Due to the richness of the collected (\(\stackrel{-}{\text{n}}\)) data in this article, a chosen simple examples are summarized in Tables (2–4).
Table (2): \(\stackrel{-}{\text{n}}\) data for the UO22+ complex with phenylglycine at 25 ºC and µ = 0.15.
pH
|
\(\stackrel{-}{\text{n}}\)
|
[H2L+]
|
[HL]
|
[L−]
|
4.38
4.91
5.10
5.26
5.45
|
0.07
0.40
0.61
0.83
1.05
|
2.57 x 10− 4
1.28x 10− 4
9.13 x 10− 5
6.70 x 10− 5
4.54 x 10− 5
|
4.17 x 10− 4
7.04x 10− 4
7.78 x 10− 4
8.25 x 10− 4
8.66 x 10− 4
|
4.47 x 10− 9
2.56 x 10− 8
4.38 x 10− 8
6.71 x 10− 8
1.09 x 10− 7
|
Table (3): \(\stackrel{-}{\text{n}}\)data for La3+ complex with phenylglycine at 25 ºC and µ = 0.15.
pH
|
\(\stackrel{-}{\text{n}}\)
|
[H2L+]
|
[HL]
|
[L−]
|
8.65
9.63
9.66
|
0.04
0.41
0.51
|
3.25 x 10− 8
3.44 x 10− 9
3.21 x 10− 9
|
9.82 x 10− 4
9.92 x 10− 4
9.91 x 10− 4
|
1.96 x 10− 4
1.89 x 10− 3
2.03 x 10− 3
|
Table (4):
\(\stackrel{-}{\text{n}}\) data for Zr
4+ complex with phenylglycine at 25 ºC and µ = 0.15.
pH
|
\(\stackrel{-}{\text{n}}\)
|
[H2L+]
|
[HL]
|
[L−]
|
3.60
3.92
4.21
5.19
5.77
|
0.13
0.49
0.63
0.84
1.03
|
2.89 x 10− 4
3.20 x 10− 4
2.89 x 10− 4
7.67 x 10− 5
2.29 x 10− 5
|
7.78 x 10− 5
1.80 x 10− 4
3.17 x 10− 4
8.04 x 10− 4
9.14 x 10− 4
|
1.39 x 10− 10
6.70 x 10− 10
2.30 x 10− 9
5.57 x 10− 8
2.41 x 10− 7
|
Inspecting these data in Tables (2–4), we observed that at low pH range (4.38 ≤ pH ≤ 4.91 for UO22+ and 3.60 ≤ pH ≤ 3.92 for Zr4+complexes), H2L+ has only weak interactions as it is shown from the very low \(\stackrel{-}{\text{n}}\)values (less than 0.5). At high pH values (4.91 < pH ≤ 5.45 for UO22+, 9.63 < pH ≤ 9.66 for La3+ and 3.92 < pH ≤ 5.77 for Zr4+), the concentration of HL is high and seem to be constant, while the concentration of L− increased and H2L+ concentration decreased. In this pH region, we note that 0.5<\(\stackrel{-}{\text{n}}\)≤ 1.05 (i.e. 1:1 complexes were formed).
Since complex formation is observed as pH increases and insoluble precipitates are formed, then the titrations were stopped. At high pH values, no chance for complexes can be formed due to the precipitation of the hydroxide. The stoichiometric and thermodynamic stability constants are tabulated in Tables (5 and 6).
Table (5): Stability constants of MZ+ - phenylglycine complexes according to the reaction scheme I and scheme II.
Metal ion
|
µ
|
Log K110(Scheme I)
|
Log K111 (Scheme II)
|
25ºC
|
35ºC
|
45ºC
|
25ºC
|
35ºC
|
45ºC
|
UO22+
|
0.05
0.10
0.15
|
7.13
7.23
7.22
|
7.52
7.48
7.31
|
7.75
7.71
7.70
|
-2.03
-2.06
-2.01
|
-1.76
-1.74
-1.84
|
-1.52
-1.50
-1.45
|
La3+
|
0.05
0.10
0.15
|
3.44
2.92
2.47
|
4.28
3.94
3.48
|
5.00
4.70
4.37
|
-5.94
-6.37
-6.76
|
-5.00
-5.27
-5.66
|
-4.27
-4.51
-4.78
|
Zr4+
|
0.05
0.10
0.15
|
10.14
9.67
9.74
|
9.95
9.75
9.68
|
9.77
9.73
9.62
|
0.76
0.38
-0.09
|
0.67
0.43
-0.06
|
0.51
0.52
0.48
|
Table (6): Thermodynamic stability constants of
MZ+- phenylglycine complexes.
Metal ion
|
Log Kº110(Scheme I)
|
Log Kº111(Scheme II)
|
25ºC
|
35ºC
|
45ºC
|
25ºC
|
35ºC
|
45ºC
|
UO22+
La3+
Zr4+
|
7.10
3.91
10.25
|
7.65
4.70
10.06
|
7.78
5.52
9.86
|
-2.05
-5.54
1.08
|
-1.70
-4.65
1.00
|
-1.56
-4.01
0.53
|
From Tables 5 and 6, we can observe that logK110 >>> logK111. The suggested equations were to get an idea about the difference between the two suggested reactions of the metal ion with L− and HL:
ΔlogKº= log Kº110 (reaction I) - log Kº111 (reaction II) (2)
ΔΔGº= ΔGº(reaction I) - ΔGº(reaction II) (3)
ΔΔHº= ΔHº(reaction I) - ΔHº(reaction II) (4)
ΔΔSº= ΔSº(reaction I) - ΔSº(reaction II) (5)
Tables (7 and 8) illustrate the standard thermodynamic parameters ΔGº, ΔHº and ΔSº (as well as the differences of the thermodynamic parameters ΔlogK1º, ΔΔGº, ΔΔHº and ΔΔSº) for all possible complexation processes.
Table (7): Standard thermodynamic parameters of MZ+-phenylglycine complexes
Metal ion
|
T (ºC)
|
Reaction with L−(Scheme I)
|
Reaction with HL(Scheme II)
|
-ΔGº
(KJ/mole)
|
ΔHº
(KJ/mole)
|
ΔSº
(J/deg. mole)
|
ΔGº
(KJ/mole)
|
ΔHº
(KJ/mole)
|
ΔSº
(J/deg. mole)
|
UO22+
|
25
35
45
|
40.51
45.12
47.37
|
62.08
|
344.26
348.05
344.18
|
11.70
10.03
9.50
|
44.64
|
110.54
112.37
110.50
|
La3+
|
25
35
45
|
22.31
27.72
32.39
|
128.04
|
504.53
505.71
504.50
|
31.61
27.42
24.42
|
139.00
|
360.37
362.27
360.32
|
Zr4+
|
25
35
45
|
58.48
59.33
60.04
|
-35.36
|
77.58
77.83
77.61
|
-6.16
-5.90
-3.23
|
-49.50
|
-145.44
-141.56
-145.50
|
Table (8): The difference of thermodynamic parameters for M
Z+-phenylglycine complexes
MZ+
|
T (ºC)
|
Δ logKº
|
-ΔΔGº
(KJ/mole)
|
ΔΔHº
(KJ/mole)
|
ΔΔSº
(J/ deg. mole)
|
UO22+
|
25
35
45
|
9.15
9.35
9.34
|
52.21
55.15
56.87
|
17.44
|
233.72
235.68
233.68
|
La3+
|
25
35
45
|
9.45
9.35
9.53
|
53.92
55.14
56.81
|
-10.96
|
144.16
143.44
144.18
|
Zr4+
|
25
35
45
|
9.16
9.06
9.33
|
52.32
53.43
56.81
|
14.14
|
233.02
219.39
223.11
|
The high negative ΔGº values for reaction of the metal ion with L−(Scheme I) indicate that these complexation processes are spontaneous, while the complexation processes for reaction of the metal ion with HL (Scheme II) are nonspontaneous due to their positive ΔGº values [with exception of complexation of Zr4+ which characterized by its negative ΔHº values (i.e. have exothermic nature), therefore, it can be described asenthalpy favored processes] [9]. The differences of the thermodynamic parameters ΔlogK1º, ΔΔGº, ΔΔHº and ΔΔSº indicate that the most predominant reaction is the reaction of the metal ion with L−.
Although L− reacting species have a lower concentration than HL reacting species in most cases [see Table (2–4)], we can interpret the high spontaneity of reaction of the metal ion with L− due to the electrostatic attraction between the two opposite charged reactants according to the following Eq. (6) which supported with the high ΔlogK1º values.
$${\text{M}}^{\text{z}+ }+{\text{L}}^{-}\underleftrightarrow{{K}_{110}}{\text{M}\text{L}}^{\text{z}-1}$$
6
Inspecting ΔSº values, we found that ΔSº values were positive (with exception of some cases in reaction of the metal ion with HL such as the complexation of Zr4+ which have negative ΔSº values). The high positive ΔΔSº values indicate that the standard entropy changes for reaction of the metal ion with L− were higher than those for reaction of the metal ion with HL in all cases under study. This reflects the more spontaneity of reaction of the metal ion with L−. Therefore, the high negative ΔGº values for reaction of the metal ion with L− is attributed to the higher contribution of ΔSº term which indicate that these complexation processes are entropy favored processes. This conclusion was supported by the positive ΔΔSº.
In order that, we shall direct our attention to reaction of the metal ion with L− to determine another factor that control the complexation processes under study.
Table (9): Thermodynamic stability constants of M2+- phenylglycine complexes as presented in our previous paper [9]
Metal ion
|
Log Kº110(Scheme I)
|
Log Kº111(Scheme II)
|
25ºC
|
35ºC
|
45ºC
|
25ºC
|
25ºC
|
25ºC
|
Ni2+
Cu2+
Zn2+
Cd2+
|
5.08
9.22
5.44
4.44
|
5.06
8.96
5.66
5.03
|
5.00
8.62
5.10
3.94
|
-4.31
-0.24
-4.02
-5.03
|
-4.40
-1.38
-3.90
-4.31
|
-5.00
-1.12
-4.23
-5.39
|
The nature of metal ion plays a great role in the complexation processes. Inspecting ΔGº values, we notice that the spontaneity and stability of the complex formations were increased in the following order Zr4+>UO22+>La3+.
Comparing the thermodynamic stability constants, Log Kº110(Scheme I) of MZ+- phenylglycine in the present work (forZr4+>UO22+>La3+) (Tables 5 and 6) with that in our previous paper [9] (for Cu2+> Zn2+> Ni2+> Cd2+) Table 9), we can conclude that the stability of the formed complexes were increased in the following order:
Zr4+>Cu2+>UO22+>Zn2+>Ni2+> Cd2+>La3+
This is a good agreement with Irving-Wiliams order [20]. According to Davies, a simple relation exists between the stability of the formed complexes and the radius, r, of the unhydrated ion and its valancy, z, as reported in Table (10). Therefore, the less stable complexes of La3+ than the other studied transition metal complexes are attributed to the high value of its radius in comparison with the other studied metal ions [21 &22]. It can be concluded that Zr4+complexes are more stable than that for other metal ions complexes due to the larger ratio of (valance/radius) as well as Jahn-Teller effect [23–25].
Table (10): Ionic radii of studied metal ions
Metal ion
|
Radius (Ǻ)
|
z/r
|
Ni2+
Cu2+
Zn2+
Cd2+
Zr4+
UO22+
La3+
|
0.72
0.69
0.74
0.97
0.86
0.66
1.06
|
2.78
2.90
2.70
2.06
4.65
3.03
2.83
|