Study of malachite green fading in water-ethanol-ethylene glycol ternary mixtures

Article abstract of DOI:10.1007/s10953-012-9916-2

The rate constant of malachite green (MG⁺) alkaline fading was measured in water-ethanol-ethylene glycol ternary mixtures. This reaction was studied under pseudo-first-order conditions at 283-303 K. In each series of experiments, the concentration of ethanol was kept constant and the concentration of ethylene glycol was changed. It was shown that due to hydrogen bonding and hydrophobic interaction between MG⁺ and alcohol molecules the observed reaction rate constant, k_obs, increased in the water-ethanol-ethylene glycol ternary mixtures. The fundamental rate constants of MG⁺ fading in these solutions (k₁, k_{- 1} and k₂) were obtained by the SESMORTAC model. Analysis of k₁ and k₂ values in solutions containing constant ethanol concentrations show that in low concentrations of ethylene glycol, hydrogen bonding formed between ethanol and ethylene glycol molecules and in high concentrations of ethylene glycol, ethanol as a solvent for ethylene glycol affected the reaction rate.

Full text of DOI:10.1007/s10953-012-9916-2

J Solution Chem (2013) 42:151–164
DOI 10.1007/s10953-012-9916-2
Study of Malachite Green Fading in Water–Ethanol–
Ethylene Glycol Ternary Mixtures
•
Babak Samiey Somayeh Ahmadi
Received: 29 June 2011 / Accepted: 1 February 2012 / Published online: 11 December 2012
Ó Springer Science+Business Media New York 2012
Abstract The rate constant of malachite green (MG?) alkaline fading was measured in water–
ethanol–ethylene glycol ternary mixtures. This reaction was studied under pseudo-first-order
conditions at 283–303 K. In each series of experiments, the concentration of ethanol was kept
constant and the concentration of ethylene glycol was changed. It was shown that due to hydrogen
bonding and hydrophobic interaction between MG? and alcohol molecules the observed reaction
rate constant, kobs, increased in the water–ethanol–ethylene glycol ternary mixtures. The
fundamental rate constants of MG? fading in these solutions (k1, kꢀ1 and k2) were obtained
by the SESMORTAC model. Analysis of k1 and k2 values in solutions containing constant
ethanol concentrations show that in low concentrations of ethylene glycol, hydrogen bonding
formed between ethanol and ethylene glycol molecules and in high concentrations of eth-
ylene glycol, ethanol as a solvent for ethylene glycol affected the reaction rate.
Keywords SESMORTAC model ꢁ Ethylene glycol ꢁ Ethanol ꢁ Malachite green ꢁ Kinetics
List of symbols
SESMORTAC Study of effect of solvent mixture on the one-step reaction rates using the
transition state theory and cage effect
ACSM
ACSMbm
ACSM1
AC
Activated complex formed in the second mechanism
ACSM formed at the bm point
ACSM formed in the first zone
Activated complex
n
Number of molecules of solvent 1 in the solvent cage of transition state
that are replaced by the same number of solvent 2 molecules in the
transition state
mc
kmcðiꢀ1Þ
kbm
mechanism change
Rate constant at the mciꢀ1 point
Observed rate constant
Reaction rate
v
B. Samiey (&) ꢁ S. Ahmadi
Department of Chemistry, Faculty of Science, Lorestan University, 68137-17133 Khoramabad, Iran
e-mail: babsamiey@yahoo.com
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Subscripts
bm Binary mixture
ter Ternary mixture
i
The ith zone
1 Introduction
Solvent effects on reactivity may be very large. Alcohols, as cosolvents, can change the
rates of chemical reactions [1–5]. Malachite green (MG?) is a triphenylmethane dye. These
dyes represent a class of dyes of commercial and analytical importance [6, 7]. Malachite
green is used to dye materials like silk, leather, cotton and paper and can be used as a
saturable absorber in dye lasers, as a pH indicator or as a bacteriological stain [8]. In
continuation of our earlier works [9, 10], in this work, we studied the MG? alkaline fading
in ternary mixtures of water with different weight percentages of ethanol and ethylene
glycol at 283–303 K. The MG? fading is a one-step reaction [11, 12].
2 Experimental
2.1 Chemicals
Malachite green oxalate (for analysis), ethanol (C99.9 %), ethylene glycol (C99 %), and
NaOH were purchased from Merck.
2.2 Procedure
The fading of MG? was followed at its maximum wavelength ðkMaxÞ values in a thermostatted cell
compartment of a Shimadzu UV–1650PC spectrophotometer. The experiments were con-
ducted at 283, 293 and 303 K (ꢂ0:1 K) in a stoppered cell. All of the kinetic runs were carried
out at least in triplicate. To perform each kinetic run, a 100 lL aliquot of 1.38 9
10-4 molꢁL-1 MG? solution was added by a microsyringe into 2.9 mL of a solution containing
5.4 9 10-4 molꢁL-1 sodium hydroxide and a certain concentration of the alcohols. The reaction
between MG? and hydroxide ion is very fast and thus the reaction was studied at 283–303 K and
very low concentrations of NaOH. This reaction is bimolecular, first order with respect to each
reactant, and pseudo-first-order conditions (excess alkali) were used in all cases (Fig. 1).
We used the second-order reaction rate constants in our calculations. Ethanol and
ethylene glycol have one and two hydroxyl groups, respectively, and the effect of ethylene
glycol on the rate of this reaction is much greater than that of ethanol.
In this work, we investigated the simultaneous effect of various concentrations of
ethanol and ethylene glycol on the kinetics of MG? fading.
3 Results and Discussion
3.1 Effect of Ethylene Glycol on MG? Fading in Constant Concentrations of Ethanol
These experiments were carried out in solutions containing 5, 10, 15, 20 and 25 weight
percentages of ethanol and variable concentrations of ethylene glycol. As seen in Fig. 2, with
increase in weight percentage of ethylene glycol, the kMax value of MG? is red shifted.
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J Solution Chem (2013) 42:151–164
153
N(CH3)2
(CH3)2N+
OH-
OH
+
(CH3)2N
N(CH3)2
MG+
carbinol base
Fig. 1 Schematic representation of the MG? fading reaction
626
624
622
620
618
616
0
10
20
30
40
50
60
70
WEG
%
Fig. 2 kMax values of the MG? versus weight percentages of ethylene glycol in ternary mixtures of water–
ethanol–ethylene glycol under alkaline conditions at room temperature. Weight percentages of ethanol in these
solutions are: filled diamond, 5 %; open square, 10 %; open triangle, 15 %; open diamond, 20 % and ?25 %
The red shift has been previously reported for other compounds upon going from polar
to apolar solvents, as a result of hydrophobic interaction [13]. Comparison of these data to
results obtained from the ethylene glycol–water binary mixtures [10] shows that, especially
in low concentrations of ethanol, kMax values of MG? change similarly to their trend in
binary aqueous ethylene glycol mixtures.
Reaction of MG? fading is an electrophile–nucleophile combination reaction. As shown
in Tables 1, 2, 3, 4, 5 and Fig. 3, with increasing content of ethylene glycol, the rate
constant of the reaction increases and then levels off over a small concentration range of
ethylene glycol in the presence of 5 and 10 weight percentages of ethanol.
Alcohols have a lower dielectric constant than water and due to their hydrophobicity,
according to Hughes–Ingold rules for solvent effects in nucleophilic substitution reactions
[14–16], formation of the neutral carbinol base from two oppositely charged reactants
(MG? and OH-) becomes more favorable in higher weight percentages of alcohol in
aqueous binary mixtures [17–19] and similar results are observed in this work.
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As previously reported [10], in a series of alcohol–water binary mixtures, at the same
mole fractions and temperatures, the rate constants of the MG? fading reaction at the low
mole ratios of alcohols change as follows:
kW\k2ꢀPrOH ꢃ kEtOH\k1ꢀPrOH ꢃ kPrD\kGl\kEG ꢄ kMeOH
ð1Þ
where kMeOH, kEG, kGl, kPrD, k1ꢀPrOH, kEtOH, k2ꢀPrOH and kW are the observed rate constants of
the MG? fading reaction in aqueous mixtures of methanol, ethylene glycol, glycerol, 1,2-pro-
panediol, 1-propanol, ethanol, 2-propanol and in water, respectively. Alcohols are hydrogen-
bond donating solvents and the observed trend in relation 1 is similar to the trend of changes
in hydrogen bond donor (a) and polarizability (p*) parameters of the alcohols [20]. This
shows that therole ofhydrogenbonding ininteraction between MG? andalcohol molecules is
similar to that previously reported for interaction of dyes with protic solvents [21, 22].
In high mole fractions of these alcohols, due to the high viscosity of ethylene glycol,
glycerol, and 1,2-propanediol, reaction rates change as follows:
kW\kGl\kPrD ꢄ kEG\k2ꢀPrOH ꢄ kEtOH\k1ꢀPrOH\kMeOH
3.2 Proposed Reaction Mechanism
ð2Þ
Data of Tables 1, 2, 3, 4 and 5 were analyzed by the SESMORTAC model. In the SE-
SMORTAC model [9], a range of solvent composition in which the equation of logarithm
of reaction rate constant, log10 k, versus reciprocal of dielectric constant of the solution,
Table 1 kobs and Ea values of MG? fading in water–ethanol (5 %)–ethylene glycol ternary solutions at
283–303 K
WEG
%
[EG]
[H2O]
kobs (Lꢁmol-1ꢁmin-1) at
Ea
(molꢁL-1
)
283 K
293 K
303 K
(kJꢁmol-1
)
0.0
2.5
0.000
0.397
0.790
1.024
1.261
1.582
2.381
3.192
4.002
4.695
6.497
7.348
8.212
9.084
9.957
10.832
11.713
50.398
49.236
47.735
47.359
46.310
45.748
42.920
40.873
35.824
35.971
30.065
26.180
25.128
20.864
17.864
17.159
14.244
40.01 2.45
58.69 3.02
86.45 3.88
102.07 – 1.23
109.75 2.62
113.80 2.69
133.30 – 2.45
131.38 2.66
132.83 2.34
130.80 1.39
133.85 – 1.43
140.52 2.08
152.06 5.52
164.21 8.58
174.76 2.13
193.43 2.78
206.75 2.96
76.43 1.98
121.03 2.79
165.96 2.18
196.25 – 1.04
213.58 3.02
233.09 2.98
275.45 – 10.91
274.75 5.41
275.12 7.28
277.43 9.22
278.82 – 4.90
308.30 6.36
338.69 14.57
364.21 6.49
384.53 3.85
434.53 1.26
483.32 3.91
151.05 6.71
234.76 4.36
307.42 3.59
353.11 – 4.51
378.80 8.68
409.88 10.02
454.40 3.76
485.14 – 5.65
481.09 11.77
484.70 10.42
531.12 – 10.25
575.98 26.14
640.29 8.56
706.16 7.77
738.26 10.24
818.19 14.62
894.46 16.99
47.3 2.0
49.4 1.0
45.2 0.9
44.3 2.8
44.2 1.4
45.7 2.4
43.8 3.9
46.6 2.7
45.9 2.7
46.8 3.2
49.1 1.3
54.1 2.5
51.3 2.6
52.0 2.0
51.4 2.1
51.5 2.8
52.3 3.9
5.0
6.5
8.0
10.0
15.0
20.0
25.0
30.0
40.0
45.0
50.0
55.0
60.0
65.0
70.0
In these series of experiments, the concentration of ethanol is 1.005 molꢁL-1 (& 5 %). kmc values are shown
in bold. Zones 1, 2, 3 and 4 are in the range of (0–6.5 %, 6.5–15 %, 20–30 % and 40–70 %) at 283 and
293 K and in the range of (0–6.5 %, 6.5–20 %, 20–30 % and 40–70 %) at 303 K, respectively
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155
Table 2 kobs and Ea values of MG? fading in water–ethanol (10 %)–ethylene glycol ternary solutions at
283–303 K
WEG
%
[EG]
[H2O]
kobs (Lꢁmol-1ꢁmin-1) at
Ea
(molꢁL-1
)
283 K
293 K
303 K
(kJꢁmol-1
)
0.0
1.5
0.000
0.238
0.392
0.548
0.793
1.022
1.579
1.978
2.378
3.193
3.999
4.822
6.501
7.345
8.202
9.075
9.940
10.834
47.120
46.791
45.856
45.666
44.746
44.047
42.573
41.526
40.327
37.455
35.334
32.797
27.131
24.575
22.115
19.271
16.973
13.794
51.12 1.08
100.85 2.98
126.52 7.47
159.93 1.45
176.37 – 4.99
184.75 2.90
207.55 2.94
244.87 3.93
280.94 1.58
292.00 – 1.20
296.28 3.15
296.67 7.57
297.39 5.83
341.09 – 6.95
366.46 5.56
404.24 4.01
432.31 6.39
466.96 9.99
506.28 2.73
195.08 7.10
272.99 7.20
299.21 6.52
335.78 – 8.85
358.61 12.41
381.27 6.73
456.81 13.93
523.00 – 3.97
524.61 7.87
521.94 3.09
522.66 4.10
545.50 – 3.49
640.24 21.70
706.92 8.86
755.86 20.66
812.24 23.55
891.51 29.31
951.04 19.46
47.7 1.1
47.2 5.4
45.2 1.2
44.9 1.7
45.2 2.3
44.6 1.0
47.6 1.3
48.5 1.8
48.4 3.0
47.9 3.5
48.8 4.0
50.0 3.0
53.1 3.8
53.3 2.8
51.9 3.3
51.4 2.9
51.2 2.2
48.5 1.4
72.45 1.32
84.25 2.34
95.26 – 1.59
2.5
3.5
5.0
100.83 2.36
109.22 1.33
120.22 1.72
134.09 – 1.91
135.1 1 2.33
136.50 3.98
133.23 1.71
134.43 2.07
144.67 – 2 .96
158.89 1.18
176.62 1.85
192.3 6 3.05
212.48 3.64
244.29 8.57
6.5
10.0
12.5
15.0
20.0
25.0
30.0
40.0
45.0
50.0
55.0
60.0
65.0
In these series of experiments, the concentration of ethanol is 1.980 molꢁL-1 (& 10 %). kmc values are
shown in bold. Zones 1, 2, 3 and 4 are in the range of (0–3.5 %, 3.5–12.5 %, 12.5–30 % and 40–65 %),
(0–3.5 %, 3.5–12.5 %, 15–30 % and 40–65 %) and (0–3.5 %, 3.5–12.5 %, 12.5–25 % and 30–65 %) at
283, 293 and 303 K, respectively
D
ꢀ1, is linear [23–27], is called a ‘‘zone’’ and a solvent composition in which a zone
finishes and another zone starts is called ‘‘mechanism change point’’ (or abbreviated as mc
point). Considerating a mechanism on the basis of point charge on a dielectric continuum
suggests that plots of log10 k against Dꢀ1, should be linear. The failure of the simple
electrostatic interpretation shows the importance of hydrogen bonding and other non-
electrostatic medium effects in controlling the reactivity of the substrates [26–28].
In the SESMORTAC model, variations in the mechanism are followed through the
study of changes in the microenvironment (or solvent cage) of the activated complex.
Dielectric constants of the aqueous ethanol and ethylene glycol binary solutions were
˚
obtained from the work of Akerlof [29].
In this reaction, the solvent is not a reactant. Thus, according to the SESMORTAC
model, this reaction is of type I. If in the presence of an organic solvent the reaction rate
increases, the proposed mechanism for reaction in these solutions involves two kinds of
mechanisms. The first mechanism occurs in a pure solvent (for example water). This
mechanism can be written as follows:
k10
k20
ꢂꢀ
ꢁꢃ
¼
cage
½ðMGþ þ OHꢀÞꢅcage
ꢀ
MGdþ ꢀ OHdꢀ
ꢀ! Product
ð3Þ
kꢀ0 1
AC
where AC is an abbreviation for activated complex and k10 , kꢀ0 1 and k20 are the fundamental
rate constants of the MG? fading reaction in the pure solvent and we cannot determine
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Table 3 kobs and Ea values of MG? fading in water–ethanol (15 %)–ethylene glycol ternary solutions at
283–303 K
WEG
%
[EG]
[H2O]
kobs (Lꢁmol-1ꢁmin-1) at
Ea
(molꢁL-1
)
283 K
293 K
303 K
(kJꢁmol-1
)
0.0
2.5
0.000
0.392
0.794
1.426
1.573
1.975
2.373
3.183
3.998
4.823
6.066
6.494
7.345
8.205
9.073
44.415
43.508
42.322
40.434
39.652
38.528
37.505
35.186
32.349
29.837
26.294
24.796
21.803
19.198
16.898
80.13 1.79
90.33 1.52
107.87 2.62
122.44 1.49
130.56 – 1.84
135.36 1.21
138.04 2.52
145.87 2.39
152.03 1.68
158.39 2.78
164.85 – 3.30
182.07 4.70
199.75 2.58
216.17 2.73
231.75 10.92
141.50 2.17
173.76 2.79
205.31 7.25
251.78 1.93
269.36 2.50
292.09 – 4.00
301.92 7.27
319.79 3.02
327.07 7.49
340.51 6.25
351.46 – 16.89
392.59 5.98
431.25 3.10
483.78 4.59
537.36 8.38
273.57 3.76
325.37 4.28
385.57 7.47
468.68 7.99
488.35 5.37
534.69 – 9.76
556.66 2.71
612.17 7.98
629.96 18.58
660.56 5.03
707.19 – 9.05
779.50 23.19
863.69 15.87
990.14 14.39
1091.56 20.99
43.7 2.9
45.7 1.0
45.4 1.1
47.9 1.5
47.1 2.0
49.0 2.6
49.8 2.7
51.2 2.1
50.7 1.6
50.9 1.5
51.9 1.1
51.9 1.2
52.2 1.1
54.3 1.3
55.3 2.0
5.0
9.0
10.0
12.5
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
55.0
In these series of experiments, the concentration of ethanol is 2.93 molꢁL-1 (& 15 %). kmc values are shown
in bold. Zones 1, 2 and 3 are in the range of (0–10 %, 10–35 % and 35–55 % at 283 K and 0–10 %,
12.5–35 % and 35–55 %) at 293 and 303 K, respectively
Table 4 kobs and Ea values of MG? fading in water–ethanol (20 %)–ethylene glycol ternary solutions at
283–303 K
WEG
%
[EG]
[H2O]
kobs (Lꢁmol-1ꢁmin-1) at
Ea
(molꢁL-1
)
283 K
293 K
303 K
(kJꢁmol-1
)
0.0
5.0
0.000
0.804
1.571
1.985
2.389
3.191
4.003
4.828
5.646
6.497
7.374
8.202
9.115
41.830
39.216
36.942
35.467
34.379
32.041
29.457
26.793
23.345
21.475
18.903
16.316
13.046
89.53 2.22
117.00 2.59
144.80 2.54
154.40 – 3.73
158.22 3.83
167.31 1.77
170.50 2.47
182.19 2.41
190.57 3.12
200.70 – 1.76
230.50 2.49
261.80 1.59
299.35 8.12
176.39 8.37
232.52 3.69
294.64 1.33
320.97 – 5.49
330.20 7.06
353.05 7.23
383.92 6.71
409.07 14.46
439.39 4.36
472.86 – 10.59
513.47 15.29
587.39 3.44
666.78 14.81
310.00 4.48
440.60 10.79
550.56 7.04
603.30 – 2.17
639.38 8.17
659.70 13.89
752.40 18.08
807.80 15.70
865.53 11.37
928.85 – 19.28
1071.71 15.51
1210.00 17.75
1345.09 12.51
44.3 1.7
47.3 0.9
47.6 1.2
48.6 1.5
49.8 1.1
48.9 1.8
53.0 2.1
53.1 1.9
54.0 2.4
54.7 2.9
54.8 1.1
54.6 1.3
53.6 1.4
10.0
12.5
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
55.0
In these series of experiments, the concentration of ethanol is 3.86 molꢁL-1 (& 20 %). kmc values are shown
in bold. At all temperatures, zones 1, 2 and 3 are in the range of (0–12.5 %, 12.5–40 and 40–55 %),
respectively
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Table 5 kobs and Ea values of MG? fading in water–ethanol (25 %)–ethylene glycol ternary solutions at
283–303 K
WEG
%
[EG]
[H2O]
kobs (Lꢁmol-1ꢁmin-1) at
Ea
(molꢁL-1
)
283 K
293 K
303 K
389.03 2.36
(kJꢁmol-1
)
0.0
1.5
0.000
0.237
0.395
0.549
0.799
1.024
1.565
1.982
2.375
3.184
4.004
4.822
5.648
6.496
7.349
8.213
38.539
38.515
37.365
37.192
36.365
35.377
33.755
32.635
31.394
29.288
26.714
23.673
21.924
18.433
15.896
13.156
95.19 1.31
110.60 2.33
123.79 1.96
130.32 2.23
139.15 – 1.24
145.03 1.96
156.04 2.31
160.12 3.28
165.90 2.70
181.20 1.28
201.78 4.01
212.86 1.54
236.06 14.22
252.78 16.47
286.13 7.44
304.86 8.04
200.65 1.27
219.29 2.17
242.42 8.06
263.10 8.99
293.95 – 4.52
305.71 2.28
333.59 5.96
350.99 4.63
363.18 7.81
397.80 6.46
428.74 4.26
479.69 12.32
547.52 6.85
605.69 3.11
670.14 6.14
731.30 15.85
50.2 1.2
47.5 1.0
47.1 1.0
47.9 1.0
48.6 2.0
49.4 1.6
50.1 1.7
52.4 1.4
52.2 1.5
52.4 1.5
52.4 1.1
54.6 1.4
55.1 2.1
54.6 3.6
54.0 3.0
55.3 3.2
418.80 3.59
463.96 5.21
500.14 4.92
544.16 7.88
579.44 – 3.94
635.50 9.08
695.04 6.16
716.66 4.43
787.99 6.79
877.17 10.24
983.90 8.20
1106.7 1 15.29
1168.62 18.61
1300.34 34.97
1436.07 48.38
2.5
3.5
5.0
6.5
10.0
12.5
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
In these series of experiments, the concentration of ethanol is 4.93 molꢁL-1 (& 25 %). kmc values are shown
in bold. Zones 1 and 2 are in the range of (0–5 % and 5–50 %) at 283 and 293 K and in the range of
(0–6.5 % and 6.5–50 %) at 303 K, respectively
800
600
400
200
0
0.0
0.1
0.2
0.3
0.4
0.5
Mole fraction of EG
Fig. 3 kobs values of MG? fading reaction versus mole fractions of ethylene glycol in ternary mixtures of
water–ethanol–ethylene glycol under alkaline conditions at 293 K. Weight percentages of ethanol in these
solutions are: filled diamond, 5 %; open square, 10 %; open triangle, 15 %; open diamond, 20 % and
?25 %
them. But, in these series of ethanol–water binary mixtures there is an mc point. The
reaction proceeds according to the second mechanism and the related rate equation, v1, is
written as follows:
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J Solution Chem (2013) 42:151–164
800
600
400
200
0
ACSM2 & ACSM3
ACSMbm
&
ACSM1 & ACSM2
ACSM1
mc2
mc1
bm
10
0
20
30
40
50
60
WEG%
Fig. 4 Typical representation of the SEEMORTAC model for ethanol–ethylene glycol–water ternary
mixtures involving a constant weight percentage of ethanol
v1 ¼ kbm½MGþꢅ½OHꢀꢅ
ð4Þ
where kbm is the observed rate constant in the ethanol–water binary solution. Thus, at this
point rather than AC an ACSM forms. ACSM is an abbreviation for ‘‘Activated Complex
formed in the Second Mechanism’’. This ACSM is called ACSMbm which is an abbrevi-
ation for ‘‘ACSM formed in binary mixture’’, Fig. 4.
Adding an organic solvent to a solvent (for example ethanol to water) or a binary
mixture (for example ethylene glycol to aqueous ethanol) involving reactants results in
formation of ACSM and affects the reaction rate. The mechanism of the reaction in these
mixed solvents is written as follows:
"
#
¼
k1
ꢀ
where ethanol molecules in water–ethanol solvents or ethylene glycol molecules in water–
ꢁ
k2
½ðMGþ þ OHꢀÞnH2Oꢅcage þ nS ꢁ MGdþꢀOHdꢀ nS
þ nH2O ꢀ! Product ð5Þ
k
ꢀ1
ACSM
cage
ethanol–ethylene glycol ternary mixtures are shown by S and k1, k and k2 are the
ꢀ1
fundamental rate constants of MG? fading reaction in these solvents. The solvent cage is
the microenvironment of the MGd?–OHd- contact pair and, in each zone, n molecules of
water can be replaced by n molecules of ethylene glycol. Here, two processes occur
simultaneously, chemical reaction between MG? and OH- (first-order in contact ion) and
replacement of n water molecules of ACSM microenvironment by n ethylene glycol
molecules of its surrounding (n order in solvent molecules). As seen in Table 6, the values
of n are different in each zone.
In each ternary mixture, the structure of the ACSM depends on the structure of solvent
cage. Dielectric constant values of alcohols are less than that of water and when ACSM
forms in each zone, n molecules of water existing in the solvent cage are replaced by n
molecules of ethylene glycol from its surrounding that decreases dielectric constant of the
microenvironment of (MGd?–OHd-) in ACSM while the formation of neutral product,
MGOH, becomes more favorable and results in an increase in the rate of the fading
reaction. In the first zone, an increase in ethylene glycol weight percentage increases the
concentration ACSM formed in this zone (shown as ACSM1) and decreases the
123

J Solution Chem (2013) 42:151–164
159
123

160
J Solution Chem (2013) 42:151–164
concentration of ACSMbm, and finally at mc1 only ACSM1 forms. A similar situation
occurs in the second zone and with increasing ethylene glycol weight percentage, the
concentration of ACSM1 decreases and the concentration of ACSM2 (ACSM formed in the
second zone) increases, Fig. 4. In the first zone, assuming that a steady-state concentration
of ACSM1 is reached in the ternary mixtures, we have:
n
k11½MGþꢅ½OHꢀꢅ½Sꢅ
ꢀ
ꢁ
½ACSM1ꢅ ¼
ð6Þ
n
kꢀ1 1 ½H2Oꢅbm ꢀ ½H2Oꢅ þ k21
where ½H2Oꢅbm is the concentration of water in the ethanol–water binary solution and k11,
kꢀ1 1 and k21 are the fundamental rate constants of the MG? fading reaction in the first zone.
The effect of ethylene glycol molecules on the reaction rate equation in the first zone,
v2, is as follows:
n
k11k21½MGþꢅ½OHꢀꢅ½Sꢅ
v2 ¼ k21½ACSM1ꢅ ¼
ð7Þ
n
kꢀ1 1ð½H2Oꢅbm ꢀ ½H2OꢅÞ þ k21
and the equation of reaction rate in ternary mixtures, v, is:
ꢄ
ꢅ
n
k11k21½Sꢅ
v ¼ v1 þ v2 ¼ kobs½MGþꢅ½OHꢀꢅ ¼ kbm
þ
½MGþꢅ½OHꢀꢅ
n
kꢀ1 1ð½H2Oꢅbm ꢀ ½H2OꢅÞ þ k21
ð8Þ
ð9Þ
n
k11k21½Sꢅ
where
kobs ¼ kbm þ
n
kꢀ1 1ð½H2Oꢅbm ꢀ ½H2OꢅÞ þ k21
In the second zone, v1 ¼ kmc1½MGþꢅ½OHꢀꢅ and Eq. 7 is replaced by:
ꢀ
ꢁ
n
k12k22½MGþꢅ½OHꢀꢅ ½Sꢅ ꢀ ½Sꢅmc1
v2 ¼ k22½ACSM2ꢅ ¼
ð10Þ
ꢀ
ꢁ
n
kꢀ2 1 ½H2Oꢅmc1 ꢀ ½H2Oꢅ þk22
In this zone, Eq. 9 is replaced by:
ꢀ
ꢁ
n
k12k22 ½Sꢅ ꢀ ½Sꢅmc1
ꢀ
ꢁ
kobs ¼ kmc1
þ
ð11Þ
ð12Þ
n
kꢀ2 1 ½H2Oꢅmc1 ꢀ ½H2Oꢅ þ k22
n
k11k21½Sꢅmc1
where
kmc1 ¼ kbm
þ
n
kꢀ1 1ð½H2Oꢅbm ꢀ ½H2Oꢅmc1Þ þ k21
where ½Sꢅmc1 and ½H2Oꢅmc1 are the concentrations of ethylene glycol and water in mc1
point, respectively and kmc1 is the rate constant in mc1 point. k12, kꢀ2 1 and k22 are the
fundamental rate constants of MG? fading reaction in the second zone. In the third and
fourth zones,
v1 ¼ kmcðiꢀ1Þ½MGþꢅ½OHꢀꢅ and Eq. 7 is replaced by:
ꢆ
ꢇ
n
k1i k2i ½MGþꢅ½OHꢀꢅ ½Sꢅ ꢀ ½Sꢅmcðiꢀ1Þ
kꢀi 1 ½H2Oꢅmcðiꢀ1Þ ꢀ ½H2Oꢅ þ k2i
v2 ¼ k2i ½ACSMiꢅ ¼
ð13Þ
ꢆ
ꢇ
n
and Eq. 9 is replaced by:
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J Solution Chem (2013) 42:151–164
161
ð14Þ
ð15Þ
ꢆ
ꢇ
n
k1i k2i ½Sꢅ ꢀ ½Sꢅmcðiꢀ1Þ
ꢆ
ꢇ
kobs ¼ kmcðiꢀ1Þ þ
n
kꢀi 1 ½H2Oꢅmcðiꢀ1Þ ꢀ ½H2Oꢅ þ k2i
k1iꢀ1k2iꢀ1ð½Sꢅmcðiꢀ1Þ ꢀ ½Sꢅmcðiꢀ2ÞÞ
n
where kmcðiꢀ1Þ ¼ kmcðiꢀ2Þ þ
n
iꢀ1
k
ð½H2Oꢅmcðiꢀ2Þ ꢀ ½H2Oꢅmcðiꢀ1ÞÞ þ k2iꢀ1
ꢀ1
kmcðiꢀ1Þ is the rate constant at the mciꢀ1 point, ACSMi is the ACSM formed in the ith zone
and k1i , kꢀi 1 and k2i are the fundamental rate constants of the MG? fading reaction in the ith
zone. In this reaction, kobs in the third zone of 5 and 10 % ethanol is approximately
constant, kobs ¼ kmc2
.
It has been shown that k1 values in each zone obey the Arrhenius equation [9] and the
related activation energy, Eaðk1Þ, values are given in Table 6. The observed rate constants
in the first, second, third and fourth zones were fitted suitably with Eqs. 9, 11 and 14 and
the results are given in Table 6. It was observed that at constant concentration of ethanol
and variable concentrations of ethylene glycol, with increasing temperature the k1 values
increase whereas the k2 values decrease, Table 6. Ethylene glycol has two hydroxyl groups
and its viscosity is more than ethanol’s [30] and thus the fundamental rate constants of
MG? fading in ethylene glycol binary mixtures are different from those of ethanol–water
binary mixtures [10] (Table 6). It is found that in the ethylene glycol concentration range
used, with increasing ethanol concentration, the number of zones of water–ethanol–
ethylene glycol solutions decreases from four to two (Tables 1, 2, 3, 4, 5) and the trend of
variation of kobs values becomes more similar to those of ethanol–water binary mixtures.
In 5 and 10 % ethanol, the reaction rate remains constant in the third zone and in the
fourth zone. It seems that there is a competition between the increase in viscosity of the
solution and the interaction between ethylene glycol and MG?. Due to the presence of
ethanol in the process of ACSM formation, the reaction is zone-three in 15 and 20 %
ethanol and is zone-two in 25 % ethanol (Tables 1, 2, 3, 4, 5). Comparison of rate con-
stants of MG? fading in low concentrations of ethylene glycol, zones 1 and 2 in 5–20 %
ethanol and zone 1 in 25 % ethanol (Tables 1, 2, 3, 4, 5), to those in ethanol–water and
ethylene glycol–water binary mixtures shows [10] that
k1EG [ k1ter [ k1EtOH; nEG\nter\nEtOHðin the most casesÞ; k2EG\k2ter\k2EtOH
ð16Þ
where superscripts EG, EtOH and ter are used for n, k1 and k2 values in binary mixtures of
ethylene glycol–water, ethanol–water and ternary mixtures of water–ethanol–ethylene
glycol solutions, respectively. k1 values in relation (16) show that formation of ACSM in
ethylene glycol–water binary mixtures is more favorable than its formation in these ternary
mixtures. It seems that in low concentrations of ethylene glycol, hydrogen bonding
between ethanol and ethylene glycol molecules competes with interactions of ethylene
glycol molecules with MG? molecules.
In higher concentrations of ethylene glycol, zone 4 in 5 and 10 % ethanol, zone 3 in 15
and 20 % ethanol and zone 2 in 25 % ethanol, the k1 and k2 values become greater and the
n values become lesser than those in water–ethanol or water-ethylene glycol binary
solutions [10] and formation of ACSM in these ternary mixtures is more favorable than its
formation in ethylene glycol–water binary mixtures. It seems that with increasing weight
percentage of ethanol, its concentration in the microenvironment of ACSM increases and
acts as a solvent for better dissolution of ethylene glycol molecules in ACSM.
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J Solution Chem (2013) 42:151–164
600
500
400
300
200
100
0
0
100
200
300
400
500
600
700
kter (L mol-1 min-1)
Fig. 5 Sum of the MG? fading rate constants in ethanol–water and ethylene glycol–water binary mixtures
versus the observed rate constants in ternary water–ethanol–ethylene glycol mixtures containing: filled
diamond, 10 %; and open square, 20 % ethanol and different weight percentages of ethylene glycol at 293 K
-70
-60
-50
-40
-30
-20
-10
0
0
10
20
30
40
50
60
70
80
WEG
%
Fig. 6 DS values of the MG? fading reaction versus weight percentages of ethylene glycol in ternary
mixtures of water–ethanol–ethylene glycol under alkaline conditions. Weight percentages of ethanol in these
solutions are: filled diamond, 5 %; open square, 10 %; open triangle, 15 %; open diamond, 20 % and ?25 %
¼
To confirm these results, the sum of MG? fading rate constants in ethanol–water [10]
(kEtOH) and ethylene glycol–water (kEG) binary mixtures are greater than the observed rate
constants in ternary water–ethanol–ethylene glycol mixtures (kter) containing similar eth-
anol and ethylene glycol weight percentages in low concentrations of ethylene glycol, and
are less than those values in high concentrations of ethylene glycol, respectively (Fig. 5).
¼
¼
As seen in Figs. 6 and 7, the DS and DH values of the fading reaction are negative and
positive, respectively, which is due to dissolution of ethylene glycol molecules in the solvent
cage and hydrogen binding and hydrophobic interactions [31] between MG? and ethylene
glycol molecules when ACSM forms, and the formation of ACSM is enthalpy driven.
As shown experimentally, dissolution of hydrocarbons in water is exothermic and
results in a more ordered structure of water around the dissolved hydrocarbon molecules
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J Solution Chem (2013) 42:151–164
163
55
50
45
40
0
20
40
60
80
WEG
%
Fig. 7 DH values of the MG? fading reaction versus weight percentages of ethylene glycol in ternary
mixtures of water–ethanol–ethylene glycol under alkaline conditions. Weight percentages of ethanol in these
solutions are: filled diamond, 5 %; open square, 10 %; open triangle, 15 %; open diamond, 20 % and ?25 %
¼
[32]. Due to hydrophobic interaction between hydrocarbon molecules, fewer water mol-
ecules are in direct contact with them. Thus, the ordering influence of the hydrophobic
molecules will be decreased and the entropy decreases and thermal energy is required for
the destructuring of the hydration shells around hydrocarbon molecules [32]. Also, dis-
solution of ethylene glycol in water is exothermic and increases the entropy of reaction.
¼
¼
Therefore, with increase in ethylene glycol concentration the DS and DH values become
less negative and more positive, respectively.
4 Conclusions
The rate constant of the MG? fading reaction increases in ternary mixtures of water–
ethanol–ethylene glycol. The fundamental rate constants of MG? fading reaction in the
used ternary solvent systems are obtained by the SESMORTAC model. It was observed
that, at constant concentration of ethanol and variable concentrations of ethylene glycol,
with increasing temperature, the k1 values increase. The results show that formation of
ACSM in these ternary mixtures is more favorable than its formation in the related
alcohol–water binary mixtures. Analysis of the k1 and k2 values shows that, at low con-
centrations of ethylene glycol, interaction of ethanol and ethylene glycol affects the
reaction rate and in high concentrations of ethylene glycol, ethanol acts as a solvent for
ethylene glycol molecules. Hydrogen bonding and then hydrophobic interactions between
MG? and alcohol molecules, result in an increase in the observed reaction rates.
References
1. Abraham, M.H.: Solvent effects on reaction rates. Pure Appl. Chem. 57, 1055–1064 (1985)
2. Um, I.H., Park, Y.M., Shin, E.H.: The effect of solvent on reaction rates and equilibria for the reactions
of p-nitrophenyl acetate with alicyclic secondary amines in H2O and DMSO. Bull. Korean Chem. Soc.
20, 392–394 (1999)
3. Um, I.H., Shin, E.H., Kwon, D.S.: The effect of solvent on reactions of p-nitrophenyl acetate with
alicyclic secondary amines and with anionic nucleophiles in MeCN–H2O mixtures of varying com-
positions. Bull. Korean Chem. Soc. 17, 234–239 (1996)
123

164
J Solution Chem (2013) 42:151–164
4. Mora-Diez, N., Keller, S., Alvarez-Idaboy, J.R.: The Baeyer–Villiger reaction: Solvent effects on
reaction mechanisms. Org. Biomol. Chem. 7, 3682–3690 (2009)
5. Hazarika, S., Goswami, P., Dutta, N.N.: Lipase catalysed ttransesterification of 2-o-benzylglycerol with
vinyl acetate: Solvent effect. Chem. Eng. J. 94, 1–10 (2003)
6. Gregory, P.: Dye and dye intermediates. In: Kroschwitz, J.I. (ed.) Encyclopedia of Chemical Tech-
nology, vol. 8, p. 544. Wiley, Indianapolis (1993)
7. Duxbury, D.F.: The photochemistry and photophysics of triphenylmethane dyes in solid and liquid
media. Chem. Rev. 93, 381–433 (1993)
8. http://en.wikipedia.org/wiki/malachite_green (23 October 2012)
9. Samiey, B., Alizadeh, K., Mousavi, M.F., Alizadeh, N.: Study of kinetics of bromophenol blue fading in
alcohol–water binary mixtures by SESMORTAC model. Bull. Korean Chem. Soc. 26, 384–392 (2005)
10. Samiey, B., Raoof Toosi, A.: Kinetics of malachite green fading in alcohol–water binary mixtures. Int.
J. Chem. Kinet. 42, 508–518 (2010)
11. Ritchie, C.D.: Cation–anion combination reactions. XIII.c of the reactions of nucleophiles with esters.
J. Am. Chem. Soc. 97, 1170–1179 (1975)
12. Ritchie, C.D., Wright, D.J., Huang, D.S., Kamego, A.A.: Cation–anion combination reaction. XII.
Rates, equilibriums, and activation parameters for reactions of triarylmethyl cations in aqueous solution.
J. Am. Chem. Soc. 97, 1163–1170 (1975)
13. Caetano, W., Tabak, M.: Interaction of chlorpromazine and trifluoperazine with anionic sodium dodecyl
sulfate (SDS) micelles: Electronic absorption and fluorescence studies. J. Colloid Interface Sci. 225,
69–81 (2000)
14. Hughes, E.D.: Mechanism and kinetics of substitution at a saturated carbon atom. Trans. Faraday Soc.
37, 603–631 (1941)
15. Ingold, C.K.: Structure and Mechanism in Organic Chemistry. Bell, London (1993)
16. Burton, C.A.: Nucleophilic Substitution at a Saturated Carbon Atom. Elsevier, London (1963)
17. Wyman, J.: Dielectric constants: ethanol–diethyl ether and urea–water solutions between 0 and 50.
J. Am. Chem. Soc. 55, 4116–4121 (1933)
18. Bhattacharya, A., Das, A.K., Kundu, K.K.: Determination of absolute transfer free energies of hydroxyl
ion from water to aqueous 2-methoxy ethanol. Can. J. Chem. 59, 1153–1159 (1981)
19. Datta, J., Kundu, K.K.: Thermodynamics of autoionization of aqueous tetrahydrofuran and 1,2-dime-
thoxyethane and the structuredness of solvents. Can. J. Chem. 59, 3141–3148 (1981)
20. Marcus, Y.: The Properties of Solvents. Wiley (1999)
21. Rauf, M.A., Soliman, A.A., Khattab, M.: Solvent effect on the spectral properties of neutral red. Chem.
Cent. J. 2, 19–27 (2008)
22. Fita, P., Fedoseeva, M., Vauthey, E.: Ultrafast excited-state dynamics of eosin B: A potential probe of
the hydrogen-bonding properties of the environment. J. Phys. Chem. A 115, 2465–2470 (2011)
23. Reichardt, C.: Solvents and Solvent Effects in Organic Chemistry. 2nd edn., pp. 189–207. VCH Pub-
lishers (1998)
24. Zaghloul, A.A.: Solvent effects on the kinetics of aquation of j-chloro(diethylenetriamine) (ethylene-
diamine)cobalt(III) ion in mixed aqueous solvents. Int. J. Chem. Kinet. 29, 431–436 (1997)
25. Ismail, A.M., Zaghloul, A.A.: Kinetics and mechanism of isatin ring opening in aqueous binary mix-
tures of methanol and acetonitrile cosolvents. Int. J. Chem. Kinet. 30, 463–469 (1998)
26. El-Subruiti, G.M.: Medium effects on the initial and the transition states upon the solvolysis of trans-
dichlorobis(N-methyl-ethylenediamine)cobalt(III) complex in water–mixed solvents. Int. J. Chem.
Kinet. 34, 495–499 (2002)
27. El-Subruiti, G.M., Chehata, A.K., Massoud, S.S.: Influence of the solvent structure on the aquation of
j-chloro(diethylenetriamine)(ethylenediamine) cobalt(III) ion in water and mixed aqueous solvents. Int.
J. Chem. Kinet. 34, 1–6 (2002)
28. Laidler, K.J., Landskroener, P.A.: The influence of the solvent on reaction rates. Trans. Faraday Soc. 52,
200–210 (1956)
˚
29. Akerlof, G.: Dielectric constants of some organic solvent–water mixtures at various temperatures.
J. Am. Chem. Soc. 54, 4125–4139 (1932)
30. CRC Handbook of Chemistry and Physics. In: Lide, D.L. (ed), 87th edn., Section 6, pp. 175–176. CRC
Press/Taylor and Francis, Boca Raton, FL (2006)
31. Matulis, D.: Thermodynamics of the hydrophobic effect. III. Condensation and aggregation of alkanes,
alcohols, and alkylamines. Biophys. Chem. 93, 67–82 (2001)
32. Reichardt, C.: Solvents and Solvent Effects in Organic Chemistry. 2nd edn., pp. 25–26. VCH Publishers
(1998)
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