150 F. Sanchez et al. Transition Met. Chem., 13, 150-154 (1988)

Kinetics of peroxodisulphate oxidation of octacyano- molybdate(IV) in concentrated aqueous salt solutions Francisco Sanehez*, Maria J. Nasarre, Maria M. Graeiani, Ragael Jimenez, Maria L. Moya Department of Physical Chemistry, University of Seville, 41012 Seville, Spain

John Burgess and Michael J. Blandamer Department of Chemistry, University of Leicester, Leicester, LE1 7RH U.K.

Summary

Rate constants are reported for the oxidation by peroxo- disulphate ions of octacyanomolybdate(IV) in concen- trated aqueous salt solutions containing up to 6moldm -3 salt including mixed salt solutions. The dependence of the logarithm of rate constant on salt concentration is discussed in terms of ionic hydration enthalpies and B-viscosity coefficients. The analysis con- firms that ion-pairs play a key role in determining reactivities in these systems.

Introduction

Salt effects on reactions between ions in dilute aqueous solution have long been studied~l); more recently interest has grown in more concentrated solutions, up to 6 mol dm-3~2). Many such studies have involved peroxo- disulphate oxidation of cyano-transition metal com- plexes(3-12), established to be of 2:1 stoichiometry but to have bimolecular rate-determining steps ~8' 9). At mode- rate ionic strengths the expected positive salt effect is obser- ved [Equation (1)]. The constants kc and k ~ here both

kob ~ = k ~ + k~[C] (1)

depend on the nature of the cation C as a consequence of ion-pairing, electron transfer occuring between, e.g., KS2Og and KFe(CN)~ -(3's'13'14). At low ionic strengths partial ion-pairing causes deviations from Equation (1). At high ionic strengths (> 1 dm 3 mol- 1) the S208 z-/Fe(CN)~- reaction follows Equation (2) rather than Equation (1)(4,10).

log kob s = c -k- S I-el (2)

Both cation hydration and ion association now have to be invoked, while anion hydration effects are also significant. Salts of Mg 2+ have unexpectedly small effects on this reaction, while salts of Be 2+ or AI 3 + give negative salt effects. These non-classical results have been ascribed to hydrolysis of these high charge/radius aqua-cations and consequent proton transfer to give less reactive [Fe(CN)5(CNH)]3-(2, 5). This paper details an extension to $20~- oxidation of the Mo(CN)~- anion.

Experimental

K4[Mo(CN)8]2H20 was prepared in ca. 90% yield from molybdenum trioxide by the method of Van de Poel and Neumann (15). The purity of the product was checked by cerium(IV) oxidimetry. K2S208, alkali and alkaline earth nitrates, NaC104, NaOH and disodium edta were Merck P. A. grade; NaS2Os from Carlo Erba was of similarly high purity.

* Author to whom all correspondence should be directed.

For all runs except those in KNO3 media, initial concentrations of reagents were [K2SzOs]=0.1mol dm -3 and [KgMo(CN)5 ] = 5 x 10-3moldm -3. In KNO3 media, solubility restrictions dictated initial con- centrations as follows; [Na2S2Os] = 0.025 tool din- 3, with [NazSO4] = 0.075moldm -3 to produce the same ionic strength as in the other runs, and [KgMo(CN)8 ] = 55 x 10 -4 mol dm- 3. Disodium edta, (10- 5 mol din- 3), was added to all reaction mixtures to sequestrate any traces of transition metal ions that might act as catalysts for peroxodisulphate oxidation or dissociation. All runs employed a large excess of potassium- (sodium) peroxodisulphate so that first order kinetics were followed. Concentrations of added salts covered the 1.0 t o 6.0moldm -3 range for LiNO3, NaNO3 and NaC104, 1.0 to 2.5moldm -3 for less soluble KNO 3, and 1.0 to 3.0moldm -3 for Mg(NO3)2, Ca(NO3) 2 and Sr(NOa) 2. To avoid any possibility of hydroxide precipitation, the pH of each solution contain- ing alkaline earth nitrates was adjusted (NaOH or HNO3 as required) to 4. It had been previously established that variation of pH between 3 and 5 had no detectable effect on rate constants. Fresh solutions of peroxodisulphate and octacyanomolybdate were made up for each set of runs, since both ions are known to react, albeit very slowly, with water. All solutions were made up with deionised water (conductivity < 10 -6 S).

Kinetics were monitored spectrophotometrically by following changes in absorbance at 390rim, the wave- length of maximum absorbance for the [Mo(CN)8] 3- product (16). Runs were carried out in a thermostatted (Julabo U3) cell in an Hitachi-150-20 spectrophotometer. In each run the reference solution was the equivalent of the actual sample, lacking only the peroxodisulphate. In this way any very slight oxidation of the [Mo(CN)8]4- by dissolved oxygen was automatically compensated. Rate constants were calculated by Guggenheim's method (16) from the absorbance data for each run.

Results

Rate constants are reported in Tables 1 and 2. The latter table presents rate constants for runs carried out in potassium nitrate-lithium nitrate mixtures of combined concentrations 2.5 tool dm-3 and in magnesium nitrate- strontium nitrate mixtures of combined concentrations 3.0 tool din-3. The rate constants in Table 1 conform to Equation (2) above for each added salt [Figures l(a) and l(b)].

Slopes (S) of plots of logarithms of rate constants against added salt concentrations ([C] >> 1.0 tool din- 3) are included in Table 1. The restricted concentration range for KNO3 results in an uncomfortably large uncertainty in S for this salt.

0340-4285/88 $03.00 + .12 �9 1988 Chapman and Hall Ltd

Transition Met. Chem., 13, 150-154 (1988) Oxidation of octacyanomolybdate(IV) in aqueous salt solutions 151

Table 1. Rate constants k(obs) for peroxodisulphate oxidation of octacyanomolybdate(IV) in concentrated aqueous salt solutions.

Salt 103 k(obs)/s - 1 mol- 1 dm 3 C/mol dm -3 LiNO3 NaNO3 KNO 3 M g ( N O 3 ) 2 Ca(NO3)2 Sr(NO3)2 NaC104

1.0 0.92 2.92 2.92 1.05 1.56 2.19 1.48 1.5 3.4 2.0 1.25 2.23 4.13 1.26 1.97 2.61 2.66 2.5 5.25 3.0 1.73 2.74 1.54 2.46 3.33 3.88 4.0 2.28 3.42 1.82 3.27 4.00 5.28 5.0 3.15 4.12 2.14 4.17 4.95 7.42 6.0 4.22 4.95 2.63 5.03 6.30 10.70 S 0.132 0.087 0.160 0.157 0.207 0.183 0.149 100 x st err. 0.3 0.5 .5 .7 1.2 1.0 6.7

Table 2. Rate constants k(obs) for peroxodisulphate oxidation of octacyanomolybdate(IV) in mixed aqueous salt solutions.

LiNO3 + KNO3 103 k Mg(NO3) 2 + Sr(NO3) 2 103 k (s - 1 mol - 1 dm 3 ) (s - 1 mol- a d m 3)

0.0 2.5 5.25 0.0 3.0 6.30 0.5 2.0 4.80 0.5 2.5 5.62 1.0 1.5 3.81 1.0 2.0 4.95 1.5 1.0 3.18 1.5 1.5 4.34 2.0 0.5 2.40 2.0 1.0 3.79 2.5 0.0 1.40 2.5 0.5 3.27

3.0 0.0 2.63

Discussion

The results shown in Table 1 and Figure 1 confirm that for this reaction, as for all other analogous reactions in concentrated salt solutions studied so far, the salt effect is positive. Our conclusion in this respect is the opposite to that reached by Leipoldt's group as a result of their studies in salt concentrations in the region of 1.0 tool dm-3. We believe that these authors' use of sulphate as anion(l l) leads to complications. These may arise either by the unique nature of sulphate as product, or may simply reflect a large specific anion effect (cf. significant NO~-/C102 differences).

The observed linearity of plots of logarithm of rate constants versus salt concentration can be rationalised in relation to the classic Debye-Huckel approach and its extension to concentrated salt solutions. If the activity coefficient for a given ionic solute is related to con- centration C using a Guggenheim-Guntleberg type of equation, the final expression for the dependence of log k(obs) on C has the form shown in Equation (3).

log k(obs) = log k ~ + {a.(C)a/2/[1 + (C)Z/2] } + S.C (3)

As written here, parameters a and S are adjustable obtained by fitting the data to Equation (3). Thus at low salt concentrations where [1 + (C) 1/2 ] is ca. 1.0, log k(obs) is a linear function of (C) ~/2, the limiting slope being given by the a-parameter which under these circumstances can be calculated using the Debye-Hfickel Limiting Law. The limiting slope is common for all added salts for a given reaction, solvent, temperature, pressure and charge numbers of added ions. The intercept is the 'idealised' rate constant for the reaction described by rate constant k. With increase in salt concentration so the denominator in the second term contributes to a non-linear dependence of logk(obs) on (C) ~/2. At the same time the third term,

product S.C, assumes greater importance. Because parameter-S is characteristic of the added salt, the con- centration at which the linear dependence of log k(obs) on (C) ~/2 breaks down is also dependent on salt. With further increases in salt concentration {1 +(C) 1/2} is approx. (C) ~/2 and hence Equation 3 requires a limiting depen- dence of log k(obs) on C at high salt concentrations.

As discussed above the reactions described by rate constant k(obs) change with increase in concentration. Therefore at low concentrations both k(obs) and k ~ refer to reaction between [-Mo(CN)8] 4- and [S208] 2- ions. Hence the intercept in a plot of log k(obs) versus (C) 1/z at low concentrations refers to k ~ for reaction between these ions. At high concentrations the rate constant k(obs) characterises reaction between ion pairs: e.g., MS20 ~- and [MMo(CN)8] 3-. Hence the part of the curve showing a linear dependence of log k(obs) on C is extrapolated to an intercept, [a + logk~ Rate constant k ~ refers to the reaction between ion pairs in aqueous solution containing no added salt. Hence the intercept [a + log k ~ depends on cation M. In other words both intercept and slope (S) depend on added salt. In principle there is an enormous amount of information contained within the dependence of log k(obs) on salt concentration spanning both dilute and concentrated solutions. Thus slope S offers a measure of the medium hydration effects of added salts on the ion- pair reactions. The simple charge-charge influence is accounted for by the a-parameter which is contained within the intercept. Two factors are expected to con- tribute towards the sign and magnitude of slope-S. These are, in the first instance cosphere-cosphere interactions between, on the one hand, the ions of added salts and, on the other hand, the initial and transition states with added salts. As important is the scavenging competition for solvent between reactants, and transition states and added salt. This point is brought home in the table given

152

1 . 8 .

log k

~2.0

- 2 , 2

- 2 . 4 -

- 2 . 6

- 2 . 8

- 3 . 0

F. Sanchez et al.

a

4

C / / m o l d m 3

log k - 2 . 2

- 2 . 6

-2. ,

�9 Mg (NO3) 2

[] Ca(N 03) 2 0 Sr(N03) 2

0.5 1 1.5 2 2.5 3

C / m o l d m 3

Figure 1. Dependence of logarithm of rate constant for $20 2- oxidation of Mo(CN)64- on salt concentration for (a)added alkali metal salts and (b)added alkaline earth nitrates in aqueous solutions at 298.2 K.

by Robinson and Stokes (~9) which shows that when C = 1.0 mol dm- 3, the average distance of separation (for a 1:1 electrolyte) between ions is 9.4/~ while by C = 10.0 mol dm- 3, the average separation is only 4.4 A [cf. ionic (thermochemical) radii (19) of e.g., K + and NO~ of 1.33 and 1.89/~].

Before proceeding to a discussion of the slopes of log k(obs) versus C plots, we should mention the results for reactions in mixed salt solutions. Both for KNO3- LiNO 3 and Sr(NO3)z-Mg(NO3)2 mixtures, plots of rate constants versus composition are linear [Figures 2a and 2b]. This supports the assumption mentioned in the

103k s-lrnoJ-ldm3

5 -

4 -

Transition Met. Chem., 13, 150-154 (1988)

a �9

- "NO 3

i i ~ | i 0 ,5 1,5 2 .5 ~ K N 0 3

C / r n a l dm - 3

2 1 0 ~ L iN03

103 k s lmoJ-ldm 3

b Mg(N03)2 S r ( N 0 3 ) 2

6

5

4

3

o 4 ' ; ' ; C / tool dm -3

3 2 1 0 ~ S r ( N 0 3 ) 2

Figure 2. Dependence of rate constant for $20 ~- oxidation of Mo(CN)~- on medium compositions for (a) LiNO 3 + KNO3 mixtures at total salt concentrations of 2.5moldm -3 and (b) Mg(NO3) 2 + Sr(NO3)2 mixtures at total salt concentration of 3.0 mol dm -3 in aqueous solution at 298.2 K.

Introduction that the electron transfer is taking place only between ion pairs. It is reasonable that the ion-pairing equilibria should lie fully on the ion-pair side at the high cation concentrations used in this investigation. If this is the case, then for, e.g., the KNO3-LiNO3 series, only reaction (4) and (5) make significant contributions to k(obs), and k(obs) will be linear combination of rate constants in the separate salt solutions weighted in proportion to the concentrations of K + and Li+; (cf. Equation 3).

[KMo(CN)8] 3- + KzSO~ --+ products (4)

[LiMo(CN)s] 3- + LiSzO ~ --+ products (5)

The specific ion effects exhibited both by cations and by anions must be related to their hydration requirements and the consequences on hydration of the initial and transition states for the redox reaction. In Figures 3 and 4 we explore possible correlations between slopes S of log k(obs) vs C plots and Jones-Dole B-viscosity coe- fficients (Figure 3) and enthalpies of hydration (Figure 4). The B-coefficients used in the former plot are those for the added salts [i.e. B ( K + ) + B ( N O ~ ) f o r KNO3]; in the latter Figure we have plotted S against the corresponding standard enthalpies of hydration for the cations, and

Trans i t ion M e t . Chem., 13, 150-154 (1988) Oxidation of octacyanomolybdate(IV) in aqueous salt solutions

(NO3)

r(No3) 2

LiNO

I 0 0!20

0,20

0,1 0

B --.-~

Figure 3. Correlation of slopes S (of log k versus C plots) with Jones-Dole B-viscosity coefficents.

against the sums of these enthalpies for added cations and anions. The plot of S versus hydration enthalpies suggests a rough correlation.

Correlation of S with B-viscosity coefficients is here, as in several earlier cases, rather better with points for the nitrates of lithium, sodium, calcium and strontium linearly connected. The point for potassium nitrate lies off this line, as do analogous points for this salt for all other, outer sphere redox systems studied. This consis- tent deviation remains a mystery; the situation is not helped by the relatively low solubility of this salt which restricts the range available for study and thus produces a large uncertainty in the calculated S; cf. Figure 3. The point for magnesium nitrate also lies off the correlation line. For the majority of reactions of this type including bromate-bromide ~2~ bromate-iodide (21), peroxodi- sulphate-iodide (22), permanganate-iodide (23), and hexa- cyanoferrate-iodide (24), the magnesium nitrate point can be included in the linear correlation. The only pre- vious example of this salt deviating is supplied by peroxodisulphate-hexacyanoferrate(II) reaction. It seems that magnesium causes deviations only for cyanoanions of charge 4-, viz. [Fe(CN)6] 4- and [Mo(CN)s] 4-. But Figure 5 shows good correlation of S for these two systems; so Mg 2+ has very similar effects on the two cyanoanions having a 4-minus charge. As discussed in the Introduction, such behaviour can be attributed to local hydrolysis effects, with the 4- ion being protonated and thereby becoming less reactive. There is also some support for this hypothesis from salt effects on reactions involving hydroxide ions (a considerably stronger proton

0.2

Z 0.1

i i

153

I t O~ 0.1 O" 2

S([Mo(CN)s] c-) - - .

Figure 5. Correlations between slopes S (of log k versus C plots) for peroxodisulphate oxidation of Fe(CN)64- and Mo(CN)~-.

acceptor than [Fe(CN)6] 4- or [Mo(CN)8]4-; the for- mer ~2s) has a pK of ca. 4.3.

The positive salt effect indicates that the ions affect reactivity by reducing the activation barrier, but it is not possible to be specific without separating the observed trends in rate constants into initial and transition state components. As the reaction in question involves ion pairs, it is difficult to see how medium effects on the initial state could be established, let alone medium effects on the transition state. Nonetheless it is reasonable to suggest that the positive salt effect operating on slope S arises from a greater destabilisation of the initial state than the transition state on adding high concentrations of salt, the ions thereby making water less available for sotvating the reactants and transition state. The relative availability of water molecules for solvating initial and transition states has recently been discussed in relation to B-viscosity coefficients. These results were interpreted in terms of enhanced ion-solvent interactions in the transition state for viscous flow (26). Greater ion-water interactions with added ions in our systems implies less transition state destabilisation, as suggested above. It seems likely that here, as usual in outer sphere electron transfer reactions, solvation effects operate on the initial association of the reactants [cf. Equation (6) for 1 + cations] rather than

0,20

0 .i 5

0-I0

~K �9 ~KN03 A NaC[O~

Li § ~LiN03

~Ca2* A CaiN03)2

~Sr 2~ ASriN03)2

~ Na + ~NaNO 3

5~ I0~ I I I

1500 2000 2500

/~Hhydr/kJ m o t -1 _ _ .

~Ng(N03) 2

Figure 4. Relation between slopes S (of log k versus C plots) and enthalpies of hydration; A for cations and A for salts.

154 F. Sanchez et al.

on the actual electron transfer, Equation (7).

[MMo(CN)s] a- + [MSzO~]

Kos [MMo(CN)8] a- , 1-MS208]- (6)

[MMo(CN)s] 3-, [MSzOs]

ket [MMo(CN)8] 2- , [MSzOs] 2- (7)

We need therefore not concern ourselves at this stage with the question of whether, as generally stated or implied(i, 6,11,27), an alkali metal or alkaline earth cation actually forms a bridge for electron transfer, or whether, as seems more likely at least to one of the present authors, electron transfer occurs directly from anion periphery to anion periphery without the intermediacy of the cation bridge, which after all serves to discourage electron transfer by holding the redox centres further apart!

Acknowledgments

We thank the British Council (Acciones Integradas) and the Comision Asesora de Investigacion Cientifica Tecnica for their support of research collaboration between the Universities of Sevilla and Leicester.

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(Received 20 November 1987) TMC 1817