A solution and solid state study of niobium complexes University of ...
A solution and solid state study of niobium complexes University of ... A solution and solid state study of niobium complexes University of ...
Chapter 5 Figure 5.6: Photo-Multiplier data of [NbCl2(OMe)3(MeOH)] (5 x 10 -5 M) and [acacH] (5 x 10 -4 M) in MeOH fitted to (a) a one-step pseudo first-order reaction model and (b) a two- consecutive-step pseudo first-order mathematical model at 35.0 °C and λ = 330nm. It is clear from Figure 5.6 that the data fits the first model better, indicating a one-step pseudo first-order reaction. Preliminary experiments indicated that plots of kobs vs [acacH] for the reactions observed on the stopped-flow apparatus yield straight lines, whereas similar plots for the slower, second reaction yield non-linear results. 87 (a) (b)
5.3.3 Derivation of the rate law Chapter 5 The following rate law can be derived from Scheme 5.1: ( M-acac) d Rate= =k 2 M-acacH -k -2 M-acac dt The definition of K1 yields the following equation: [ ] [ ] [ M-acacH] [ ][ ] 88 (5.3) K 1 = (5.4) M acacH The total niobium species at any time in solution, Mtot, is defined by: M tot = [ M ] + [ M-acacH] (5.5) By substituting (5.4) in (5.5) the following equation is obtained: [ M-acacH] [ ] [ ] M tot = + M-acacH K 1 acacH ⎛ 1 ⎞ = ⎜ +1⎟ M-acacH ⎜ K 1[ acacH] ⎟ ⎝ ⎠ 1[ ] [ ] [ ] ⎛1+K acacH ⎞ = ⎜ ⎟ M-acacH ⎜ K 1 acacH ⎟ ⎝ ⎠ [ ] Substitution of (5.6) in (5.3) yields: [ ] [ ] [ ] M tot .K 1 . acacH M-acacH = 1+K 1 acacH tot [ ] [ ] k .K . ⎡ 2 1 M acacH Rate= ⎣ ⎤ ⎦ -k -2 M-acac 1+K 1 acacH [ ] (5.6) (5.7)
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5.3.3 Derivation <strong>of</strong> the rate law<br />
Chapter 5<br />
The following rate law can be derived from Scheme 5.1:<br />
( M-acac)<br />
d<br />
Rate= =k<br />
2<br />
M-acacH -k<br />
-2<br />
M-acac<br />
dt<br />
The definition <strong>of</strong> K1 yields the following equation:<br />
[ ] [ ]<br />
[ M-acacH]<br />
[ ][ ]<br />
88<br />
(5.3)<br />
K<br />
1<br />
=<br />
(5.4)<br />
M acacH<br />
The total <strong>niobium</strong> species at any time in <strong>solution</strong>, Mtot, is defined by:<br />
M<br />
tot<br />
= [ M ] + [ M-acacH]<br />
(5.5)<br />
By substituting (5.4) in (5.5) the following equation is obtained:<br />
[ M-acacH]<br />
[ ]<br />
[ ]<br />
M<br />
tot<br />
= + M-acacH<br />
K<br />
1<br />
acacH<br />
⎛ 1 ⎞<br />
= ⎜ +1⎟ M-acacH<br />
⎜ K<br />
1[<br />
acacH]<br />
⎟<br />
⎝ ⎠<br />
1[<br />
]<br />
[ ]<br />
[ ]<br />
⎛1+K acacH ⎞<br />
= ⎜ ⎟ M-acacH<br />
⎜ K<br />
1<br />
acacH ⎟<br />
⎝ ⎠<br />
[ ]<br />
Substitution <strong>of</strong> (5.6) in (5.3) yields:<br />
[ ]<br />
[ ]<br />
[ ]<br />
M<br />
tot<br />
.K<br />
1<br />
. acacH<br />
M-acacH =<br />
1+K<br />
1<br />
acacH<br />
tot [ ]<br />
[ ]<br />
k .K . ⎡<br />
2 1<br />
M acacH<br />
Rate=<br />
⎣<br />
⎤<br />
⎦<br />
-k<br />
-2<br />
M-acac<br />
1+K<br />
1<br />
acacH<br />
[ ]<br />
(5.6)<br />
(5.7)
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