The hydrolytic precipitation reaction of Mg(II) from aqueous NaNO3 solution

J inorg, nucl Chern, Vol. 43, pp. 229-233 Pergamon Press Ltd., 1981. Printed in Great Britain

0022-1902/81/0201-0229/$02.~0/0

THE HYDROLYTIC PRECIPITATION REACTION OF Mg(II) FROM AQUEOUS NaNO3 SOLUTION HISAHIKO EINAGA Institute of Materials Science, University of Tsukuba, Sakura-mura, Niihari-gun, lbaraki-ken, 300-31, Japan

(Received 29 October 1979; receivedfor publication 6 March 1980) Abstract--An equilibrium study has been made of the hydrolytic precipitation reaction of Mg(lll in 1.0 tool dm aqueous NaNO3 solution at 25.0°C by measurements of the free hydrogen ion concentration by a potentiometric method and of the dissolved Mg(II) by a complexometric method. Under the condition that the solution is saturated with precipitated Mg(II) hydroxide, such species as Mg2+, Mg2(OHI~+, Mg3(OH)~+ and Mg(OHb. may be present; their stability constants and solubility products were determined. A scheme for the hydrolytic precipitation equilibria of Mg(lI) is presented. INTRODUCTION There have been some investigations on the solution chemistry of Mg(II) hydroxide [1-4]. They are characterized by simple solubility product determinations on the neutral species, Mg(OH)2. No coherent data have been obtained yet even for the solubility product itself, as will be discussed later. To understand throughly the aqueous solution chemistry of Mg(II) hydroxide, it is necessary to elucidate the nature of the dissolved species of hydrated Mg(II), with which Mg(II) hydroxide precipitation is related. The present study aims at exploring the precipitation equilibria of Mg(II) in aqueous media, of constant ionic strength determined by 1.0 mol dm -3 NaNO3 solution [5, 6]. The equilibrium study was made at a constant temperature of 25°C.

Procedure. The hydrogen ion concentration ([H+I = ht and saturated Mg(lI) ion concentration (CMg.,,,~) at equilibrium were measured on several series of test solutions, which had the following composition; B moldm-3: Mg(II), H moldm 3: H + (l.O_2B_H)moldm-3:Na+H, moldm 3: O H , and (1.0H') mol dm 3: NO3. In practice, H' did not exceed 10 2 tool din 3 and hence H not exceed 10 9 tool dm 3 respectively. The electromotive force was measured potentiometrically for a cell of the following construction -)Hg, Hg2CI213.33 tool dm 3KCll jl.0 mol dm 3KCI4 I1.0 mol dm 3NaNO311test solutionlglass electrode (+ Storage of the test solution for 6 hr at 25.0_+0.1°C, was sufficient to attain equilibrium. The absolute error in reading of the electromotive force was less than 0.2 inV. The value of h was then calculated from the measured electromotive force according to the relation

EXPERIMENTAL

E/mV = E ~ + 59.15 log h + Ej( h )

Reagents. The stock solution of Mg(ll) was prepared from the

where E '~ is the standard electrode potential of the cell and Ej(h) the liquid junction potential of the cell, respectively, the latter could be approximated by the relation

recrystallized nitrate: it was standardized for Mg(ll) content by an EDTA titration method with Eriochrome Black T as a metallochromic indicator[7] and for free acid concentration by the Gran's potentiometric titration method[8]. Sodium hydroxide solution was prepared by dissolving about 60g of NaOH and about 5 g of Ba(OH)2 in small portions of water. The supernatant was carefully separated before use and after appropriate dilution it was standardized by the conventional titration procedure with hydrochloric acid, which had been checked by sodium carbonate as a primary standard[5]. All the chemicals used were of analytical reagent grade but care was taken to insure the absence of such elements as Si(IV), AI(III), Fe(ll and III), etc. which are liable to cause hydrolytic reactions along with Mg(ll)[9]. Apparatus. The Orion Digital pH meter, model 801, was used for measurements of the electromotive force of the cell, the constitution of which will be discussed below. A Hitachi-Horiba glass electrode, model No. 1326, with a saturated calomel electrode, model No. 2310, was used as a probe for the free hydrogen ion concentration. The cell was constructed from a 100 ml polyethylene bottle with a cap, through which the glass and the reference electrodes with the appropriate salt bridge were attached. The cell was kept at 25.0_+0.1°C by a jacket, which was connected to a thermostatic water bath of adjustable temperature (temperature fluctuation: _+0.05°C). The same water bath was used for equilibration of the test solution because the batch system[5] rather than the titration system was adopted for the present study.

E~(h) = Ej. h. The saturated concentration of Mg(ll) in the equilibrated solution was measured by taking a supernatant aliquot of the test solution and titrating it complexometrically with EDTA against Eriochrome Black T as a metallochromic indicator[7]. The ionic product of water, K~(=[OH-]h), in 1.0moldm -~ NaNO3 aqueous solution at 25.0°C was estimated, by combining published data for solutions of sodium perchlorate and potassium nitrate[10], to be log K~. = -13.80. RESULTS Figure 1 shows experimental data on the relation between the saturated concentration of Mg(II), CMg.~o~,and the free hydrogen ion concentration at equilibrium, - l o g h, in the equilibrated solution. Formation of a Mg(II) hydroxide precipitate was observed above - l o g h = 9.7 under the conditions studied and gave marked decrease in CMg.~o, with increasing - l o g h. It has been reported earlier[5] that, besides the aquomagnesium(II) ion, Mg(OH2)62+, which will be simplified hereafter as Mg 2+, there may exist polynuclear 229

230

HISAHIKO EINAGA

'5.

E "5 E "o

O

"

3 2

.o-

5

lO0

105

llO

-log h

Fig. 1. Relation between the saturated concentration of Mg(II), Cug.~o~,and the free hydrogen ion concentration, -log h. Initial concentration of Mg(II): 0.02019---0.1986mol dm-L

cationic hydrolyzed species, Mgz(OH)~+ and Mg3(OH)42+, in 1.0 mol dm -~ (Na)NO3 aqueous solution at 25°C. Under the conditions that dissolved Mg(lI) is saturated in the solution with regard to precipitated Mg(II) hydroxide, (Mg(OH)2)~o.ppt, one should also consider the presence in saturated concentration of the neutral bydrolyzed species of Mg(II), Mg(OH)2, along with these cationic species. Hence hydrolysis equilibria of Mg(II) under the conditions studied can be expressed as follows: B22

2Mg2+~

. Mg2(OH)~+ +2H +

/322 [Mg2+(OH)EZ+]hZ/[MgZ+]z =

(I) (II)

/334 = [Mg3(OH)]+]h4/[Mg2+] 4

(2)

Mg2+ o,z!, Mg(OH)2,sa, + 2H +

(III)

/3~,o = [Mg(OH)zl~a,hZ/[Mg2+]•

(3)

The solubility product of Mg(II), K~,o, can also be expressed as follows: K~1o = [Mg2+][OH~] 2 = [Mg2+] h-ZK~

(4)

where K,. is the ionic product of water. Total concentrations of Mg(II), CM~.~ot,and hydroxide ion, Con.so,, in the equilibrated solution can also be expressed by eqns (5) and (6). C}as.~o~= [Mg2+] + 2[Mg2(OH)~+] + 3[Mg3(OI'I)]+] + [Mg(OH)z]~,t

2

-4

-2 + : -4 Co..sol- [OH-] = 2(/322K~ioK~ 2f134K,~oK,, +/3~ ioh -2) × Ks IoK?~2h2

(8)

Equations (7) and (8) can be combined and written in the logarithmic form as eqn (9), log G = log 2(1 +/322K~IoK,,- 2

(I)

/334

3Mg2+ ; :~ Mg3(OH)]÷ + 4H +

-2

CMs.~ol = (1 + 2/322Ks ,oK ~. + 3/334K, ~oK,. +/3, Ioh -2) × K~ ioK~?h 2 (7)

+

1334K 2~ loKS~4)K~loK~2 + 2 log h (9)

where G is 2CMs.so,-(CoH.so,-[OH-]). Equation (9) means that there should be a'linear relation between the terms log G and log h with a slope of 2 and an inter-2 2 -4 cept of log 2(1 +/3EzK, loK~ +/334K, ioK~ )K, ~oK~2, which can be solved for Ks~o by using known values of /322, /334 and Kw (10g/322=-21.07-+0.1o, 10g/334= -39.16_+0.1o[5], and IogK~=-13.80). Experimental results are shown in Fig. 2 and K,,o was calculated to be log K~ - -9.38-+ 0.1o. Under the condition that the Mg(II) hydroxide precipitate is in equilibrium with dissolved Mg(II), the formation function F, i.e. the average number of hydroxyl groups bound per dissolved metal ion[l l], can also be defined as follows: F = (Con.soJ- [OH-])/CMg.~ol.

(10)

By applying eqns (1)-(6) to eqn (10), eqn (11) can be deduced. 2(Ks ~oK~2 (/322+ 2/334Ks~oK~3) + fls ,oh -2) F = 1 + K~ioK7~2(2/322+ 3/334K~ioK~, 2) +/3s ,oh --~

(11)

Finally eqn (12) is obtained by taking the logarithmic form of eqn (11) after the appropriate rewriting.

(5) log (2 - F) = log 211 + Ks,oK~ 2 (/322+/334Ks,oK 7~2)]

Co..~o, = [OH-] + 2[Mgz(OH)~ +] + 4[Mg3(OH)]+] + 2[Mg(OH)2] ....

(6)

Equations (5) and (6) can further be rewritten by taking eqns (1)-(4) into consideration.

-

Iog[l + Ks ~oK~,2(2/322

+ 3/334Ks

,oK~2) +/3~oh

2]

(12) Calculation with the values of K~,o /322, /334 and K,

The hydrolytic precipitation reaction of Mg(II) from aqueous NaNO3 solution

231

-4

-3 0

-2

-I

1 9.5

I00

105

I1.0

-log h

Fig. 2. Relation between the terms log G and -log h. Experimental condition is the same as that in Fig. 1. revealed that both terms Ks,oKT~2(/322+/334K, ,oK~,2) and

DISCUSSION

K, loKw-2(2f122 + 3/3~K, loK~, 2) are negligibily smaller than unity, hence eqn (12) can further be simplified to eqn (13). l o g ( 2 - F) = log 2 - log (1 + 3sloh-2).

(13)

Equation (13) can be correlated to the normalized curve y = -log (1 + X-2).

(14)

and/3, ~o can be obtained from the relation log/3s,o = -2(log X

-

log h ) .

(15)

In this study the batch system[5] was applied for the equilibrium study on the hydrolytic precipitation reaction of Mg(II) owing to the very slow attainment of equilibrium. Standing the test solution for more than 4 hr was necessary to attain equilibrium (less than-+0.2mV in variations of the electromotive force of the cell). Measurements of the electromotive force and CM,.~or were carried out 6 hr after the preparation of the solution. Besides the stability and solubility constants, 3s,o and Ks~o, for the equilibrium (III), those of/%22 and K~22 for the equilibrium (IV) and of 3~34 and Ks34 for the equilibrium iV) can also be considered.

Figure 3 shows the experimental data(dots) and theoretical curve (solid line) for the relation between the terms log (2 - F) and log h derived from the value of log /L ~o=-22.4o--_ 0.1o, which had been calculated from the experimental data by the curve-fitting method[12]. Stability and solubility constants of the neutral Mg(lI) hydroxide are summarized in Table 1.

Mg2(OH)22+ .~'22 2Mg(OH)2.~., +2H+

B,22 =[Mg(OH) 2],,,h/[Mg2(OH)2 2 2 2+] = 3,,0/322 2 (16) K~22 2+ ]h -2 Kw= 2 f122K.~loK.. • -[Mg2(OH)2 2 2

-05

.~

-

0.3

i

tTi

2

-01

O1

-40

(IV)

-3.5

-30

-25

log [OH';

Fig. 3. Relation between the terms log (2 - F) and - log [OH-]. Experimental condition is the same as that in Fig. 1. Solid line represents a theoretical curve drawn by using the value of log r, ~o= -22.4o.

(17)

232

HISAHIKO EINAGA Table 1. Stability and solubility constants of hydrolyzed species of Mg(II).(1.0mol dm-3 NaNO~, 25.0°C) Species

log ~sqp

log Ksq p

-22.40~0-i 0 Mg (OH) 2

/3sM

Mg3(OH)~+ ~

-9.38~0.i 0

q

Remarks

0

1

from Mg 2+

-23-73~0-30

-12.23~0.30

2

2

from Mg2(OH)22+

-28-04~0-40

-12.10~0.40

3

4

from Mg3(OH) 4

(V)

3Mg(OH)2.sat+ 2H +

/3,34 = [Mg(OH)j3.. h2/[Mg3(OH)~+] =/33,o//334 (18) Ks34

p

2 3 mKw. -4 =[Mg£OHh2+ ]h - 2 Kw=/334K,

(19)

The values of 3,:2, K,n, /3,34 and Kss4 were also calculated from the values of/3n, /334, /3,m, K,m and Kw and are summarized in Table I. By taking hydrolytic equilibria of Mg(II)[5] into consideration, over-all hydrolytic precipitation equilibria of Mg(II) in 1.0 mol dm -3 NAN03 aqueous solutions at 25°C can be expressed as shown in Fig. 4. As can be seen from the figure, there should be at least three different M 2"

log/~sJo

lOg f/2 2

-21.07

-2240

Mg(OH)2sat

but possible ways for the formation and precipitation of the neutral hydrolyzed species of Mg(OHh. Although thermodynamic consideration of these data implies that formation of Mg(OH)2 via polycationic "truncated-coreplus-links" species[5, 13, 14] with higher numbers of "links" may be much more favourable than those with lower numbers of "links" and especially with aquamagnesium(II) ion, kinetic studies should be carried out to decide which way Mg(OH)2 is principally formed. The hydrolytic precipitation reaction has hitherto been studied by the measurements of the so-called "solubility product" of Mg(II) hydroxide, Mg(OHh[1-4]. In these cases equilibrium (VI)

' Mg r(OH)22÷

+

Mg2 + 2 O H - , log f]3~

-23b

log Bs3~

Mg(OH) 2,sat

tog

log

938 Mg(OH)2 opt

I1-1223

Ks 10

• Mg(OH)2.pp,

2. M g.: (OH)z. ; . . . . . .

-3916

log /]s22

-28o~

Mg(OH)2,sat

log

12,o

Mg(OH)2pp,

aq. solid.

Mg(OH)2.pp~

Fig. 4. Hydrolytic precipitation equilibria of Mg(II)(1.0 mol dm-3 NaNO3 aqueous solution at 25.0°C).

Table 2. Solubilityproduct of Mg(II)hydroxide log Ksl 0

-9.2 -10.9,

-8.3*

-16.58

Remarks

References

acrive Mg(OH)2,

~ = 0, 25°C

[i]

inactive

~ = 0, 25°C

[i]

Mg(OH)2,

3 mol dm -3 NaClO4,

[3]

-ii.03

[2]

-11.15 -9.38~0.10

* Ksl I = [blgOH+] [OH-].

2+

[4] 1 mol dm -3 NAN03,

25.0°C

present

study

(VI)

The hydrolytic precipitation reaction of Mg(ll) from aqueous NaNO~ solution which is equivalent in principle to the equilibrium(Ill), is simply assumed and experimental data were analyzed according to the assumption, thus taking no hydrolytic equilibria of the dissolved Mg(II) into consideration. This approach may be thought valid for the present case because of the rather small values of Ksm, but the data analysis taking into account the hydrolytic equilibria of the aquamagnesium(II) ion should be carried out to obtain a solubility product of Mg(II) hydroxide of higher reliability. Published data on this solubility product, K, m, are summarized in Table 2 together with that from the present study. So far as the value of K,m is concerned, the data in the present study are fairly in good agreement with that from active form of Mg(II) hydroxide, though no corrections were made for activity coefficients, which however may cause no fundamental discrepancies. It can be pointed out that the data obtained by using the inactive form of Mg(II) hydroxide as a starting material and those by Hostetler[2] and Pitzer et a/.[4] might have been obtained under conditions removed from equilibrium. Hence the data obtained by using the active form of Mg(II) hydroxide as starting material is suggested for use in equilibrium calculations. It is noteworthy to point out that the stability constant of MglIl) hydroxide, Mg(OH)> can also be obtained,

233

along with the solubility product, by the treatment adopted in the present study. REFERENCES

I. W. Feitknecht and P. Schindler, Pure' :4ppl. Chem. 6. 1f8 (1%3). 2. P. B. Hostetler, Am. J. Sci. 26I, 372 (1%8). 3. G. Horn. Rade.r-Rundschau I, 430 (l%q). 4, C. F. Baes and R. E. Mesmer, The, Hydrolysis of ('atiom, p. 195. Wiley (1976) and Refs cited therein. 5. H. Einaga, J. Chem. Soc. Dalton Tr. 912 (1977). 6, G. Biedermann and L. G. Sillen, Arkiv. Kemi 5,425 11953). 7, G. Biedermann and G. Schwarzenbach, Chimiya 2, 56 (1948); K. Ueno, Chelatn)metric Titrations, p. 334. Nankad,~. Kyoto (1976). 8. G. Gram Analyst 77, 661 (19521. 9. Chemical Society of Japan (Edn.I Handbook of ('hemistry, Fundamental Section, 2nd Edn., p. 1524. Maruzen, Tokyo, (1975). 10. L. G. Sillen and A. E. Martell, Stability Constants ~q MetalIon Complexes. (The Chemical Society (I,ondonl). Sp. Publ. No. 17, p. 41 (1%4): No. 25, p. 16 (1971). 11. F. J. C. Rossotti and H. Rossotti, The, Determination of Stahility Constants, p. 40. McGraw-Hill(1%1I. 12, L. G. Sill6n, Acta Chem. Stand. 10, 186 (1956). 13. L. G. Sill6n, Acta Chem. Scand. 8, 299, 31g 11954). 14. S. Hientanen and L. G. Sill~n, Aeta Chem. Stand. 8, 1607 (1954L