A solution and solid state study of niobium complexes University of ...

Chapter 5
The values of k1, k-1 and K1 (first reaction) obtained from fits of the data to Equation
5.9 are given in Table 5.2. Similarly, the values for the rate constants k2 and k-2,
together with the values obtained for the stability constant for the first step, K1, from
fits of the data to Equation 5.12 are also given in Table 5.2.
Table 5.2: Rate constants for both the fast and slow reactions.
Rate Constants 15 °C 25 °C
Fast Reaction
35 °C 45 °C
k1 (M -1 s -1 ) a
96 (2) 237 (4) 574 (6) 1440 (15)
k-1 (s -1 ) a
0.051 (6) 0.12 (1) 0.29 (4) 0.66 (6)
K1 (M -1 ) b
1882 (216) 1975 (201)
Slow Reaction
1979 (273) 2181 (235)
k2 (s -1 ) c
1.51 (8) x 10 -5 3.7 (3) x 10 -5 8.0 (9) x 10 -5 15.1 (9) x 10 -5
k-2 (s -1 ) c
0.91 (8) x 10 -5 1.8 (4) x 10 -5 3.9 (8) x 10 -5 10.1 (8) x 10 -5
K1 (M -1 ) c
1356 (231) 1403 (379) 1213 (604) 1695 (303)
K2 d
1.6 (2) 2.0 (5) 2.1 (6) 1.5 (2)
a b c d
Fig. 5.7, Eq. 5.9; Fig. 5.7, Eq. 5.10; Fig. 5.8, Eq. 5.12; Fig. 5.8, Eq. 5.11
It is clear from Table 5.2 and Figures 5.9 and 5.10 that the fits of the rate data are
representative of the rate law, indicating specifically that the equilibrium constant for
the fast, first reaction (although with large esd’s) agrees quite well with the second
observed reaction which describes the total process.
Figure 5.9 and Figure 5.10 shows the Eyring plots of the data in Table 5.2, to yield
the activation parameters for the two steps. The Eyring equation is given as:
k ΔH k ΔS
ln = ≠ ln B ≠
T RT h R
(5.13)
With ∆H ‡ = enthalpy of activation, ∆S ‡ = entropy of activation, kB = Boltzmann
constant, R = gas constant and h = Planck’s constant.
91