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The oxidation of nitrous acid by chromium(VI)
.I. in¢wg, nucl. Chem,. 197 I, Vol. 33, pp. 2971 to 2979.
Pergamon Press.
Printed in Great Britail~
T H E O X I D A T I O N OF N I T R O U S A C I D BY CHROMIUM(VI) D. A. D U R H A M , L. DOZSA and M. T. BECK Institute of Physical Chemistry, Kossuth Lajos University, Debrecen 10. Hungary. (Received 10 September 1970) A b s t r a c t - T h e reaction of nitrous acid and chromium(Vl) has been studied in dilute solution at 25°C, with an ionic strength of 0.5, over the pH range 0.4-1 "3. The rate of reaction was obtained spectrophotometrically following changes in the absorbance of chromium(V1), and the determined rate-law was of the form d[Cr(Vl)l [HN O2]/[Cr(V l)]tkl + k2[H +] + k:~[Cr(Vl)]~ dt I + k4[HNO~], + k.~[HNO~]t'-' the rate-determining steps involving the two-electron reduction of Cr(VI) to Cr(IV). INTRODUCTION
WE HAVE recently been carrying out investigations into the role of mixed ligand formation in the reduction of Cr(VI) [ 1], and into the effect of coordination on the reactivity of the nitrite ion[2]. We are now studying the effect of E D T A on the Cr(VI)-HNO2 reaction for which a knowledge of the kinetics and mechanism of the basic C r ( V I ) - H N O e reaction was necessary. Very little work has been reported on the kinetics of this reaction. One of the most thorough studies was that of Kurtenacker[3] who found the following rate-law dx - - = (kl + k., [S]2)[H._,Cr~OT][HNO.,]([S] = acid concentration). dt His study was carried out in a sulphate or acetate medium. It is known that sulphate and acetate react with Cr(VI) in acid solution to yield C r S O / - [4, 5] and AcOCrO:~- [6, 7], respectively. Hence a comparison of Kurtenacker's results with those obtained in a perchlorate medium appeared useful. EXPERIMENTAL The kinetics of reactions were followed continuously using a Hitachi-Perkin Elmer 139 spectrophotometer fitted with a constant temperature cell compartment. In all cases the temperature was maintained at 25°C. The ionic strength was adjusted with sodium perchlorate and, except for one series of experiments in which the reaction rate was studied as a function of ionic strength, was maintained at 0.5. Nitrite was added in the form of its sodium salt, while the hydrogen ion concentraI. 2. 3. 4. 5. 6. 7.
M.T. Beck and D. A. Durham, J. inorg, nucl. Chem. 33, 461 (1970). M.T. Beck and L. D6zsa. Inorg. Chim. Acta 1,134(1967). A. Kurtenacker, Monatsh. Chim. 41, 101 (1920). A. Carrington and M. C. R. Symons, Chem. Rev. 63, 443 (1963). G. P. Haight. Jr., D. C. Richardson and N. H. Coburn, lnorg. Chem. 3, 1797 (1964). M. Cohen and F. H. Westheimer, J . A m . chem. Soc. 74. 4387 (1952). M . C . R . Symons. J. chem. Soc. 4331 ( 1963). 2971
2972
D . A . D U R H A M , L. D O Z S A and M. T. BECK
tion was varied by addition of perchloric acid. No buffer solutions were employed. The required component solutions were mixed externally, sodium nitrite (always the last component to be added) being injected from a syringe. Absorbance was measured within 20-30 sec after mixing, measurement being continued for 2-3 min. Chromium(VI) absorbance was measured at 405 nm, and not at the absorption maximum, to minimise spectral interference by the nitrite. A separate study of the rate of decomposition of nitrous acid under the conditions used showed that during the time of measurement of the loss of Cr(VI) the decomposition of the nitrous acid could be neglected. This is in agreement with other observations[8]. No attempt was made to exclude air or oxygen from the system. The strengths of the various solutions were determined by standard volumetric procedures. RESULTS AND DISCUSSION
The reaction of nitrous acid with Cr(VI) takes place[3] according to the following overall equation 2CrO4H- + 3HNO2 + 5H + ---> 2Cr a+ + 5H20 + 3NOa-.
(1)
As mentioned above the interference by the decomposition of nitrous acid was neglected. Rates of reaction were obtained by plotting Cr(VI) absorbance against time. The resulting graphs were practically linear and the initial slopes could be measured quite simply. From the slopes and the initial chromium(VI) absorbances, the initial rates of loss of Cr(VI) were calculated. A study was first made of the effect of the ionic strength on the reaction rate. The results are shown in Fig. 1 from which it is clear that the reaction rate is almost totally independent of the ionic strength over the range studied. Despite this independence, the ionic strength was adjusted to 0.5 in all the subsequent work.
T
1.55
L >
I" 5 0
K O 1-45
0.25
I 0.55
I 0.45 Ionic
1 0,55
0~5 .
0~5 •
strength
Fig. 1. Variation of rate of reaction with ionic strength. [HNO2] = 4.177 × 10-ZM, [Cr(VI)] = 6"208 × 10-4M; [H +] = 0" 198M. 8. E . D . Hughes, C. K. Ingold and J. H. Ridd, J. chem. Soc. 58 (1958); and subsequent papers.
T h e oxidation of nitrous acid by c h r o m i u m ( V I )
2973
A detailed kinetic investigation of the reaction was made within the fairly limited concentration ranges: [H ÷] = 0.485-0.315M; [HNO2]t = 4.18 × 10- 3 0.101M; [Cr(VI)]t = 1.552 x 10- 4 - 1.552 × 10-3M (t = total). It was found that at nitrite concentrations less than about 5 x 10-3M, there appeared to be an induction period for the reaction; above this concentration there was no apparent sign of such an induction period after the initial 20-30 sec, and reaction rates could be measured quite straightforwardly. The results of the kinetic investigation are as follows. A t constant [HNO2] a n d [H+], plots of Rate against [Cr(VI)]t are almost straight lines, but at higher values of [Cr(VI)]t there is a definite tendency to an upwards deviation from iinearity. Plots of Rate/[CrIVI)]t against [Cr(VI)]t, however, are linear and no deviation is observed. (Fig. 2). Hence the rate depends upon the chromium concentration in the following way d[Cr(VI)] = cl[Cr(VI)lt + c2[Cr(VI)], z. dt
(2)
A t c o n s t a n t [Cr(VI)t and [H+], the plots of Rate against [HNO2]t gave rise to S-shaped curves such as that in Fig. 3. By trial and error it was found that the curves could all be approximated by my functions
d[Cr(VI)] = c3[HNOz]t 2 dt 1 + c4[HNO2]t 2
(3)
but even better fits were obtained using functions
--
d[Cr(VI)] _ cs[HNO2]t z dt - t + c r [ H N O z ] t + c7[HNO2]t 2"
(4)
A plot of this function is compared with the measured data for one series of results in Fig. 3.
2.2
T
2(
- -
/,,/"
2.
./
1"9
• i~'-~"I-8
~'~'
,.7 1.6
,;
I-!
,to
[cr(vl)] xtO4M Fig. 2. Variation o f Rate/[Cr(Vl)] with [Cr(VI)]. [HNO2] = 4.177 × 10-2M; [H ÷] = 7-80 × 10-2M; l = 0.5.
2974
D.A.
DURHAM,
L. D O Z S A and M. T. B E C K
A t constant [HNO2]t and [Cr(VI)]t, changes in the pH bring about changes
in the concentrations of all the various nitrite and chromium(VI) species (see for example [9]). The rate-law under these conditions was found to be of the form ( F i g . 4).
_ d [ C r ( V I ) ] = c s [ H + ] + c9 dt
f/"
45 40 T
=
(5)
35
T... 3O ~
25
o
~ 2o
i
.//
~" u5 ¢u o n.-
I0
0
2
4
6
[HNO2] K IO2M
Fig. 3. Variation of rate of reaction with [HNO2]. IH ÷] = 0.137M, [Cr(VI)] = 9.312 × 10-4M; 1 = 0.5. The plotted points are those measured, and the curve is the calculated function: 2.30 × 10-3[HNO2] 2 Rate = 1 + 10.2[HNOz] + 300[HNO2] 2' 1.8
1.7
I-6 Z. I-5
_e
K
~
1"4
1.2--
g. I" I'(
o.~
~
~
,~
,~
~to
~
~
~
[H+]x IoZM
Fig. 4. Variation of rate of reaction with [H+].[HNO2] = 4.177x 10-=M; [Cr(VI)] = 6.208 x |0-4M; 1 = 0.5. 9, D . A . Durham, J. inorg, nucl. Chem. 31, 3549 (1969).
The oxidation of nitrous acid by chromium(V I)
2975
T h e only combination of Equations (2), (4) and (5) which consistently fitted the measured results was d[Cr(VI)] = [HN 02]tZ[Cr(VI)]t(k, + kz[H +] + k3[Cr(VI)]t) 1 + k4[HNO2]t + ks[HNO2]t 2 dt
(6)
T h e results of 115 (tifferent rate determinations involving changes of all three variables were analysed mathematically on the basis of Equation (6) in order to find the best values of the constants kl, k2, k3, k4 and ks, according to a programme seeking the least squares deviation. T h e results of this were. k = k2 = k3 = k4 = k5 =
1.4 mole -2 lit z sec -1 5.0 mole -a lit 3 sec -~ 3.9 x 102 mole -z lit ~ sec -~ 10 mole -~ lit 3.00 x 102 mole -2 lit z.
T h e differences between experimentally observed rates and those calculated on the basis of these k values were always less than 10 per cent and in the vast majority of cases were less than 5 per cent. T h e mechanism of the reaction of Cr(VI) with nitrous acid is envisaged as follows. T h e first step involves the fast equilibrium condensation of the two m o n o p r o t o n a t e d reactants O-
O-
O = ~ r - - O H + H O - - N = O . I " 1 0 = ~ r - - O - - N = O + H20
(7)
T h e condensation product is capable of an internal two-electron redox reaction O-
O~---~r--O--N=O k° ~ Cr(IV)+NO3[~)
slow
(8)
or of condensation with a further molecule of nitrous acid
OO~r--O---N--O
+
K2
HO---N==O " fast
0~... ~ 0 o'~Cr..o I I N~o/N -O / "OH
(9)
The cyclic product is also capable of an internal redox reaction
N~o/N -0 / "OH
kb slow
Cr(IV)+ HONO + NOa-
(lO)
2976
D. A. DURHAM, L. DOZSA and M. T. BECK
or of protonation
(11) "0 /
"OH
HO
OH
followed by slow decomposition
%r: ?-- --? N~.o/N HO ~ "OH
ke slow
Cr(IV) + H ++ HONO + NOs-.
(12)
The complex produced in Eq. (7) is also believed to undergo dimerisation O-
~P--O--N-~-~O . K, ~) fa~t
dimer
°~c~° to ~ "o.
-O--N..0
/o/N--O-
ka ) 2 C r ( I V ) + 2 N O z slow
(13)
(14)
Equations (7)-(14) give rise to the rate equation d[Cr(VI)] = kzK~[CrO4H-][HONO] + kbK~K2[CrO4H-][HONO] 2 dt + kcKtK2Ka[CrO4H-][HONO]2[H +] + kaK~2K4[CrO4H-]2[HONO] 2.
(15)
Since no term involving the concentration of nitrous acid to the first power is found in the experimentally determined rate-law, the decomposition of the I : 1 condensation product of Equation (7) by the route shown in Equation (8) must be negligible. i.e. ka ~ kbK2[HONO], etc.
(16)
In acid solution, the nitrite ion undergoes the reactions N O 2 - + H + . rill , H O N O (Kin = 1"1 X 10-3110])
(17)
H O N O + H + . K m • H 2 0 + NO+(K,2 = 2 X 10-r[11])
(18)
2 H O N O . r° " N2On + H20(Ko = 0-2112]).
(19)
It may be seen from these constants that under the conditions employed in the 10. P. Lumme and J. Tummavuori,A cta chem. scand. 19, 617 (1965). 11. T. A. Turney and G. A. Wright, J. chem. Soc. 2415 (1958). 12. T.A. Turney, J. chem. Soc. 4263 (1960).
The oxidation of nitrous acid by chromium(VI)
2977
present study, the added nitrite is present almost exclusively as H O N O . Since the concentration of Cr(VI) is very small in comparison with that of the total nitrite, [HONO] in Equation (15) may readily be replaced by [HNO215 to give d[Cr(VI)] = [CrO4H-][HNO2]t2(kbKIK2 + kcK1KzK3[H +] dt + kaKlZK4[CrO4H-]).
(20)
That [HNOz]t appears in the denominator of Equation (6) can only be explained as a result of the formation of relatively stable Cr(VI)-nitrite species. Therefore [Cr(VI)]t = [CrO4H-] + [CrOsN-] + [CrOTN2H-] + [CrOTN2H2] + [Cr2OaoN~2-].
(21)
If the analytical concentrations of the products of the reactions in Equations (11) and (13) are negligible (and this is quite conceivable), Equation (21) reduces to [Cr(VI)]t = [CrO4H-] + [CrO~N-] + [CrOrN2H-] = [CrO4H-] -4-KI[CrO4H-][HNO2]t-4- K~Kz[CrO4H-][HNOz], 2 or
(22)
[Cr(VI)], [CrO4H-] = 1 + KI[HNOz]t + K1K2[HNO2]t z
(23)
K3[H +] ~ 1 and KzK3[H+][HNO2]t ~ 1
(24)
K~[CrO4H-] ,~ K2 and K~[CrO4H-][HNO2]t ~ 1.
(25)
while and
The final term of Equation (20) is relatively far less important than the other two terms. Hence, from Equations (20) and (23) we have, to a first approximation _ d[Cr(VI)] = [HNOz]t2[Cr(VI)]t(kbK~K2 + kcK1K2Ka[H +] + kaK12K4[Cr(VI)]t) dt 1 + K1[HNO2]t + KIK2[HNO2]t 2 (26) This is the same form as Equation (6) the experimentally found rate-law. Direct comparison of these two equations gives K~ = 10 mole -1 lit K2 = 30 mole -~ lit kb = 4.7 × 10-3 sec -1. It must be remembered that Equation (26) is an approximation; under other reaction conditions, i.e. other combinations of reactant concentrations, this approximation will not be valid and the full expansion of Equation (20 is required. From Equation (16), with atypical value of [HONO] of 2 × 10-z, k,, ~ 2.76 × 10-3.
2978
D . A . D U R H A M , L. DOZSA and M. T. BECK
That is, k, is probably at most 10-4 sec-'. Similarly, from Equation (24), with a value of [H ÷] = 0.1, K3 ~ 10 and is probably at most 0.5 mole -~ lit. Therefore. since kcK3 = 1.7 × 10-5, kc is probably greater than 3 × 10-z sec -~. The value of K1 = 10 mole -1 lit can be compared with the formation constants of the Cr(VI) condensation products with acids, e.g. K -- 9.4 mole -1 lit for the reaction with H3PO4 [ 13], 2.9 mole -~ lit for the reaction with H2PO4- [ 13], and 36 mole -1 lit for the reaction with HSO3- [14]. The fact that the equilibrium constant Ks is appreciably higher than Kx suggests that the complex formed is of a different type than the first condensation product. This prompted the postulation of the ring compound of Equation (9). Its formation constant is given by / [CrOrN~H-]
KaK2 = [CrO4H_][H~,IO2]t 2 = 300. This formation constant is somewhat higher than those normally found for Cr(VI) complexes, although that for the dimerisation of CrO4H- is 100[15], but the extra stability in this case could be due to the chelation. That the figure is not unreasonably high may be seen by comparison with the formation constant [ 16] K
=
[CrS~O62]
=
1'2 × 104
[CrO4H-][HS203-] although it is believed that in this case a chromium-sulphur bond is formed in the condensation product. -The formation constant KIK2 could, of course, refer to the reaction of Equation (19) followed by
CFOaH- + NzO3
N-.oIN -0 /
"OH
This reaction path is kinetically identical with that of Equations (7) and (9). However, because of the relative concentrations of the nitrite species ([HNO2] -> [N203]), and because the condensation product of Equation (7) must be present due to the appearance of its concentration in the denominator of Equation (6), we feel it more likely that the reaction occurs via two molecules of H O N O and not via one molecule of N203. It is a little surprising that Equation (8) does not play an important role in the kinetics; the atoms would not appear to be too unfavourably situated for the direct formation of a nitrate ion and Cr(VI). However, in complexes such as 13. F. Hoiloway, J. Am. chem. Soc. 74, 224 (1952). 14. G. P. Haight, Jr., E. Perchonock, F. Emmenegger and G. Gordon, J. Am. chem. Soc. 87, 3835 (1965). 15. J. Y. Tong and E. L. King, J. A m. chem. Soc. 75, 6180 (1953). 16. I. Baldea and G. Niac, lnorg. Chem. 7, 1232 (1968).
The oxidation of nitrous acid by chromium(VI)
2979
those formed in Equation (9), (11) and (13) the structure of the nitrate ion is already present, and these routes are clearly preferred. Unfortunately, there are extremely few studies of the oxidation of nitrous acid from a kinetic viewpoint and it is not possible to compare the results except for the case of the oxidation by permanganate[17]. In this latter reaction, the redox steps involving the permanganate were relatively much faster than the corresponding steps involving chromium; it was found that the rate of reaction was practically independent of permanganate concentration and that the kinetics were governed by the rates of formation of reactive nitrite species. The reason for the induction period observed at low concentrations of nitrite in the Cr(VI) reaction is quite unknown. Similar induction periods have been observed in the oxidations by Cr(VI) of sulphite [ 14], and of thiosulphate [ 18], and thus the phenomenon appears worthy of further study. 17. L. D6zsa and M. T. Beck, Inorg. Chim. A cta 4, 219 (1970). 18. I. Baldea and G. Niac, lnorg. Chem. 9, 110 (1970).
Pergamon Press.
Printed in Great Britail~
T H E O X I D A T I O N OF N I T R O U S A C I D BY CHROMIUM(VI) D. A. D U R H A M , L. DOZSA and M. T. BECK Institute of Physical Chemistry, Kossuth Lajos University, Debrecen 10. Hungary. (Received 10 September 1970) A b s t r a c t - T h e reaction of nitrous acid and chromium(Vl) has been studied in dilute solution at 25°C, with an ionic strength of 0.5, over the pH range 0.4-1 "3. The rate of reaction was obtained spectrophotometrically following changes in the absorbance of chromium(V1), and the determined rate-law was of the form d[Cr(Vl)l [HN O2]/[Cr(V l)]tkl + k2[H +] + k:~[Cr(Vl)]~ dt I + k4[HNO~], + k.~[HNO~]t'-' the rate-determining steps involving the two-electron reduction of Cr(VI) to Cr(IV). INTRODUCTION
WE HAVE recently been carrying out investigations into the role of mixed ligand formation in the reduction of Cr(VI) [ 1], and into the effect of coordination on the reactivity of the nitrite ion[2]. We are now studying the effect of E D T A on the Cr(VI)-HNO2 reaction for which a knowledge of the kinetics and mechanism of the basic C r ( V I ) - H N O e reaction was necessary. Very little work has been reported on the kinetics of this reaction. One of the most thorough studies was that of Kurtenacker[3] who found the following rate-law dx - - = (kl + k., [S]2)[H._,Cr~OT][HNO.,]([S] = acid concentration). dt His study was carried out in a sulphate or acetate medium. It is known that sulphate and acetate react with Cr(VI) in acid solution to yield C r S O / - [4, 5] and AcOCrO:~- [6, 7], respectively. Hence a comparison of Kurtenacker's results with those obtained in a perchlorate medium appeared useful. EXPERIMENTAL The kinetics of reactions were followed continuously using a Hitachi-Perkin Elmer 139 spectrophotometer fitted with a constant temperature cell compartment. In all cases the temperature was maintained at 25°C. The ionic strength was adjusted with sodium perchlorate and, except for one series of experiments in which the reaction rate was studied as a function of ionic strength, was maintained at 0.5. Nitrite was added in the form of its sodium salt, while the hydrogen ion concentraI. 2. 3. 4. 5. 6. 7.
M.T. Beck and D. A. Durham, J. inorg, nucl. Chem. 33, 461 (1970). M.T. Beck and L. D6zsa. Inorg. Chim. Acta 1,134(1967). A. Kurtenacker, Monatsh. Chim. 41, 101 (1920). A. Carrington and M. C. R. Symons, Chem. Rev. 63, 443 (1963). G. P. Haight. Jr., D. C. Richardson and N. H. Coburn, lnorg. Chem. 3, 1797 (1964). M. Cohen and F. H. Westheimer, J . A m . chem. Soc. 74. 4387 (1952). M . C . R . Symons. J. chem. Soc. 4331 ( 1963). 2971
2972
D . A . D U R H A M , L. D O Z S A and M. T. BECK
tion was varied by addition of perchloric acid. No buffer solutions were employed. The required component solutions were mixed externally, sodium nitrite (always the last component to be added) being injected from a syringe. Absorbance was measured within 20-30 sec after mixing, measurement being continued for 2-3 min. Chromium(VI) absorbance was measured at 405 nm, and not at the absorption maximum, to minimise spectral interference by the nitrite. A separate study of the rate of decomposition of nitrous acid under the conditions used showed that during the time of measurement of the loss of Cr(VI) the decomposition of the nitrous acid could be neglected. This is in agreement with other observations[8]. No attempt was made to exclude air or oxygen from the system. The strengths of the various solutions were determined by standard volumetric procedures. RESULTS AND DISCUSSION
The reaction of nitrous acid with Cr(VI) takes place[3] according to the following overall equation 2CrO4H- + 3HNO2 + 5H + ---> 2Cr a+ + 5H20 + 3NOa-.
(1)
As mentioned above the interference by the decomposition of nitrous acid was neglected. Rates of reaction were obtained by plotting Cr(VI) absorbance against time. The resulting graphs were practically linear and the initial slopes could be measured quite simply. From the slopes and the initial chromium(VI) absorbances, the initial rates of loss of Cr(VI) were calculated. A study was first made of the effect of the ionic strength on the reaction rate. The results are shown in Fig. 1 from which it is clear that the reaction rate is almost totally independent of the ionic strength over the range studied. Despite this independence, the ionic strength was adjusted to 0.5 in all the subsequent work.
T
1.55
L >
I" 5 0
K O 1-45
0.25
I 0.55
I 0.45 Ionic
1 0,55
0~5 .
0~5 •
strength
Fig. 1. Variation of rate of reaction with ionic strength. [HNO2] = 4.177 × 10-ZM, [Cr(VI)] = 6"208 × 10-4M; [H +] = 0" 198M. 8. E . D . Hughes, C. K. Ingold and J. H. Ridd, J. chem. Soc. 58 (1958); and subsequent papers.
T h e oxidation of nitrous acid by c h r o m i u m ( V I )
2973
A detailed kinetic investigation of the reaction was made within the fairly limited concentration ranges: [H ÷] = 0.485-0.315M; [HNO2]t = 4.18 × 10- 3 0.101M; [Cr(VI)]t = 1.552 x 10- 4 - 1.552 × 10-3M (t = total). It was found that at nitrite concentrations less than about 5 x 10-3M, there appeared to be an induction period for the reaction; above this concentration there was no apparent sign of such an induction period after the initial 20-30 sec, and reaction rates could be measured quite straightforwardly. The results of the kinetic investigation are as follows. A t constant [HNO2] a n d [H+], plots of Rate against [Cr(VI)]t are almost straight lines, but at higher values of [Cr(VI)]t there is a definite tendency to an upwards deviation from iinearity. Plots of Rate/[CrIVI)]t against [Cr(VI)]t, however, are linear and no deviation is observed. (Fig. 2). Hence the rate depends upon the chromium concentration in the following way d[Cr(VI)] = cl[Cr(VI)lt + c2[Cr(VI)], z. dt
(2)
A t c o n s t a n t [Cr(VI)t and [H+], the plots of Rate against [HNO2]t gave rise to S-shaped curves such as that in Fig. 3. By trial and error it was found that the curves could all be approximated by my functions
d[Cr(VI)] = c3[HNOz]t 2 dt 1 + c4[HNO2]t 2
(3)
but even better fits were obtained using functions
--
d[Cr(VI)] _ cs[HNO2]t z dt - t + c r [ H N O z ] t + c7[HNO2]t 2"
(4)
A plot of this function is compared with the measured data for one series of results in Fig. 3.
2.2
T
2(
- -
/,,/"
2.
./
1"9
• i~'-~"I-8
~'~'
,.7 1.6
,;
I-!
,to
[cr(vl)] xtO4M Fig. 2. Variation o f Rate/[Cr(Vl)] with [Cr(VI)]. [HNO2] = 4.177 × 10-2M; [H ÷] = 7-80 × 10-2M; l = 0.5.
2974
D.A.
DURHAM,
L. D O Z S A and M. T. B E C K
A t constant [HNO2]t and [Cr(VI)]t, changes in the pH bring about changes
in the concentrations of all the various nitrite and chromium(VI) species (see for example [9]). The rate-law under these conditions was found to be of the form ( F i g . 4).
_ d [ C r ( V I ) ] = c s [ H + ] + c9 dt
f/"
45 40 T
=
(5)
35
T... 3O ~
25
o
~ 2o
i
.//
~" u5 ¢u o n.-
I0
0
2
4
6
[HNO2] K IO2M
Fig. 3. Variation of rate of reaction with [HNO2]. IH ÷] = 0.137M, [Cr(VI)] = 9.312 × 10-4M; 1 = 0.5. The plotted points are those measured, and the curve is the calculated function: 2.30 × 10-3[HNO2] 2 Rate = 1 + 10.2[HNOz] + 300[HNO2] 2' 1.8
1.7
I-6 Z. I-5
_e
K
~
1"4
1.2--
g. I" I'(
o.~
~
~
,~
,~
~to
~
~
~
[H+]x IoZM
Fig. 4. Variation of rate of reaction with [H+].[HNO2] = 4.177x 10-=M; [Cr(VI)] = 6.208 x |0-4M; 1 = 0.5. 9, D . A . Durham, J. inorg, nucl. Chem. 31, 3549 (1969).
The oxidation of nitrous acid by chromium(V I)
2975
T h e only combination of Equations (2), (4) and (5) which consistently fitted the measured results was d[Cr(VI)] = [HN 02]tZ[Cr(VI)]t(k, + kz[H +] + k3[Cr(VI)]t) 1 + k4[HNO2]t + ks[HNO2]t 2 dt
(6)
T h e results of 115 (tifferent rate determinations involving changes of all three variables were analysed mathematically on the basis of Equation (6) in order to find the best values of the constants kl, k2, k3, k4 and ks, according to a programme seeking the least squares deviation. T h e results of this were. k = k2 = k3 = k4 = k5 =
1.4 mole -2 lit z sec -1 5.0 mole -a lit 3 sec -~ 3.9 x 102 mole -z lit ~ sec -~ 10 mole -~ lit 3.00 x 102 mole -2 lit z.
T h e differences between experimentally observed rates and those calculated on the basis of these k values were always less than 10 per cent and in the vast majority of cases were less than 5 per cent. T h e mechanism of the reaction of Cr(VI) with nitrous acid is envisaged as follows. T h e first step involves the fast equilibrium condensation of the two m o n o p r o t o n a t e d reactants O-
O-
O = ~ r - - O H + H O - - N = O . I " 1 0 = ~ r - - O - - N = O + H20
(7)
T h e condensation product is capable of an internal two-electron redox reaction O-
O~---~r--O--N=O k° ~ Cr(IV)+NO3[~)
slow
(8)
or of condensation with a further molecule of nitrous acid
OO~r--O---N--O
+
K2
HO---N==O " fast
0~... ~ 0 o'~Cr..o I I N~o/N -O / "OH
(9)
The cyclic product is also capable of an internal redox reaction
N~o/N -0 / "OH
kb slow
Cr(IV)+ HONO + NOa-
(lO)
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D. A. DURHAM, L. DOZSA and M. T. BECK
or of protonation
(11) "0 /
"OH
HO
OH
followed by slow decomposition
%r: ?-- --? N~.o/N HO ~ "OH
ke slow
Cr(IV) + H ++ HONO + NOs-.
(12)
The complex produced in Eq. (7) is also believed to undergo dimerisation O-
~P--O--N-~-~O . K, ~) fa~t
dimer
°~c~° to ~ "o.
-O--N..0
/o/N--O-
ka ) 2 C r ( I V ) + 2 N O z slow
(13)
(14)
Equations (7)-(14) give rise to the rate equation d[Cr(VI)] = kzK~[CrO4H-][HONO] + kbK~K2[CrO4H-][HONO] 2 dt + kcKtK2Ka[CrO4H-][HONO]2[H +] + kaK~2K4[CrO4H-]2[HONO] 2.
(15)
Since no term involving the concentration of nitrous acid to the first power is found in the experimentally determined rate-law, the decomposition of the I : 1 condensation product of Equation (7) by the route shown in Equation (8) must be negligible. i.e. ka ~ kbK2[HONO], etc.
(16)
In acid solution, the nitrite ion undergoes the reactions N O 2 - + H + . rill , H O N O (Kin = 1"1 X 10-3110])
(17)
H O N O + H + . K m • H 2 0 + NO+(K,2 = 2 X 10-r[11])
(18)
2 H O N O . r° " N2On + H20(Ko = 0-2112]).
(19)
It may be seen from these constants that under the conditions employed in the 10. P. Lumme and J. Tummavuori,A cta chem. scand. 19, 617 (1965). 11. T. A. Turney and G. A. Wright, J. chem. Soc. 2415 (1958). 12. T.A. Turney, J. chem. Soc. 4263 (1960).
The oxidation of nitrous acid by chromium(VI)
2977
present study, the added nitrite is present almost exclusively as H O N O . Since the concentration of Cr(VI) is very small in comparison with that of the total nitrite, [HONO] in Equation (15) may readily be replaced by [HNO215 to give d[Cr(VI)] = [CrO4H-][HNO2]t2(kbKIK2 + kcK1KzK3[H +] dt + kaKlZK4[CrO4H-]).
(20)
That [HNOz]t appears in the denominator of Equation (6) can only be explained as a result of the formation of relatively stable Cr(VI)-nitrite species. Therefore [Cr(VI)]t = [CrO4H-] + [CrOsN-] + [CrOTN2H-] + [CrOTN2H2] + [Cr2OaoN~2-].
(21)
If the analytical concentrations of the products of the reactions in Equations (11) and (13) are negligible (and this is quite conceivable), Equation (21) reduces to [Cr(VI)]t = [CrO4H-] + [CrO~N-] + [CrOrN2H-] = [CrO4H-] -4-KI[CrO4H-][HNO2]t-4- K~Kz[CrO4H-][HNOz], 2 or
(22)
[Cr(VI)], [CrO4H-] = 1 + KI[HNOz]t + K1K2[HNO2]t z
(23)
K3[H +] ~ 1 and KzK3[H+][HNO2]t ~ 1
(24)
K~[CrO4H-] ,~ K2 and K~[CrO4H-][HNO2]t ~ 1.
(25)
while and
The final term of Equation (20) is relatively far less important than the other two terms. Hence, from Equations (20) and (23) we have, to a first approximation _ d[Cr(VI)] = [HNOz]t2[Cr(VI)]t(kbK~K2 + kcK1K2Ka[H +] + kaK12K4[Cr(VI)]t) dt 1 + K1[HNO2]t + KIK2[HNO2]t 2 (26) This is the same form as Equation (6) the experimentally found rate-law. Direct comparison of these two equations gives K~ = 10 mole -1 lit K2 = 30 mole -~ lit kb = 4.7 × 10-3 sec -1. It must be remembered that Equation (26) is an approximation; under other reaction conditions, i.e. other combinations of reactant concentrations, this approximation will not be valid and the full expansion of Equation (20 is required. From Equation (16), with atypical value of [HONO] of 2 × 10-z, k,, ~ 2.76 × 10-3.
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D . A . D U R H A M , L. DOZSA and M. T. BECK
That is, k, is probably at most 10-4 sec-'. Similarly, from Equation (24), with a value of [H ÷] = 0.1, K3 ~ 10 and is probably at most 0.5 mole -~ lit. Therefore. since kcK3 = 1.7 × 10-5, kc is probably greater than 3 × 10-z sec -~. The value of K1 = 10 mole -1 lit can be compared with the formation constants of the Cr(VI) condensation products with acids, e.g. K -- 9.4 mole -1 lit for the reaction with H3PO4 [ 13], 2.9 mole -~ lit for the reaction with H2PO4- [ 13], and 36 mole -1 lit for the reaction with HSO3- [14]. The fact that the equilibrium constant Ks is appreciably higher than Kx suggests that the complex formed is of a different type than the first condensation product. This prompted the postulation of the ring compound of Equation (9). Its formation constant is given by / [CrOrN~H-]
KaK2 = [CrO4H_][H~,IO2]t 2 = 300. This formation constant is somewhat higher than those normally found for Cr(VI) complexes, although that for the dimerisation of CrO4H- is 100[15], but the extra stability in this case could be due to the chelation. That the figure is not unreasonably high may be seen by comparison with the formation constant [ 16] K
=
[CrS~O62]
=
1'2 × 104
[CrO4H-][HS203-] although it is believed that in this case a chromium-sulphur bond is formed in the condensation product. -The formation constant KIK2 could, of course, refer to the reaction of Equation (19) followed by
CFOaH- + NzO3
N-.oIN -0 /
"OH
This reaction path is kinetically identical with that of Equations (7) and (9). However, because of the relative concentrations of the nitrite species ([HNO2] -> [N203]), and because the condensation product of Equation (7) must be present due to the appearance of its concentration in the denominator of Equation (6), we feel it more likely that the reaction occurs via two molecules of H O N O and not via one molecule of N203. It is a little surprising that Equation (8) does not play an important role in the kinetics; the atoms would not appear to be too unfavourably situated for the direct formation of a nitrate ion and Cr(VI). However, in complexes such as 13. F. Hoiloway, J. Am. chem. Soc. 74, 224 (1952). 14. G. P. Haight, Jr., E. Perchonock, F. Emmenegger and G. Gordon, J. Am. chem. Soc. 87, 3835 (1965). 15. J. Y. Tong and E. L. King, J. A m. chem. Soc. 75, 6180 (1953). 16. I. Baldea and G. Niac, lnorg. Chem. 7, 1232 (1968).
The oxidation of nitrous acid by chromium(VI)
2979
those formed in Equation (9), (11) and (13) the structure of the nitrate ion is already present, and these routes are clearly preferred. Unfortunately, there are extremely few studies of the oxidation of nitrous acid from a kinetic viewpoint and it is not possible to compare the results except for the case of the oxidation by permanganate[17]. In this latter reaction, the redox steps involving the permanganate were relatively much faster than the corresponding steps involving chromium; it was found that the rate of reaction was practically independent of permanganate concentration and that the kinetics were governed by the rates of formation of reactive nitrite species. The reason for the induction period observed at low concentrations of nitrite in the Cr(VI) reaction is quite unknown. Similar induction periods have been observed in the oxidations by Cr(VI) of sulphite [ 14], and of thiosulphate [ 18], and thus the phenomenon appears worthy of further study. 17. L. D6zsa and M. T. Beck, Inorg. Chim. A cta 4, 219 (1970). 18. I. Baldea and G. Niac, lnorg. Chem. 9, 110 (1970).