اﻟﺨﻼﺻــﺔ - Arabian Journal for Science and Engineering

A STUDY OF THE SHAPE OF ACTIVATED COMPLEX IN
REACTION BETWEEN POTASSIUM PEROXYDISULFATE
AND POTASSIUM IODIDE
ﺔــﺻﻼﺨﻟا
ﻦﻴﺑو ، ﺖﻴﻔﻠﺳ ياد ﻲﺴآوأﺮﻴﺑ مﻮﻴﺳﺎﺗﻮﺑ ﻦﻴﺑ ﻞﻋﺎﻔﺘﻟا لﺪﻌﻣ ﺖﺑﺎﺛ سﺎﻴﻘﺑ ﺚﺤﺒﻟا اﺬه ﻲﻓ ﺎﻨﻤﻗ
ﺔﺟردو
ﺔﻳﻮﺌﻣ
( ٠٫١ + ٣٠)
ةﺪﻘﻌﻤﻟا
تﺎﺒآﺮﻤﻟا رﺎﻄﻗأ فﺎﺼﻥأ ﺎﻨﺒﺴﺡو
ﻲﻥﺎﻴﺒﻟا ﻢﺳﺮﻟا ﻲﻓ طﻮﻄﺨﻟا
ﺔﺟرد ﺪﻨﻋ نﻮﺘﻴﺳﻷاو ءﺎﻤﻟا ﻦﻣ ﻂﻴﻠﺧ ﻲﻓ ﻚﻟذو ، مﻮﻴﺳﺎﺗﻮﺒﻟا ﺪیدﻮی
ﻞﻴـَﻣ
. ( µ )
ماﺪﺨﺘﺳﺎﺑ ﻚﻟذو ،
ﻦیﺄﺘﻟا ةﺪﺷ ﻢﻴﻗ ﻦﻣ دﺪﻌﻟ
( ٠٫١ + ٤٠)
July 2003 The Arabian Journal for Science and Engineering, Volume 28, Number 2A. 137
ﺔﻳﻮﺌﻣ
ةﺮﻜﻟا
ﻲﺉﺎﻨﺛو يدﺎﺡأ جذﻮﻤﻥﻷ
ﺔﻄﺸﻨﻤﻟا
ﺖﺑﺎﺛ سﻮﻜﻌﻣ ﻦﻴﺑو – ﺮﻔﺹ = ﻦیﺄﺘﻟا ةﺪﺷ نﻮﻜﺗ ﺎﻣﺪﻨﻋ – لﺪﻌﻤﻟا ﺖﺑﺎﺛ ﻦﻴﺑ ﻲﻤﺛرﺎﻏﻮﻠﻟا
. ( ١/
٤)
لﺰﻌﻟا
ةﺪﻘﻌﻤﻟا تﺎﺒآﺮﻤﻠﻟ ﻒﻴﺹﻮﺗ ﻞﻀﻓأ ﻲﻄﻌی
ةﺮﻜﻟا
يدﺎﺡأ جذﻮﻤﻥﻷا
نأ ﺞﺉﺎﺘﻨﻟا تﺮﻬﻇأ ﺪﻗو
∆G ) ةﺮﺤﻟا
ﺔﻗﺎﻄﻟا ﻲﻓ ﺮﻴﻐﺘﻟا ﺔﻤﻴﻗ بﺎﺴﺡ ﺔﻟوﺎﺤﻤﺑ ﺎﻨﻤﻗ ﺎﻤآ . ﺔﻄﺸﻨﻤﻟا
‡ ﺔﻴﺉﺎﺑﺮﻬﻜﻟا ﻦﻋ ﺔﺠﺗﺎﻨﻟا ( e.s
. رﻮآﺬﻤﻟا ﻞﻋﺎﻔﺘﻠﻟ ﺔﻨآﺎﺴﻟا
ABSTRACT
Fahim Uddin* and Huma Kazmi
Department of Chemistry
University of Karachi
Karachi-75270, Pakistan
The rate constants of the reaction between potassium peroxydisulfate and potassium
iodide have been measured in a series of water–acetone mixtures at 30 ± 0.1°C and
40 ± 0.1°C at various ionic strengths (µ). The radii of activated complex for single
sphere and double sphere models have been calculated from the slopes of linear plots
of logarithm of rate constant at zero ionic strength (ko) versus reciprocal of dielectric
constant (1/ε). Results show that the description of the activated complex could best be
given by the single sphere model.
An attempt has also been made to evaluate the values of electrostatic contributions to
the free energy changes ∆G ‡ e.s. for the above reaction in acetone–water mixtures.
* To whom all correspondence should be sent.

Fahim Uddin and Huma Kazmi
A STUDY OF THE SHAPE OF ACTIVATED COMPLEX IN REACTION BETWEEN
POTASSIUM PEROXYDISULFATE AND POTASSIUM IODIDE
INTRODUCTION
The reaction between peroxydisulfate and iodide ions takes place in two steps [1, 2]:
- - - - - -
S2O8 + I IS2O8
slow… (1)
- - - - - -
IS2O8 + I I2 + 2SO4 . fast … (2)
This reaction follows second order kinetics:
- - - - -
-d [S2O8 ] / dt = k [S2O8 ] [I ] (3)
where t is time and k is the rate constant.
The influence of dielectric constant on the rate of ionic reactions having similar charges was studied by Amis [3],
Scatchard [4], Laidler [5], Laidler–Eyring [6], Christiansen [7], Ghaziuddin et al. [8, 9], and Fahimuddin et al. [10–13].
Ghaziuddin et al. [14] and Fahimuddin et al. [15] also studied the reaction between peroxydisulfate–iodine ions in
ethanol–water and methanol–water mixtures respectively and found that the activated complex is single sphere for both
the media, i.e. ethanol–water and methanol–water mixtures.
In the present work, the reaction between potassium peroxydisulfate and potassium iodide in acetone–water mixtures
has been studied to confirm whether the activated complex consists of a single sphere or a double sphere model.
EXPERIMENTAL
Potassium peroxydisulfate, potassium iodide, sodium thiosulfate, potassium dichromate, starch, and acetone used were
obtained from E. Merck. Double distilled water was used throughout the course of experiments. Dielectric constants of
the medium were varied by changing the proportions of the water–acetone mixtures. The compositions of water–acetone
mixtures used (w/w) were 8.08%; 12.25%; 16.51%; 20.07%; and 25.32%, and respective values of dielectric constants
were taken from Akerlof [16, 17]. The rate constants of the reaction were measured by a titrometric method. Calculated
volumes of K2S2O8 and KI were taken in 25 ml volumetric flasks and diluted up to the mark. These two diluted solutions
were kept in a thermostatic bath (Type K-33 Haake, Karlsruhe, Germany) at a constant temperature for half an hour.
Then these two solutions were mixed and the time was recorded. A 5 ml portion of this reaction mixture was drawn after
each interval of 5 minutes. The mixture was chilled to freeze the reaction and titrated against a standard solution of
sodium thiosulfate. Two drops of starch solution were added as an indicator. Iodine gives an intense blue absorption
complex with starch. At the end point when iodide ion predominates, the blue color disappears.
RESULTS AND DISCUSSIONS
The rate constants were calculated using the integrated form of the rate expression for the second order reaction with
the same initial concentration i.e.,
1 x
k = ⋅
(4)
t a(
a − x)
where a is the initial concentration of potassium peroxydisulfate and potassium iodide, x is the concentration of product
and time t, and (a – x) is remaining concentration of product at time t.
Plots of [x/a(a – x)] against time t were drawn at different ionic strengths and composition of solution i.e. acetone–
water mixtures. A representative plot of [x/a(a – x)] versus t at µ = 7.8 × 10 –2 mol.dm –3 in 10% acetone–water mixture at
138 The Arabian Journal for Science and Engineering, Volume 28, Number 2A. July 2003

Fahim Uddin and Huma Kazmi
40°C is shown in Figure 1. From the slopes of the plots, rate constants were evaluated. The values of rate constants for
the reaction between peroxydisulfate and iodide ions in acetone–water mixture at 30° and 40°C are summarized in
Tables 1 and 2 respectively.
[x/a(a–x)] (dm 3 mol.)
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0
0
Solvent : 10% acetone
Temperature : 40°C
102 m = 7.8 (mol/dm3 )
0.30
0.60
0.90
t/10 3 (Seconds)
July 2003 The Arabian Journal for Science and Engineering, Volume 28, Number 2A. 139
1.20
Figure 1. Plot of [x/a(a–x)] versus t at 40°C.
It was also noted that for the same value of dielectric constant, the rate constant increased with increasing ionic
strength. These results are in agreement with those reported earlier [14, 15]. The results also show that the rate constant
at constant ionic strength and dielectric constant increase as the temperature is increased. The values of ko (rate constant
at zero ionic strength) were calculated by using Debye–Huckel–Brønsted (DHB) equation [18] which is a relationship
between ionic strength and rate constant:
3
e ( 8πNA
/ 1000)
logk = logk
o +
ZA
ZB
µ
(5)
3 2
2.
303(
εK
T )
B
1 2
where e, NA, KB, and T are electronic charge, Avogadro number, Boltzmann’s constant, and absolute temperature
respectively. ZA and ZB are the charges of the ions A and B respectively. The values of ko are also tabulated in Tables 1
and 2 respectively.
1.50
1.80

Fahim Uddin and Huma Kazmi
10 2 µ
(mol. dm –3 )
Table 1. Rate Measurements Data for the Medium:
Acetone–Water Mixtures (Temperature: 30 o C).
ε
10 3 k
(dm 3 /mol.s)
10 2 [K 2S 2O 8] = 10 2 [K I] = 1.40 (mol. dm –3 )
140 The Arabian Journal for Science and Engineering, Volume 28, Number 2A. July 2003
10 4 k o
(dm 3 /mol.s)
5.6 72.25 0.23 0.68
5.6 69.75 0.20 0.56
5.6 67.25 0.18 0.46
5.6 64.25 0.17 0.40
5.6 62.20 0.16 0.35
10 2 [K 2S 2O 8] = 10 2 [K I] = 1.96 (mol. dm –3 )
7.8 72.25 0.68 1.59
7.8 69.75 0.62 1.35
7.8 67.25 0.42 0.83
7.8 64.25 0.34 0.62
7.8 62.20 0.28 0.45
10 2 [K 2S 2O 8] = 10 2 [K I] = 2.52 (mol. dm –3 )
10.1 72.25 1.82 3.47
10.1 69.75 1.09 1.91
10.1 67.25 0.96 1.55
10.1 64.25 0.87 1.26
10.1 62.20 0.65 0.83
10 2 [K 2S 2O 8] = 10 2 [K I] = 3.08 (mol. dm –3 )
12.3 72.25 2.17 2.09
12.3 69.75 1.32 1.95
12.3 67.25 1.04 1.95
12.3 64.25 0.98 1.15
12.3 62.20 0.88 0.85
10 2 [K 2S 2O 8] = 10 2 [K I] = 5.04 (mol. dm –3 )
20.2 72.25 2.78 2.69
20.2 69.75 2.67 2.29
20.2 67.25 2.03 1.51
20.2 64.25 1.54 0.98
20.2 62.20 1.50 0.81
10 2 [K 2S 2O 8] = 10 2 [K I] = 7.00 (mol. dm –3 )
28.0 72.25 5.84 3.52
28.0 69.75 3.96 2.19
28.0 67.25 3.51 1.66
28.0 64.25 3.23 1.27
28.0 62.20 2.60 0.83

10 2 µ
(mol. dm –3 )
Table 2. Rate Measurements Data for the Medium:
Acetone–Water Mixtures (Temperature: 40 o C).
ε
10 3 k
(dm 3 /mol.s)
10 2 [K 2S 2O 8] = 10 2 [K I] = 1.40 (mol. dm –3 )
Fahim Uddin and Huma Kazmi
July 2003 The Arabian Journal for Science and Engineering, Volume 28, Number 2A. 141
10 4 k o
(dm 3 /mol.s)
5.6 69.00 1.97 5.62
5.6 66.75 1.82 4.90
5.6 64.25 1.59 3.98
5.6 62.00 1.10 2.52
5.6 59.75 1.06 2.24
10 2 [K 2S 2O 8] = 10 2 [K I] = 1.96 (mol. dm –3 )
7.8 69.00 3.82 8.71
7.8 66.75 3.68 7.76
7.8 64.25 2.52 4.79
7.8 62.00 1.62 2.82
7.8 59.75 1.48 2.34
10 2 [K 2S 2O 8] = 10 2 [K I] = 2.52 (mol. dm –3 )
10.1 69.00 4.76 8.85
10.1 66.75 4.33 7.43
10.1 64.25 3.33 5.13
10.1 62.00 3.00 4.17
10.1 59.75 3.56 3.16
10 2 [K 2S 2O 8] = 10 2 [K I] = 3.08 (mol. dm –3 )
12.3 69.00 6.07 9.33
12.3 66.75 5.87 8.32
12.3 64.25 3.53 4.47
12.3 62.00 3.49 3.94
12.3 59.75 3.42 3.39
10 2 [K 2S 2O 8] = 10 2 [K I] = 5.04 (mol. dm –3 )
20.2 69.00 8.11 7.50
20.2 66.75 6.90 5.62
20.2 64.25 5.28 3.71
20.2 62.00 4.40 2.69
20.2 59.75 4.39 2.40
10 2 [K 2S 2O 8] = 10 2 [K I] = 7.00 (mol. dm –3 )
28.0 69.00 8.90 5.37
28.0 66.75 7.43 3.89
28.0 64.25 6.58 2.88
28.0 62.00 5.00 1.74
28.0 59.75 4.84 1.49

Fahim Uddin and Huma Kazmi
The effect of dielectric constant on the rate constant can be explained by the Laidler–Eyring equation [6] for single and
double sphere models respectively. The equations are expressed as follows:
2 ⎡
2 2 2
e ( Z
⎤
A + Z B)
ZA
ZB
ln k o = ln k∞
− ⎢
− −
‡
⎥ (for single sphere model) (6)
2εK
BT
⎢⎣
r rA
rB
⎥⎦
Z AZ
Be
1
ln k o = ln k∞
− ⋅
(for double sphere model) (7)
K T r ε
B
2
AB
where k∞ is rate constant at zero ionic strength and infinite dielectric constant. r ‡ and r AB are the radii of the activated
complex for the single sphere model and the double sphere model respectively. rA and rB are the radii of the ions A and
B respectively. The plots of logarithm of rate constant at zero ionic strength (log k o) against the reciprocal of the
di-electric constant of the medium (1/ε) at various ionic strength and temperatures were straight lines with negative
slopes. A representative graph is shown in Figure 2. The experimental values of r ‡ and rAB calculated from the slopes of
straight lines using Equations (6) and (7) are tabulated in Table 3.
(5 + log k 0)
1.40
1.30
1.20
1.10
1.00
0.90
0.80
13.5
Solvent : acetone
Temperature : 30°C
--
[S2O8 ]
–
= [I ]
14.0
= 3.8 ´ 10 –2 (mol/dm 3 )
14.5
142 The Arabian Journal for Science and Engineering, Volume 28, Number 2A. July 2003
10 3 /e
15.0
15.5
Figure 2. Plot of log k o versus 1/ε in aqueous–acetone medium at 30°C.
16.0
16.5

Table 3. Calculated Values of Radii of Activated Complexes.
10 2 [K 2S 2O 8]
(mol/dm 3 )
10 2 [K I]
(mol/dm 3 )
Temperature: 30°C
Fahim Uddin and Huma Kazmi
July 2003 The Arabian Journal for Science and Engineering, Volume 28, Number 2A. 143
r ‡
rAB (Å)
1.40 1.40 3.04 3.74
1.96 1.96 2.23 1.86
2.52 2.52 2.25 1.89
3.08 3.08 2.70 2.77
5.04 5.04 2.26 1.91
7.00 7.00 2.19 1.81
Temperature: 40°C
Average Average
2.4 ± 0.4 2.3 ± 0.8
1.40 1.40 2.57 2.48
1.96 1.96 2.13 1.72
2.52 2.52 2.49 2.33
3.08 3.08 2.44 2.22
5.04 5.04 2.30 1.98
7.00 7.00 2.20 1.83
The radius of peroxydisulfate ion was calculated as follows [15]:
where V is the volume of ion.
2−
= 2V 6+
+ 8V
2−
2 O8
S O
S
Average Average
2.4 ± 0.2 2.1 ± 0.3
V (8)
4
3
3 ⎛ 4 3 ⎞ ⎛ 4 3 ⎞
r 2− = 2⎜
πr
6 + ⎟ + 8⎜
πr
2
S O
S
O ⎟
(9)
2 8 ⎝ 3 ⎠ ⎝ 3 ⎠
π −
2−
O
r 2−
= 2.
80Å,
r = 1.
40Å
. (1 Å = 10 –10 m) (10)
S O
2
8
The radius of activated complex for a single sphere model (r ‡ ) is calculated on the basis of assumption that the volume
of single sphere activated complex (V ‡ ) is the sum of the volumes of the reactants.
V (11)
= V − + V 2− I S 8
2O
r ‡ = 3.176 Å. (12)

Fahim Uddin and Huma Kazmi
The radius of the activated complex for the double sphere model is calculated assuming that the radius of activated
complex is the sum of the radii of reactants.
r
AB
= r
2− +
2 8
S O
r
I
−
r I – = 2.16 Å (taken from Emeleus [19]) (14)
rAB = 2.80 + 2.16 = 4.96 Å. (15)
In all calculations the values of radii of individual ions were taken from Emeleus [19] and confirmed by Wilson [20].
It has been concluded from the comparison of average experimental values of r ‡ and rAB with their theoretical values as
shown in Table 4, that the shape of the activated complex could best be given by single sphere model for reaction
between peroxydisulfate and iodide ions because the values of r ‡ expt is closer to the theoretical value of single sphere
model. The results show that change in temperature has no effect on the shape of activated complex. The values of r ‡
Table 4. Comparison of Values of Radii Determined Experimentally with Theoretical Values.
Experimental
30° 40°
Theoretical % error
r # (Å) 2.4 ± 0.4 2.4 ± 0.2 3.18 25
r AB (Å) 2.2 ± 0.8 2.1 ± 0.3 4.96 50
Table 5. Electrostatic Contribution to ∆G ‡
e.s
10 Dielectric constant (ε)
2 µ
(mol/dm 3 ) 72.25 69.75 67.25 64.75 62.20
Temperature: 30°C ∆G ‡
e.s (kJ/mol)
5.60 1.028 1.065 1.105 1.147 1.194
7.84 2.062 2.136 2.215 2.300 2.394
10.08 2.027 2.100 2.178 2.262 2.355
12.32 1.386 1.436 1.489 1.547 1.610
20.16 2.010 2.083 2.160 2.243 2.335
28.00 2.133 2.209 2.291 2.380 2.477
Dielectric constant (ε)
69.00 66.57 64.25 62.00 59.75
Temperature: 40°C ∆G ‡
e.s (kJ/mol)
5.60 1.621 1.676 1.741 1.804 1.872
7.84 2.349 2.429 2.523 2.615 2.713
10.08 1.735 1.793 1.863 1.930 2.003
12.32 1.809 1.870 1.943 2.014 2.089
20.16 2.035 2.103 2.186 2.265 2.350
28.00 2.214 2.289 2.378 2.464 2.555
144 The Arabian Journal for Science and Engineering, Volume 28, Number 2A. July 2003
(13)

Fahim Uddin and Huma Kazmi
and rAB are slightly less than the values given by Ghaziuddin et al. [14]. This may be due to the volatile nature of
acetone. This may affect the values of rate constant at zero ionic strength of the medium (ko).
Electrostatic contributions to the changes in free energy of activation ∆G ‡ e.s in the formation of activated complex for
the single sphere model were evaluated using the following expression [5]:
2 ⎡
2 2 2 ⎤
‡ NAe
( Z A + Z B)
ZA
ZB
∆G
e.s = ⎢
− −
‡
⎥ . (16)
2 ⎢⎣
r rA
rB
⎥⎦
The values of ∆G ‡ e.s at different temperatures i.e. 30 o and 40 o C and ionic strengths as a function of dielectric constant
are summarized in Table 5. The results show that as the ionic strength increases, the values of ∆G ‡ e.s increase with a
decrease in dielectric constant values, at both the temperatures i.e. 30° and 40°C. Moreover with a rise in temperature,
the values of ∆G ‡ e.s increase as a function of with strength with a decrease in dielectric constant values. This is in
accordance with the results reported earlier [12].
CONCLUSIONS
A comparison of the theoretical and experimental values of r ‡ (radii of single sphere activated complex) and rAB (radii
of double sphere activated complex) obtained from the slopes of the linear plots of log k o (logarithm of rate constant at
zero ionic strength) versus 1/ε (reciprocal of the dielectric constant of the medium) leads to the conclusion that the shape
of the activated complex could best be described by the “single sphere model”.
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[15] Fahimuddin, Riffat Naheed, and S. Muneebullah Husaini, “Shape of the Activated Complex for the Reaction between Iodide
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July 2003 The Arabian Journal for Science and Engineering, Volume 28, Number 2A. 145

Fahim Uddin and Huma Kazmi
[16] G. Akerlof, “Dielectric Constant of Some Organic Solvent–Water Mixtures at Various Temperatures”, J. Am. Chem. Soc.,
54 (1932), pp. 4126– 4139.
[17] P.S. Radakhishnamurti and P.C. Patro, “Consecutive First Order Reactions: Part II. Hydrolysis of Dicarboxylic Esters”,
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[18] K.J. Laidler, Reaction Kinetics. New York: Pergamon Press, 1963, p. 19.
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[20] J.W. Wilson and A.B. Newall, General and Inorganic Chemistry. Cambridge: Cambridge University Press, 1967.
Paper Received 3 September 2001; Revised 5 January 2002; Accepted 2 April 2002.
146 The Arabian Journal for Science and Engineering, Volume 28, Number 2A. July 2003