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Gas-Phase Reactions of Homo- and ... - Institut für Chemie

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1412<br />

Model 2:<br />

D 2 ˆ f 1;1<br />

p… D2‰ dŠ†‡f1;2p…<br />

D2‰ dgŠ†‡fscr<br />

pscr… D2† KIE 2<br />

(26)<br />

H 2 ˆ f 1,2 p(H 2[dg])‡ f scr p scr(H 2) (27)<br />

HD ˆ f 1;2<br />

D 2 ˆ f 1;2<br />

p… HD‰ dgŠ†‡fscr<br />

pscr… HD†<br />

KIE<br />

p… D2‰ dgŠ†‡fscr<br />

pscr… D2† KIE 2<br />

While Models 1 <strong>and</strong> 2 reproduce the experimental data reasonably well (Table 3),<br />

some significant discrepancies remain. For equilibrium isotope effects, it is known that<br />

they are usually close to unity <strong>and</strong> much smaller than KIEs <strong>of</strong> kinetically controlled<br />

reactions, because incorporation <strong>of</strong> a heavy isotope slows down the reaction both, in the<br />

forward as well as in the reverse direction such that the overall effects on the<br />

equilibrium constant K eq are relatively small [22]. As this does not hold true for the<br />

KIEs, the latter are split into the individual contributions KIE 1,1, KIE 1,2, <strong>and</strong> KIE scr to<br />

account for the possibility that the KIE associated with the 1,1-, 1,2-elimination, <strong>and</strong> the<br />

losses <strong>of</strong> H 2/HD/D 2 after equilibration, respectively, differ. With this refined approach,<br />

Eqns. 24 ± 26 <strong>and</strong> 27 ± 29 change into Eqns. 30 ± 32 (Model 3) <strong>and</strong> 33 ± 35 (Model 4),<br />

respectively, <strong>and</strong> the results <strong>of</strong> these calculations are in much better agreement with the<br />

experimental data (Table 3). The best fits obtained <strong>and</strong> the respective parameter sets<br />

for each model are given in Table 4.<br />

(28)<br />

(29)<br />

(3<br />

Model 3:<br />

D2 ˆ f1,1 p(H2[d])‡ f1,2 p(H2[dg])‡ fscr pscr(H2) 0)<br />

HD ˆ f 1;1<br />

p… HD‰ dŠ†<br />

KIE 1;1<br />

Helvetica Chimica Acta ± Vol. 88 (2005)<br />

Table 4. Modeling Parameter Derived That Result in the Best Agreement with the Experimental Data<br />

Positions <strong>of</strong><br />

the alkyl<br />

chain involved<br />

in equilibration<br />

Models 1 <strong>and</strong> 2 Models 3 <strong>and</strong> 4<br />

KIE f1,1 f1,2 fscr KIE1,1 KIE1,2 KIEscr f1,1 f1,2 fscr Fe ‡ 2 a, b, g, d 1.8 0.2 0.16 0.1 0.41 0.1 0.43 0.1 2.5 1.1 1.9 0.2 1.5 0.1 0.24 0.1 0.41 0.1 0.35 0.1<br />

Co ‡ 2 g, d 1.3 0.1 0.00 0.1 1.00 0.1<br />

a ) 1.3 0.1 0.00 0.1 1.00 0.1<br />

Ni ‡ 2 a, b, g, d 1.4 0.5 0.53 0.2 0.47 0.2 1.1 0.4 0.6 0.4 0.57 0.2 0.43 0.2<br />

FeCo ‡ b, g, d 1.7 0.5 0.30 0.1 0.40 0.1 0.30 0.1 3.7 1.1 1.7 0.2 0.8 0.1 0.43 0.1 0.35 0.1 0.22 0.1<br />

FeNi ‡ g, d 1.4 0.5 0.53 0.2 0.47 0.2 1.7 0.4 1.6 0.4 0.57 0.2 0.43 0.2<br />

CoNi ‡ g, d 2.1 0.1 0.72 0.1 0.28 0.1 2.1 0.1 2.0 0.1 0.72 0.1 0.28 0.1<br />

a ) Selective dehydrogenation without preceding scrambling most likely does not take place; therefore, the determination <strong>of</strong><br />

KIE1,2 is arbitrary.<br />

‡ f 1;2<br />

p… HD‰ dgŠ†<br />

‡ fscr KIE 1;2<br />

pscr… HD†<br />

KIE scr<br />

(31)

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