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Kinetics and salt effects of the reduction of octacyanomolybdate(V) and octacyanotungstate(V) by sulphite ions
~oiyhedrcn~ Vol. 2, No. 12, pp. Rioted in Great Britain.
1357-1362,
0277-5387183 Q 1983 Pegnmon
1983
S3.00 + .OO Ptns Ltd.
KINETICS AND SALT EFFECTS OF THE REDUCTION OF OCTACYANOMOLYBDATE(Y) AND OCTACYANOTUNGSTATE(V) BY SULPHITE IONS
CHARLES R. DENNIS, STEPHEN S. BASSON and JOHANN G. LEIPOLDT* Department of Chemistry, University of the Orange Free State, Bloemfontein 9300, Republic of South Africa (Received 11 April 1983; accepted 23 May 1983) Abstract-The kinetics of the reduction of octacyanomolybdate( and octacyanotungstate(V) by sulphite ions has been studied over a wide pH range. The reaction is catalysed by alkali metal ions. The rate law is found to be of the form: R
=
a[A+l
+ c
+
b[H+l
[H+]
w(CN)
3-][SO 8
2-l 3
*
>
The third order rate constants at [OH -1 = 0.05 mol dme3 for the reduction of Mo(CN),~and W(CN),3- were determined as 6.2 x 103dm6mol-2 s-i and 22.3 dm6mol-2s-’ respectively at 298 K for A+ = Na+ while K. for the hydrogen sulphite ion was determined as 2.4 x 10e8 mol dmp3. It was established that the reaction proceeds via an outer-sphere mechanism. An explanation for the alkali metal ion catalysis is proposed.
The reaction between hexacyanoferrate(II1) and sulphite ions has been the subject of various publications. Both inner- and outer-sphere mechanisms have been proposed. An inner-sphere mechanism’ via a Fe(CN),S034- intermediate was proposed but later studies2 with labelled *4CN-ions disproved the existence of such a species. Brown and Higginson also prefered an inner-sphere mechanism because the hexacyanoferrate(II1) ion is a mild oxidant. Other studies4*’ suggescomplex, mechanism where a ted a is formed between the [Fe(CN),(CNSO,)]‘-, hexacyanoferrate(II1) and sulphite ions, in which the sulphito group is bonded directly to a cyan0 ligand. This was described as a compromise between an inner- and outer-sphere mechanism. A reinvestigation6 has shown that the SO; product radical ion of the rate determining step also formed a similar intermediate in the subsequent reduction of Fe(CN)63- ions. The Fe(CN)63- - S032- reaction, with first order dependences on hexaoyanoferrate(II1) and sulphite ion concentrations respectively is retarded by addition of product Fe(CN)64- ions7 whilst [OH-] had no significant effect on the reaction rate for *Author to whom correspondence should be. addressed.
the concentration range between 0.26 and 0.60mol dme3. These results led to a proposed radical and complex forming reaction mechanism in which observed alkali metal ion catalytic effects were not .provided for. The kinetics of the reduction of octacyanomolybdate(V) and octacyanotungstate(V) by sulphite ions were investigated in order to compare the kinetics of these reactions with that of Fe(CN)63- with S032-, as well as to clarify the alkali metal ion catalysis. EXPERIMENTAL Cs3Mo(CN),~2H2G and CS3W(CN)8e2H20 were prepared by literature methods”” and were used as primary standards after recrystallization. Analytical grade sodium sulphite was used as source of sulphite ions and was standardized by an iodimetric method. All other reagents were of analytical grade and redistilled water was used throughout. The desired buffer solutions at constant ionic strength for the kinetic measurements at a pH between 5 and 9 were prepared by mixing suitable volumes of 0.067 mole dme3 Na,HPO, and 0.20 mole dm - 3 NaH,PO,. An Orion pHmeter (model 701) was used for pH measurements. The sulphite ion concentrations in the reaction mixtures were at least ten-fold in excess to the
C. R. DENNIS et al.
1358
concentration of the complex cyanide to ensure pseudo-first-order reaction conditions. Sodium ethylenediaminetetraacetate was added to each reaction mixture to suppress catalysis by metal ion impurities. The reaction progress for the reduction of the Mo(CN),~- was followed by measuring the decrease in [Mo(CN),~-] at 390 nm using a Durrum D-l 10 stopped-flow spectrophotometer while the reduction of W(CN)83- was followed by measuring the decrease in w(CN),3-] at 357 nm using a Pye Unicam SP 1700 spectrophotometer. In both cases the temperature was controlled to within 0.1 K. The stoichiometry of both reactions was determined volumetrically by oxidation of the products M(CN&“- (M = MO, W), with standard Ce(IV) solutions using N-phenylanthranilic acid as indicator. RESULTS AND DISCUSSION
The stoichiometry determinations confirmed the overall reaction in alkaline medium to be: 2M(CN); - + SO: - +2M(CN);-
+ SO: - . (1)
The pseudo-first-order plots of log [M(CN),3-] vs time were linear for at least two half lives. The
0.2
kinetic results show that the reactions are also first order with respect to [SO,*-] while the concentration of the product, [M(CN),4-], had practically no effect on the reaction rate. Both reactions show first order dependence with respect to the alkali metal ion concentration. The effect of the different alkali metal ions on the rate of the reaction between W(CN)zand SO:at [OH-] = 0.05 mole dme3 are shown in Fig. 1. It was also found that the reaction rate is independent of [OH-] for pH > 9.0 and dependent on [OH-] for pH < 9.0. The effect of the pH on the reaction rate for the reaction between Mo(CN),‘- and SO:- in the presence of sodium ions is shown in Fig. 2. The third order rate constants for the various alkali metal ions for the reduction of Mo(CN),~ - and W(CN),3- at high pH are shown in Fig. 3. The fact that a plot of the first order rate constant against alkali metal ion concentration is linear with a zero intercept (Fig. 1) show a very strong alkali metal ion catalvsis. To show that this r effect -’is not due to the variation of the ionic strength, the alkali metal ion concentration was varied at constant ionic strength using KCl, KrSO, and K,Co(CN), as electrolytes (Table 1). These results clearly show the alkali metal ion catalysis. The observed dependence of kobson the pH (Fig. 2) as well as the first-order dependence in each of alkali metal (A+), sulphite and M(CN)83- ion
OP4 [Alkali metal
0,6 ion]
0,8
(mol dmm3)
for the W(CN)83reFig. 1. A plot of kobs vs alkali metal ion concentration action [w(CN),3-] = 5 x 10m4, [SO,*-] = 5 x 10m3, [OH-] = 0.05, [EDTA] = 1 x 10-smol dm-3, T = 293 K.
1359
Kinetics and salt effects of the reduction of octacyanomolybdate(V)
3,O
2,o
r;” I ul
x
x0 1.0
6,‘3
9,o
12.0
PH
Fig.
2. A
plot [SO:-]
reaction. wo(CN),‘-]= of kobs vs pH for the Mo(CN),~= 5 x 10-3, [Na+] = 0.1, [EDTA] = 1 x low5 mol dmF3, T = 298 K.
5 x tOe4,
20.0
10.0
Polarisability
x lO*'C m3
Fig. 3. A plot of the rate constant vs polarisability of the alkali metal cations. [OH-] = 0.05 mol dme3; T = 298 K. [EDTA] = 1 x lo-‘mol dmm3. 0, Mo(CN):reaction; n , W(CN),3 - reaction.
1360
C. R. DENNIS et nl. Table 1. Experimental third order rate constants at constant ionic strength with different electrolytes for the Mo(CN),S- reaction. [OH-] = 0.05 mol dme3, T = 298 K. [EDTA] = 1 x lo-‘mol dm-’
concentrations -d
1,27
0,40
1,28
0,15
1,28
0,30
1.28
show the rate law to be
[M(CN),3-I
dt
0,20
a[A+] + b[H+]
=
c + [H+] ( > x [M(CN)r3 -1 [S03’ -1
(2)
The following equilibria exist in solution: HSO, sH+
+SO,2-
(3)
A + + M(CN),3- $ AM(CN),2 -
A+ + SO:-
(4)
2 ASO;
formal charge on the sulphur atom in :SO,Z- is + 1 and - 1 at each oxygen atom while in the case of S042- the formal charge on the sulphur atom is zero and - f on each oxygen atom. A cation paired to SO/- gets thus less nett repulsion from the nearby sulphur atom than in S032-. Apart from this, it is expected (as in the case of HSO;) that ASO; will be less reactive than S032-. It is clear from the above discussion that reactions 4 and 5 cannot explain the strictly first order dependence (see Fig. 1) of the reaction in the alkali metal ion concentration range employed. The experimental results may be explained by the following reaction mechanism:
(5) HSO; $H+
Equilibrium 3 explains the observed hydrogen ion dependence. The increase in the reaction rate with increase of pH (see Fig. 2) shows that the S032ion is much more reactive than the HSO; ion. The lower reactivity of the HSO; ion may be explained as follow: Connick” has shown that the following equilibria exist in aqueous solution
+ SO;-
(3)
A + + M(CN),3 - 2 [(CN),MCN : A12-
(6)
[(CN),MCN : Al2 - + SO; 2 [(CN),MCN : A : S0314-
(7)
:S032 - + H + + H : SO; = HOSO; I
[(CN),MCN : A : S0314- 1: SO3 :
II
I is the dominant form while isomer II is present in only a small amount. Both isomers I and II will be unreactive; in I the lone pair is tied up by the H+ ion while in II electron density will be withdrawn from the sulphur atom by the H+ ion. Equilibria 4 and 5 represent the outer-sphere ion-pair formation reactions. The association constants, K2, for a few cations with Mo(CN),~- and W(CN),3- were determined with specific-ion electrodes, see Table 2. These values are of the same magnitude as found for cyanocomplexes (3: 1 conductivity determined by electrolytes) measurements’2. The association constant K3 is not known. It is however expected to be lower than the value for SOA2- with K+ ions fannrox. 3 dm3 mol-9. The T
\
II
I
+ M(CN),4 - + A +
(8)
Table 2. Association constants for alkali metal ions with complex cyanide ions. T = 298 K; I = 0.1 mol dm-’ Catim
AIllOll
Kf
WCN)6 3-
K*
;;zC;;:
Na+
I
8
Kass (dm3 ml-])
+ 1 4,8 _ t 3 9.6 _ 13.5 + 6
Na+
3Mo(CNJ6
10.0 + 2
CS+
3Mo(CN)6
t 3 9.5 _
W(CN);-
7.9
CS+
+
2 J
1361
Kinetics and salt effects of the reduction of octacyanomolybdate(V) HSO; + M(CN): - 2 [(CN),MCN : H : SO,]‘- (9)
[(CN),MCN : H : S03j4 - 2 SO3 : + M(CN),4- + H +
(10)
SOS’ + M(CN),3 - 2 SO,* - + M(CN),4(11)
fast
Reactions 6-8 represent the contact ion-pair formation between complex cyanide and alkali metal ions, bridging of the lone pair on S03’- with the cation part of the contact ion-pair and the slow rate determining step respectively. K;, the contact ion-pair formation constant, is expected to be much smaller than K, (reaction 4) since A + is more specifically bonded to the nitrogen lone pair of a cyanide ligand in contrast to the outer-sphere ion association of equilibrium 4. Reactions 9 and 10 explain the slow observed reaction rate in acidic solution, see Fig. 3. The hydrogen bond formation between HSO; and M(CNJ3- (reaction 9) explains the absence of any alkali metal ion catalysis in acidic solution. Such a hydrogen bond formation was also proposed for the solid state in the crystal structure determination of H4W(CN)8.4HCl*12H20’3 and tetrakis(pyridinium - 2 - carboxylicacid)octacyanomolybdate(IV)‘4. The rate law according to the proposed mechanism is given by - d[M(CN),3 -1 = dt
MW;I(4[A+l+ k,K,[H+l K, + W+l > x [S032-]T[M(CN)83 -I.
(12)
This corresponds to the experimental results (eqn 2) with a = k,K,K;&, b = k2K5 and c = K1. The value of K1 for reaction 3 was calculated from a least squares fit of the data in Fig. 2 to eqn (12). The calculated value of pK, = 7.62 at I = 0.1 mol drne3 is in very good agreement with the value given by Meites” and DickI of 7.64 at I = 0.1 moldmd3. Futher evidence for the proposed mechanism is the increase in the reaction rate from Li + to Cs + , see Fig. 3. The same phenomena as well as strictly first order dependence on the alkali metal ion concentrations were also observed for the reactions of Mo(CN)d- and/or W(CN),3- with I-“*‘*, As (III)‘9.M, Se(IV)2’, Te(IV)” and thiourea.23 The large increase in the reaction rates from Li+ to Cs+ may be due to the greater effectivity of the
2
Y0
z?
.-I
I
/
I
I
I
'3.6
0,4
0,
Reduction potential, E" (Volt)
Fig. 4. A plot of log kob vs reduction potential (A+ = Na+). larger alkali metal ion as a charge buffer (and thus stabilization of the proposed intermediate [(CN),MCN : A : SO,]‘-) and a bridge for electron transfer. Another evidence for this view on the catalytic effect of the alkali metal ions where they serve as an electron bridge is the linear relationship between the experimental rate constants and the polarizability24 of the cations, (see Fig. 3). The Marcus cross-relation (eqns (13)-(15)) predicts a type of linear behaviour with gradient 8.46 where k12is the cross-reaction rate constant, k,, and kz2 are the self exchange rate constants for the couples and K,, is the equilibrium constant:
k,z= &&W)“2 n (AE”)
logK=m
(13) (14)
log kn = 0.5(log k,, + log k22+ logf) + 8.46 n(AE”).
(15)
A logk,, (A+ =Na+ plot of and [OH-] = 0.05 mol dmd3) for the oxidation of the sulphite ions by Mo(CN),~-, W(CN)d - and Fe(CN),3- (last value from Swinehart’) vs E” of the oxidizing agents25(Fig. 4) is linear with a gradient of 9.2 V-l. This is in very good agreement with the theoretical value and show that the Marcus theory is valid for those oxidations. This result also support the outer-sphere reaction mechanism proposed for the Fe(CN)Q--sulphite reaction.’ Acknowledgement-Thanks are expressed to the South African C.S.I.R. and the Central Research Fund of the University for financial assistance.
C. R. DENNIS
1362
R~ERENC~ 1. J. Veprek-Siska, ef al., Colt. Czech. Chem. Commun.
1965, 30, 1390; 1966, 31, 1248 and 3287. 2. K. 3. W&erg, H. Maitz and A. G. Fogg, inorg. Chenk 1968, 7, 830. 3: A. Brown and W. C. E. Higginson, J. Chem. Sot. Chem. Commun 1967, 725. 4. R. S. Murray, J. Chem. Sot. Chem. Commun 1968, 842. 5. J. M. Lancaster and R. S. Murray, J. Chem. Sot. A 1971, 2755. 6. R. S. Murray, J. Chem. Sot. Dalton 1974, 2381. 7. J. H. Swinehart, J. Inorg. Nuci. Chem. 1967, 29, 2313. 8. J. G. Leipoldt, L. D. C. Bok and P. J. Cilliers, 2. Anorg. Allg. Chem. 1974, 407, 350. 9. J. G. Leipoldt, L. D. C. Bok and P. J. Ciiliers, Z. Anorg. A&. Chem 1974, 409, 343. 10. L. D. C. Bok, J. G. Leipoldt and S. S. Basson, 2. Anorg. Al/g. Chem. 1975, 415,81. 11. R. E. Connick, T. M. Tam and E. von Denster, Znorg. Chem. 1982, 21, 103. 12. R. J. Lemire and M. W. Lister, J. Solution Chem. 1976, 5, 171. 13. L. D. C. Bok, J. G. Leipoidt and S. S. Basson, 2. Anorg. Alfp. Chem. 1972, 392, 303.
et al.
14. S. S. Basson J. G. Leipoldt and A. J. van Wyk, Acfa Cryst. 1980, KS, 2025. 15. L. Meites, Ha&n& OS Analytical Chemistry. McGraw-Hill, New York (1963). 16, J. G. Dick, A~~yt~al Chem~try. McGraw-Hill. Kogakusha (1973). 17. M. H. Ford-Smith and J. H. Rawsthorne, J. Chem. Sot. A 1969, 160. 18. L. D. C. Bok, J. G. Leipoidt and S. S. Basson, J. Inorg. Nucl. Chem 1975, 37, 2151. 19. 1. G. Leipoldt, L. D. C. Bok and C. R. Dennis, J. Inorg. Nucl, Chem. 1976, 38, 1655. 20. J. G. Leipoldt, L. D. C. Bok and A. J, van Wyk, J. inorg. Duct. Chem. 1977, 39, 2019. 21. J. G. Leipoldt, C. R. Dennis, A. J. van Wyk and L. D. C. Bok, Inorg. Chim. Acta 1978, 31, 187. 22. J. G. Leipoldt, C. R. Dennis A. J. van Wyk and L. D. G. Bok, Inorg. Chim. Acta 1979, 34, 237. 23. J. G. Leipoldt, L. D. C. Bok, S. S. Basson and C. R. Dennis, React. Kin. Cat. L&t. 1978, 8, 93. 24. C. N. R. Rao, A Hobnob of Chemistry and Physics. Affiliated East-West Press (1967). 25. A. G. Sharpe, The Chemistry of Cyan0 Complexes of the Transition Metals. Academic Press, London (1976).
1357-1362,
0277-5387183 Q 1983 Pegnmon
1983
S3.00 + .OO Ptns Ltd.
KINETICS AND SALT EFFECTS OF THE REDUCTION OF OCTACYANOMOLYBDATE(Y) AND OCTACYANOTUNGSTATE(V) BY SULPHITE IONS
CHARLES R. DENNIS, STEPHEN S. BASSON and JOHANN G. LEIPOLDT* Department of Chemistry, University of the Orange Free State, Bloemfontein 9300, Republic of South Africa (Received 11 April 1983; accepted 23 May 1983) Abstract-The kinetics of the reduction of octacyanomolybdate( and octacyanotungstate(V) by sulphite ions has been studied over a wide pH range. The reaction is catalysed by alkali metal ions. The rate law is found to be of the form: R
=
a[A+l
+ c
+
b[H+l
[H+]
w(CN)
3-][SO 8
2-l 3
*
>
The third order rate constants at [OH -1 = 0.05 mol dme3 for the reduction of Mo(CN),~and W(CN),3- were determined as 6.2 x 103dm6mol-2 s-i and 22.3 dm6mol-2s-’ respectively at 298 K for A+ = Na+ while K. for the hydrogen sulphite ion was determined as 2.4 x 10e8 mol dmp3. It was established that the reaction proceeds via an outer-sphere mechanism. An explanation for the alkali metal ion catalysis is proposed.
The reaction between hexacyanoferrate(II1) and sulphite ions has been the subject of various publications. Both inner- and outer-sphere mechanisms have been proposed. An inner-sphere mechanism’ via a Fe(CN),S034- intermediate was proposed but later studies2 with labelled *4CN-ions disproved the existence of such a species. Brown and Higginson also prefered an inner-sphere mechanism because the hexacyanoferrate(II1) ion is a mild oxidant. Other studies4*’ suggescomplex, mechanism where a ted a is formed between the [Fe(CN),(CNSO,)]‘-, hexacyanoferrate(II1) and sulphite ions, in which the sulphito group is bonded directly to a cyan0 ligand. This was described as a compromise between an inner- and outer-sphere mechanism. A reinvestigation6 has shown that the SO; product radical ion of the rate determining step also formed a similar intermediate in the subsequent reduction of Fe(CN)63- ions. The Fe(CN)63- - S032- reaction, with first order dependences on hexaoyanoferrate(II1) and sulphite ion concentrations respectively is retarded by addition of product Fe(CN)64- ions7 whilst [OH-] had no significant effect on the reaction rate for *Author to whom correspondence should be. addressed.
the concentration range between 0.26 and 0.60mol dme3. These results led to a proposed radical and complex forming reaction mechanism in which observed alkali metal ion catalytic effects were not .provided for. The kinetics of the reduction of octacyanomolybdate(V) and octacyanotungstate(V) by sulphite ions were investigated in order to compare the kinetics of these reactions with that of Fe(CN)63- with S032-, as well as to clarify the alkali metal ion catalysis. EXPERIMENTAL Cs3Mo(CN),~2H2G and CS3W(CN)8e2H20 were prepared by literature methods”” and were used as primary standards after recrystallization. Analytical grade sodium sulphite was used as source of sulphite ions and was standardized by an iodimetric method. All other reagents were of analytical grade and redistilled water was used throughout. The desired buffer solutions at constant ionic strength for the kinetic measurements at a pH between 5 and 9 were prepared by mixing suitable volumes of 0.067 mole dme3 Na,HPO, and 0.20 mole dm - 3 NaH,PO,. An Orion pHmeter (model 701) was used for pH measurements. The sulphite ion concentrations in the reaction mixtures were at least ten-fold in excess to the
C. R. DENNIS et al.
1358
concentration of the complex cyanide to ensure pseudo-first-order reaction conditions. Sodium ethylenediaminetetraacetate was added to each reaction mixture to suppress catalysis by metal ion impurities. The reaction progress for the reduction of the Mo(CN),~- was followed by measuring the decrease in [Mo(CN),~-] at 390 nm using a Durrum D-l 10 stopped-flow spectrophotometer while the reduction of W(CN)83- was followed by measuring the decrease in w(CN),3-] at 357 nm using a Pye Unicam SP 1700 spectrophotometer. In both cases the temperature was controlled to within 0.1 K. The stoichiometry of both reactions was determined volumetrically by oxidation of the products M(CN&“- (M = MO, W), with standard Ce(IV) solutions using N-phenylanthranilic acid as indicator. RESULTS AND DISCUSSION
The stoichiometry determinations confirmed the overall reaction in alkaline medium to be: 2M(CN); - + SO: - +2M(CN);-
+ SO: - . (1)
The pseudo-first-order plots of log [M(CN),3-] vs time were linear for at least two half lives. The
0.2
kinetic results show that the reactions are also first order with respect to [SO,*-] while the concentration of the product, [M(CN),4-], had practically no effect on the reaction rate. Both reactions show first order dependence with respect to the alkali metal ion concentration. The effect of the different alkali metal ions on the rate of the reaction between W(CN)zand SO:at [OH-] = 0.05 mole dme3 are shown in Fig. 1. It was also found that the reaction rate is independent of [OH-] for pH > 9.0 and dependent on [OH-] for pH < 9.0. The effect of the pH on the reaction rate for the reaction between Mo(CN),‘- and SO:- in the presence of sodium ions is shown in Fig. 2. The third order rate constants for the various alkali metal ions for the reduction of Mo(CN),~ - and W(CN),3- at high pH are shown in Fig. 3. The fact that a plot of the first order rate constant against alkali metal ion concentration is linear with a zero intercept (Fig. 1) show a very strong alkali metal ion catalvsis. To show that this r effect -’is not due to the variation of the ionic strength, the alkali metal ion concentration was varied at constant ionic strength using KCl, KrSO, and K,Co(CN), as electrolytes (Table 1). These results clearly show the alkali metal ion catalysis. The observed dependence of kobson the pH (Fig. 2) as well as the first-order dependence in each of alkali metal (A+), sulphite and M(CN)83- ion
OP4 [Alkali metal
0,6 ion]
0,8
(mol dmm3)
for the W(CN)83reFig. 1. A plot of kobs vs alkali metal ion concentration action [w(CN),3-] = 5 x 10m4, [SO,*-] = 5 x 10m3, [OH-] = 0.05, [EDTA] = 1 x 10-smol dm-3, T = 293 K.
1359
Kinetics and salt effects of the reduction of octacyanomolybdate(V)
3,O
2,o
r;” I ul
x
x0 1.0
6,‘3
9,o
12.0
PH
Fig.
2. A
plot [SO:-]
reaction. wo(CN),‘-]= of kobs vs pH for the Mo(CN),~= 5 x 10-3, [Na+] = 0.1, [EDTA] = 1 x low5 mol dmF3, T = 298 K.
5 x tOe4,
20.0
10.0
Polarisability
x lO*'C m3
Fig. 3. A plot of the rate constant vs polarisability of the alkali metal cations. [OH-] = 0.05 mol dme3; T = 298 K. [EDTA] = 1 x lo-‘mol dmm3. 0, Mo(CN):reaction; n , W(CN),3 - reaction.
1360
C. R. DENNIS et nl. Table 1. Experimental third order rate constants at constant ionic strength with different electrolytes for the Mo(CN),S- reaction. [OH-] = 0.05 mol dme3, T = 298 K. [EDTA] = 1 x lo-‘mol dm-’
concentrations -d
1,27
0,40
1,28
0,15
1,28
0,30
1.28
show the rate law to be
[M(CN),3-I
dt
0,20
a[A+] + b[H+]
=
c + [H+] ( > x [M(CN)r3 -1 [S03’ -1
(2)
The following equilibria exist in solution: HSO, sH+
+SO,2-
(3)
A + + M(CN),3- $ AM(CN),2 -
A+ + SO:-
(4)
2 ASO;
formal charge on the sulphur atom in :SO,Z- is + 1 and - 1 at each oxygen atom while in the case of S042- the formal charge on the sulphur atom is zero and - f on each oxygen atom. A cation paired to SO/- gets thus less nett repulsion from the nearby sulphur atom than in S032-. Apart from this, it is expected (as in the case of HSO;) that ASO; will be less reactive than S032-. It is clear from the above discussion that reactions 4 and 5 cannot explain the strictly first order dependence (see Fig. 1) of the reaction in the alkali metal ion concentration range employed. The experimental results may be explained by the following reaction mechanism:
(5) HSO; $H+
Equilibrium 3 explains the observed hydrogen ion dependence. The increase in the reaction rate with increase of pH (see Fig. 2) shows that the S032ion is much more reactive than the HSO; ion. The lower reactivity of the HSO; ion may be explained as follow: Connick” has shown that the following equilibria exist in aqueous solution
+ SO;-
(3)
A + + M(CN),3 - 2 [(CN),MCN : A12-
(6)
[(CN),MCN : Al2 - + SO; 2 [(CN),MCN : A : S0314-
(7)
:S032 - + H + + H : SO; = HOSO; I
[(CN),MCN : A : S0314- 1: SO3 :
II
I is the dominant form while isomer II is present in only a small amount. Both isomers I and II will be unreactive; in I the lone pair is tied up by the H+ ion while in II electron density will be withdrawn from the sulphur atom by the H+ ion. Equilibria 4 and 5 represent the outer-sphere ion-pair formation reactions. The association constants, K2, for a few cations with Mo(CN),~- and W(CN),3- were determined with specific-ion electrodes, see Table 2. These values are of the same magnitude as found for cyanocomplexes (3: 1 conductivity determined by electrolytes) measurements’2. The association constant K3 is not known. It is however expected to be lower than the value for SOA2- with K+ ions fannrox. 3 dm3 mol-9. The T
\
II
I
+ M(CN),4 - + A +
(8)
Table 2. Association constants for alkali metal ions with complex cyanide ions. T = 298 K; I = 0.1 mol dm-’ Catim
AIllOll
Kf
WCN)6 3-
K*
;;zC;;:
Na+
I
8
Kass (dm3 ml-])
+ 1 4,8 _ t 3 9.6 _ 13.5 + 6
Na+
3Mo(CNJ6
10.0 + 2
CS+
3Mo(CN)6
t 3 9.5 _
W(CN);-
7.9
CS+
+
2 J
1361
Kinetics and salt effects of the reduction of octacyanomolybdate(V) HSO; + M(CN): - 2 [(CN),MCN : H : SO,]‘- (9)
[(CN),MCN : H : S03j4 - 2 SO3 : + M(CN),4- + H +
(10)
SOS’ + M(CN),3 - 2 SO,* - + M(CN),4(11)
fast
Reactions 6-8 represent the contact ion-pair formation between complex cyanide and alkali metal ions, bridging of the lone pair on S03’- with the cation part of the contact ion-pair and the slow rate determining step respectively. K;, the contact ion-pair formation constant, is expected to be much smaller than K, (reaction 4) since A + is more specifically bonded to the nitrogen lone pair of a cyanide ligand in contrast to the outer-sphere ion association of equilibrium 4. Reactions 9 and 10 explain the slow observed reaction rate in acidic solution, see Fig. 3. The hydrogen bond formation between HSO; and M(CNJ3- (reaction 9) explains the absence of any alkali metal ion catalysis in acidic solution. Such a hydrogen bond formation was also proposed for the solid state in the crystal structure determination of H4W(CN)8.4HCl*12H20’3 and tetrakis(pyridinium - 2 - carboxylicacid)octacyanomolybdate(IV)‘4. The rate law according to the proposed mechanism is given by - d[M(CN),3 -1 = dt
MW;I(4[A+l+ k,K,[H+l K, + W+l > x [S032-]T[M(CN)83 -I.
(12)
This corresponds to the experimental results (eqn 2) with a = k,K,K;&, b = k2K5 and c = K1. The value of K1 for reaction 3 was calculated from a least squares fit of the data in Fig. 2 to eqn (12). The calculated value of pK, = 7.62 at I = 0.1 mol drne3 is in very good agreement with the value given by Meites” and DickI of 7.64 at I = 0.1 moldmd3. Futher evidence for the proposed mechanism is the increase in the reaction rate from Li + to Cs + , see Fig. 3. The same phenomena as well as strictly first order dependence on the alkali metal ion concentrations were also observed for the reactions of Mo(CN)d- and/or W(CN),3- with I-“*‘*, As (III)‘9.M, Se(IV)2’, Te(IV)” and thiourea.23 The large increase in the reaction rates from Li+ to Cs+ may be due to the greater effectivity of the
2
Y0
z?
.-I
I
/
I
I
I
'3.6
0,4
0,
Reduction potential, E" (Volt)
Fig. 4. A plot of log kob vs reduction potential (A+ = Na+). larger alkali metal ion as a charge buffer (and thus stabilization of the proposed intermediate [(CN),MCN : A : SO,]‘-) and a bridge for electron transfer. Another evidence for this view on the catalytic effect of the alkali metal ions where they serve as an electron bridge is the linear relationship between the experimental rate constants and the polarizability24 of the cations, (see Fig. 3). The Marcus cross-relation (eqns (13)-(15)) predicts a type of linear behaviour with gradient 8.46 where k12is the cross-reaction rate constant, k,, and kz2 are the self exchange rate constants for the couples and K,, is the equilibrium constant:
k,z= &&W)“2 n (AE”)
logK=m
(13) (14)
log kn = 0.5(log k,, + log k22+ logf) + 8.46 n(AE”).
(15)
A logk,, (A+ =Na+ plot of and [OH-] = 0.05 mol dmd3) for the oxidation of the sulphite ions by Mo(CN),~-, W(CN)d - and Fe(CN),3- (last value from Swinehart’) vs E” of the oxidizing agents25(Fig. 4) is linear with a gradient of 9.2 V-l. This is in very good agreement with the theoretical value and show that the Marcus theory is valid for those oxidations. This result also support the outer-sphere reaction mechanism proposed for the Fe(CN)Q--sulphite reaction.’ Acknowledgement-Thanks are expressed to the South African C.S.I.R. and the Central Research Fund of the University for financial assistance.
C. R. DENNIS
1362
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