-P angle of 147 deg.

Each phosphate ion interacts with about eight wa-

ter molecules. INTRODUCTION Phosphate ion c o m p l e x i n g with various cations,

e.g. cal-

cium, m a g n e s i u m is important to an u n d e r s t a n d i n g of its behaviour in certain biological

systems;

the possibility of complex

formation b e t w e e n m a g n e s i u m and phosphate ion is of interest also in g e o c h e m i s t r y with regard to w a t e r and fresh water chemistry. While several solid m a g n e s i u m phosphates have been studied [la-d ] n o study by using X-ray diffraction has been done on the complex formation between m a g n e s i u m and phosphate ion in aqueous solution.

Now,

the X-ray diffraction technique has proved

0167-7322/84/$03.00

© 1984 Elsevier Science Publishers B.V.

192

to play an important role in the d e t e r m i n a t i o n of the coordination state of the metal ions in c o n c e n t r a t e d solutions.

Hydra-

tion and complex p h e n o m e n a can be deeply investigated by this me t hod

[2]

Previous diffractometrlc studies on trivalent

[3a-c] and b i v a l e n t

[4a-d I ions have shown the existence of di-

rect interactions b e t w e e n cation and sulphate anion. The existence of complex formation for the system MgH2P04 was shown by Havel and H~gfeldt

[6]

The techniques

used did not give direct evidence about the nature of the complexes but the values of the e q u i l i b r i u m constants strongly suggested an inner complex formation. A n a l y s i s of X-ray and neutron diffraction data from concentrated aqueous salt solutions gives details about the environment of the ions and information about the g e o m e t r y of the c o o r d i n a t i o n polyedra.

This is p a r t i c u l a r l y useful

in the ca-

se of direct interaction between the anion and the cation,

sin-

ce information about their relative o r i e n t a t i o n cannot be obtained through other experimental techniques than diffraction. A n o t h e r object of this w o r k was to study the h y d r a t i o n of phosphate anion.

The h y d r a t i o n of the oxyanlons has been

e x t e n s i v e l y studied in the case of sulphate solutlons while only a study has been done on the phosphate solutions

[5]

E X P E R I M E N T A L AND DATA TREATMENT The solution was p r e p a r e d by d i s s o l v i n g w e i g h e d amounts of M g ( H 2 P 0 4 ) 2 . 3 H 2 0 in water;

the compositions were determined

by standard volumetric methods. was o b t a i n e d by denslmeter.

The density of the solution

In table 1 we report the analyti-

cal data of the solution studied.

The temperature of the sam-

ple was 20ZI °C. TABLE 1 C o m p o s i t i o n of the solution in moles/liter, and ~

d is

the density

the linear absorption coefficient calculated for Mok~

radiation. [ M E 2+]

[ H2P0 ~]

1.5

3.0

[H20] 51.047

d(gcm -31

~(cm -11

1.2471

2.2459

193

The X - r a y ction

has b e e n

apparatus described

ducibility

of d a t a w e r e

each

were

point

was w i t h i n

1%

i(s) where

fi are

intensity puted

A

proposed mer

the

atomic

unit

and W a b e r

scattering

units.

The

[8~

for H 2 0

proposed

from

The

International

correlation

function

corrected

Ie.u.

factors

those

proposed factors

solution

com-

coefficients

[iO]

[ii]

in is the

were

the

et al.

of the

and

using

Tables

for a-

coefficients

scattering

by S t e w a r t

.

from

(i)

of atoms

and

obtained

)2

scattering

and P,

Details

to

amplitudes

formula

used.

[Sb-c,4a,7a-b] was

stolchimetrlc

m kinds

[9] for 0 atom.

taken

The

m ) / ( i=l ~ xifi

to an a n a l y t i c a l

those

by a F o u r i e r

according

for

reproducibility was

given

of r e p r o -

collected

the o v e r a l l

already

the

checks

) radiation

Ie.u.

x i are

for d a t a c o l l e -

counts

of the s o l u t i o n

containings

by H a J d ~

they w e r e

been

m _ i=l ~ xif~

in e l e c t r o n

H atom were

G(r)

have

intensities

according

The

(O.7107

function

seifert)

Continuous

Mok~

dispersion,

a structural

.

and

structure

= ( Ie.u.

nomalous

[7a-b]

performed. or m o r e

.

the n o r m a l i z e d

S. D.

iOOO00

of d a t a n o r m a l i z a t i o n The

( G.

by C r o -

for the

, for Mg a t o m

. was

calculated

transformation

= i + ( 2 ~2r

~Smax @o)-lJ si(s)sin(rs)ds

(2)

Smin here

@o

is the

s is the usual re ~ the

is h a l f

average

bulk

scattering

density

variable

the s c a t t e r i n g

angle

of s t o i c h i o m e t r i c

( s = ( 4~/l and

units,

) sin~

, whe-

A is the w a v e l e n g t h

of

radiation emploJed, Moka ) (0.65 ~-i ) and s ( 0 -i ' stain max ) are the l o w e r and u p p e r l i m i t s of the e x p e r i m e n t a l

15.5 A data.

In o r d e r

incoherent mator

was

stematic removal

radiation estimated

residual

up

the

reaching by

function,

the c o u n t e r

are c o r r e c t e d

peaks

in the

of c o r r e c t i o n

for i n a c c u r a t e

i(s)

a semi-empirlcal

errors

of s p u r i o u s

The m e t h o d makes

to e v a l u a t e

G(r)

through

procedure

fraction

curve

of

the m o n o c h r o I12]

by a m e t h o d

of s y s t e m a t i c

determination

the

•

based

Syon the

at low r [12] errors

.

generally

of the m o n o c h r o m a t o r

tran-

194 smission alters

factor

the

but

real

data normalization c

squares

Ic(S)

the c o r r e c t e d

=

xif

and

species.

tion

intensities

(s) +

~ xii i i=l

incoherent

In this

function

is a b s o r b e d constant

details

the m e t h o d

the

Ic(S)

~s

about

comparison

Habenschuss-Spedding short

distances

ction

c.f.

fitted

and

of 13a-

this

by

least

method

(3)

fi(s)

the

second

and

of

(3). For

functions identical

the

) obtained

The further

.

provide

( Fig.

IinC(s)i

discrimina-

~ = ( A + { B k )-I.

function

term

(3)

of the v a r i -

the m o n o c h r o m a t o r

gives

function

~ Bkexp( k=l

amplitudes

[13a-c]

methods

2, p o i n t s

In

correlation

in the G(r)

the si(s)

( Fig.

into

is g i v e n

of the

two n o r m a l i z a t i o n

analysis

Following

are

+

scattering

formulation

normalization

The

persists

the m e t h o d

and S p e d d i n g

u s e d here.

A , B k , C k and D k are p a r a m e t e r s .

are c o h e r e n t ous

was

error

curve

i 1 where

some

Therefore,

by H a b e n s c h u s s

[14] used,

to a s m o o t h

that

in the G(r).

proposed

and p r e v i o u s l y

procedure

it is p o s s i b l e

peaks

lower

shows

spurious

and so in the

l, p o i n t s with

that

results.

The

peaks

at

following

) and G(r)

this m e t h o d

have

funbeen

used. The p r o c e d u r e

based

on the

removal

present

in the G(r)

function

at small

fective

if a r a t h e r

extended

range

this

end

and so i n t r a m o l e c u l a r

in the p r e s e n t peak

at about

tributions tation

case

the O-H p e a k

1.50-1.55

are o b v i o u s

of the results.

for N - 0 solutions

( in n i t r a t e

A

) were

and not The

peaks

at a b o u t also

very

ef-

can be u s e d

appearing

at

to

low r (

1.0 A and the P-0

removed

important

) [15]

and for P-O

peaks

of r is m o r e

of d i s t a n c e s

same p r o c e d u r e

solutions

) [3c,4c,16]

[ 5 ] distances.

real

of u n p h y s i c a l

values

was

since

these

for the used

, for S-0

( in p h o s p h a t e

con-

interpre-

elsewhere

( in s u l p h a t e solutions

)

195

si

1.C

0.~

0.(

-02

-1.0 '

0

Fig.

~

'

i

'

4

i. E x p e r i m e n t a l

lution

(points)

(solid

line)

I

6

obtained

ANALYSIS

OF THE R E S U L T S

lue

at 2 . 1 A

is c o m p a r a b l e

solutions

[la-d] [17a-c]

scribed

to 0-O

-bonded

water

in the

i

si(s)

i

I

10

I

12

I

s,k I ,

14

I

16

for 1.5 M M g ( H 2 P O 4 ) 2 so-

the s y n t h e t i c

the best

,

fit

structure

function

( parameters'

values

functions

In the e x p e r i m e n t a l

structures

with

from

2 ).

centered

~}

structure

compared

in T a b l e

Correlation

i

cation

G(r)

( see

is a s c r i b a b l e

Fig.

with

the M g - O

distance

and

in a g r e a t

number

The

double

2 ) the

to the M g - O

peak

nearest

neighbours

molecules,

which

hydration

shells;

found

crystal aqueous

2.8 A is to be

interactions

are p r e s e n t

peak this va-

in the

of m a g n e s i u m

at about

further

first

distance;

both

between

hydrogen

in the b u l k

contributions

a-

and

to this

196

peak

come

from

interactions

te ion and a n i o n i c tributions inside

could

among

hydration

also

come

the p h o s p h a t e

oxygen

water

from

atoms

molecules

of the p h o s p h a [5,18a-c]

0-0 d i s t a n c e s

(about

; con2.56 A

)

ion. o

A large In the

composite

solution

peak

is v i s i b l e

are v i s i b l e

three

in the

components

range

3.3-4.5

at about

3.6,

A.

3.9

o

and 4.25 H20II

A ascribable

interactions,

essentially

to the Mg-P,

respectively.

In the

P-H20

solid

and Mg-

structures

4c

o

the

distance

the

aqueous

Mg-P

is b e t w e e n

solutions

3.4-3.5

previously

A;

the P - H 2 0

studied

5

was

distance found

in

in the

o

range the

3.75-3.91

second

range

A;

the

distance

coordination

4.1-4.25

shell

Mg-H20II

(water

) has b e e n

found

molecules [17a-c]

in

in the

A.

G(r)

1.0

I

1

Fig.

2.

2

I

3

Experimental

Mg(H2P04) 2 solution the s t r u c t u r e

I

I

4

5

correlation (points)

function

with

r,A

6

function

compared

obtained

I

with

I

7

G(r)

for 1.5 M

that

calculated

the p a r a m e t e r s

from

of Table

2.

197

Model For a q u a n t i t a t i v e analysis we tested a synthetic function w h i c h was refined by least squares, tal structure function.

against the experimen-

The c h a r a c t e r f s t i c s of the approach

used and the c o m p u t a t i o n p r o c e d u r e are the same as those employed in previous papers

~b,5,17c]

.

For calculating the i(s)

theoretical function we used the w e l l - k n o w n formula m n i(s) = i=l~ J=l~ixififj

m ( i=12 xifi

)-2 exp ( -1/2 o 21j s2 )x

m

x sin(srij)/srij

x exp ( -1/2

+ 4~@o

~9]

~ i=l

m

m

~ xixiflfj J=l

(

• xifi )-2 i=l

aoi j s 2 ) x ( S r o i j C O S ( S r o l J ) - s i n ( s r o i J ) )

x i/s 3

(4)

where m is the number of atoms in the stolchiometric unit, n i is the n u m b e r of atoms with discrete structure origin atom of the i type;

" seen " by an

rij is the mean radial distance of

the jth atom from an origin atom of the i type;

o ij is the

r o o t - m e a n - s q u a r e d e v i a t i o n for rij; roi j is the mean radius of the discrete structure of the J atoms around one of the i type; and Coi j is the r o o t - m e a n - s q u a r e deviation for roi j.

In eq.

(4) the first term derives from the discrete interactions, while the second is the c o n t r i b u t i o n deriving from the continuous d i s t r i b u t i o n of distances. The model used was based on the h y p o t h e s i s that first and second n e i g h b o u r w a t e r m o l e c u l e s around the cation have a discrete structure. noncorrelated.

The h y d r a t e d ions were considered spatially

The discrete structure of anions only extends

up to the first neighbours. A c c o r d i n g to these assumptions,

the model used has the

f o l l o w i n g features: i) M a g n e s i u m in octahedral g e o m e t r y was d e s c r i b e d by three independent parameters:

the distance rMg_w I and two root-mean

-square d e v i a t i o n s O M g _ w I

ando

Wl-W 1

198

2) For

the p h o s p h a t e

assumed, ters

with

the usual

tetrahedral

r0p_O P d i s t a n c e

and

interactions

M g - O 7, Mg-08, are

Only

three

arising

Mg-09

correlated

orientation

from

the oomplex,

was

parame-

between

octahedron

independent

and

tetrahedron

parameters

one m e a n - s q u a r e

deviations

for all

into

interactions

account.

groups

the d i s c r e t e

around

cations

Mg-w 2 interactions

independent

parameters:

root-mean-square

z,

interact-

deviation

the

(Mg-w2)

were

distance

aMg_w 2 and

were

described rMg_w

taby

, the

the c o o r d i n a t i o n

nMg_w 2 .

number

5) W l - W 2 i n t e r a c t i o n s shells

belonging

of the cation.

mean-square dent

to d e s c r i -

phosphate

the Mg-O6-P.

4) S e c o n d - o r d e r

three

is fixed.

are n e c e s s a r y

of b o n d e d

and

Mg-P,

(Wl)i=6_z-(0P03H2)z ( see Fig. 3), ^ to the M g - O 6 - P angle, once the r e c i p r o c a l

the n u m b e r

ions,

namely,

and

the complex:

ken

structure

the ~ 0 p _ 0 p

to be refined.

3) The

be

ion,

the

The

deviation

parameters,

a

while

to two s u b s e q u e n t

distance

hydration

r

and the rootWl-W 2 a s s u m e d to be i n d e p e n -

were Wl-W 2 the c o o r d i n a t i o n

number

n

is r e l a t e d Wl-W 2

to n M g _ w 2 by No

fixed

the

orientation

6) No g e o m e t r i c a l and

the

was

number

for w 2 m o l e c u l e s .

was made rip_w

as an i n d e p e n d e n t

and r o o t - m e a n - s q u a r e

nwl_w 2 = nMg_w2/(6-z)w I .

chosen

assumption

frequency

troduced ces

relationship

about

of P - w

parameter

deviations

anionic

hydration

interactions together

with

for 0 p - w

is indistan-

and P-w

inte-

ractions. 7) In a d d i t i o n nuum for

region loss

Only

four

to d i s c r e t e - s t r u c t u r e

interactions,

was

each

introduced

of p o s i z i o n a l distances

ir r o o t - m e a n - s q u a r e O-H20

and H 2 0 - H 2 0

rameters.

around

correlation

of the

start

deviations pairs

were

species

at h i g h e r

a contito a c c o u n t

distances.

of the c o n t i n u u m

for

the Mg-H20,

considered

and the-

P-H20,

as i n d e p e n d e n t

pa-

199

9

)6

Fig.

3.

The

phosphate unit

has

bridging angle

resulted

being the

plane

06, in

model

assumed

the h y d r a t e d

the

147

for

magnesium

the b o n d i n g ion.

containing

the

M g 2+

P atom

the

oxygen

and

The

ion,

of

the w l,

07 .

the

structural

The

the

Mg-0-P

degrees.

least

squares refinements were o_ 1 0.65-15.5 A , the f u n c t i o n

s intervall

U = ~ s

to

a mirror oxygen

The

s

geometrical

group

carried

out

using

the

max . mln

i(S)ob s _ i(S)calc

minimized

classical

Marquardt

by means Gauss-Newton

[20] .

This

of

)2

the

(5)

LSHS

program;

linearization

program

this

method

is a p e r s o n a l

is b a s e d

on

as m o d i f i e d

by

version

in F o r t r a n

200

IV, that allows the simultaneous fitting of the parameters with a calculation time lesser than the least-squares programs previously used. Results In Figs.

1 and 2, the structure functions and the corre-

lation functions obtained from the best fit are compared with the experimental data.

The final values of the most signifi-

cant p a r a m e t e r s are listed in Table 2. Table 2.

P a r a m e t e r values [r = distance

squares deviation viations

(A), o = root-mean-

° (A), n = frequency factor

(in parentheses)

]

and standard de-

obtained from least squares fitting

and used in the final c a l c u l a t i o n of the synthetic structure function;

z = the average number of phosphate bonded to magne^

slum. Mg-06-P angle in degrees. Cation

Anion

rMg_Wl = 2.11(1)

rOp_Op= 2.58(1)

OMg_Wl 0.126(8)

OOp_Op=0.05(1)

=

rwl_w 2 = 2.76(1) =

o Wl-W2

0.118(8)

rMg_w2 = 4.28(6) o

Mg-w 2

nMg_w 2

= 0.47(4) =

9.5(5)

rOp_ w = 2.878(8) o Op-W rp_ w o

P-w

np_ w

=

Complex z

=

1.0(i)

o = 0.189(5) Mg-O6-P

= 147(2)

0.135(7)

= 3.87(2) = 0.33(1)

= 8.8(4)

The consistency of the model with experimental data is supported by the very good agreement obtained and also by the low value of R = 0.15

R is an agreement factor expressed by

R = ( ~ (si(S)ob s - si(S)calc)2) ~ /( Z ( s i ( s ) o b s ) 2 )

~

(6)

commonly used in crystallography. Obviously the agreement between model and experimental

201

data

is n o t b y

rect.

The

necessary

condition

is i m p o s s i b l e only

itself

difficulty

for

the

respect

is to s p e c i f y

that

an u s e f u l o f this

basis

The function This

AND

experiment

shown

in line w i t h

te c o m p l e x in the

Coordination

lecules

procedure

or phosphate

[17a-o]

is c o n f i r m e d

bing

ions

phase.

selected

Moreover,

[3a-c,4a-c,~

it c o u l d

that p o i n t s

it

prove

that on the

be c o n s i d e r e d

correlation conctacts.

to c a t i o n - p h o s p h a -

o f the p a r a m e t e r s some

obtained

conclusions:

presence

) arranged

the p r e c i s i o n

of a second

solutions

shell

and

around

bonding

mo-

The v a l u e is

in s o l u t i o n the c a t i o n

among

o f the p a r a m e t e r s are

confirm

( from water

o f the m e t h o d ,

Jim-d]

shell

of hydrogen

The v a l u e s

hydration

atoms

octahedrally.

structures

coordination

in o t h e r

the c a t i o n

by six oxygen

in s o l i d

by a network

Cation-phosphate As

describing

molecules.

the s e c o n d

se f o u n d

suggest

Mg-w I within

found The

outer water

( see Fig.

in fact

of cation-phosphate

161

The v a l u e s

is s u r r o u n d e d

as

the p h o s p h a t e

of c a t i o n

o f the d i s t a n c e the same

for

o f the e x p e r i m e n t a l

the e x i s t e n c e literature

The p a r a m e t e r s that M g ( I I )

analysis

in d e t a i l .

o f the m o d e l ,

only

This

ones.

analysis

formation.

fitting

work

it

employed

CONCLUSIONS

qualitative has

studies

but

data.

structural

It w a s

in s o l i d

f o r the c h o i c e

single

valid,

o f the c a t i o n

ones.

the p r e v i o u s

one o f the m a n y p o s s i b l e DISCUSSION

if the

is c o r -

only a

" o f the m o d e l

orientation

possible

o f the s t r u c t u r e

to be

Judged

diffractometric

to the o c t a h e d r a l

on the g r o u n d

ground

to be

the m o d e l

of course,

in the p r e s e n t

selected

3 ) is one o f the m a n y

that

is,

" uniqueness

especially

the

two

the m o d e l s

discussed

For example,

proof

the

of our single

is s e r i o u s

the m o d e l s

anion with

between

to a s s e s s

on the g r o u n d

treats

a conclusive

consistency

in a g r e e m e n t

inner and descriwith

tho-

[l?a-c]

complex

f a r as r e g a r d i n g

the a v e r a g e

number

of phosphate

gro-

202

ups d i r e c t l y ments

bonded

gives

ment with

final values

those

ty constants centration

to the cations, of z about

calculated

[8]

range used

in the present

the m a g n e s i u m - O - P

is very

similar

stance

is,

angle

to that found

solid

[idl

is similar

lid c o m p o u n d

1 .

on the average,

given

analysis.

and c o n s e q u e n t l y

is agree-

to be valid

obtained

in the con-

As far as re-

in our solution,

also

fragment

determined

it

of

the cation-P

and solid structure.

of phosphate

refine-

for the stabili-

in c o r r e s p o n d i n g

in solution

the n u m b e r

This value

by the values

, if these are assumed

garding

MgHPO4-3H20

the least-squares

di-

In the so-

groups b o n d e d

toscation

by the s t o i c h i o m e t r y ~ f r ~ h e

substance. What

seems

to persist

( solid and liquid clusion phate

in the two different

) is the b u i l d i n g

is in line with

the findings

solutions[3a-c,4a-c]and

and also

in p h o s p h a t e

of a structural ctures

and c o m p l e x e s

[5~

between

itself.

in several

in nitrate

solutions

continuity

unit

This con-

cases

solutions

, in which fragments

in c o n c e t r a t e d

conditions

of sul-

[21a-b]

the existence

of solid

solution

stru-

has been confir-

med. Moreover, be consistent Phosphate

the a g g r e g a t i o n

with

~roups

and anionic

From the final value sible

to calculate

geometry

for the phosphate with

those

solutions

nic h y d r a t i o n

of the Op-0p distance of P-0 by assuming

group;

. Regarding

they are different

ned in the p r e v i o u s

the value

found in the crystal

[5]

study.

complexes

the p a r a m e t e r s respect

to the values

in the solution

tions

p H in our solution [22].

in which,

studied.

should have

It w o u l d be interesting on increasing

should be present.

and in

of the anio-

We think that the average

prevailing cies H2PO ~

it is pos-

1.58 A is in a-

around the anion obtained,

species

to

constants.

a tetrahedral

structures

of w a t e r m o l e c u l e s and 3.0,the

proved

from e q u i l i b r i u m

hydration

the value

greement aqueous

of these

the one o b t a i n e d

depends

obtainumber on the

Being w i t h i n

2.0

the p r e d o m i n a n t

spe-

to study other ~solu-

the pH, also the species P0~-

In such a way we may check

if, also in

203 _

aqueous number

solution

( pH 710),

of 12 as f o u n d

studies

may

in s o l i d

contribute

ral p r o b l e m .

We

the PO

to c l a r i f y

are w o r k i n g

ion has

structure this

in this

a coordination

~l~a-c]

aspect

Further

of the s t r u c t u -

direction.

ACKNOWLEDGMENTS This work ma della All

was partially

Sardegna

the c a l c u l a t i o n s

tronico,

supported

( Assessorato

Universit&

were

done

b y the R e g i o n e

della Pubblica at the C e n t r o

Autono-

Istruzione).

di C a l c o l o

Elet-

di C a g l i a r i .

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