282
Russ.Chem.Bull., Int.Ed., Vol. 63, No. 1, January, 2014
Kiselev et al.
transparent at this wavelength. The data obtained in a temperaꢀ
ture range of 15—40 C are given above. The rates of the reaction
under elevated pressure were measured as described earlier.8
ln(D0/Dt)
1.6
9
3
The volume of reaction at 25 C (Vr–n = –26.6 0.3 cm3 mol–1
)
8
2
was calculated from the relationship between the specific volꢀ
ume of the working solution of reactants 1 and 2 and the concenꢀ
tration of adduct 3 during the reaction (Eq. (1)). The plot of 1/dt
vs. C3,t keeps linear up to the 100% conversion (Fig. 1).
5
7
1.2
0.8
0.4
6
4
1
1/dt = 1/dt=0 + C3,tVr–n/(1000dt=0).
(1)
For all measurements of the reaction rates under elevated
pressure, working solutions of reactants 1 (20.2 mmol L–1) and 2
(262 mmol L–1) were prepared and mixed in equal volumes
(1 mL each). The kinetic curves of the reaction for different
elevated pressures are shown in Fig. 2. The effect of the pressure
on the rate constant is illustrated in Table 1. The experimental
plot of ln(kp/kp=1) vs. P (Fig. 3) obeys equation (2).
500 1000 1500 2000 2500 3000
t/s
Fig. 2. Kinetic curves for the reaction (see Scheme 2) at 25 C
and P = 1 (1), 214 (2), 431 (3), 628 (4), 816 (5), 1025 (6),
1313 (7), 1618 (8), and 2013 bar (9).
ln(kp/kp=1) = 0.00133938P – 0.00000021P2
(R2 = 0.9989).
(2)
ln(kp/kp=1
1.8
)
The apparent volume of activation (V
=
1.6
1.2
0.8
0.4
app
= –33.2 1.1 cm3 mol–1) at P = 1 bar was calculated by formula (3).
Vapp = –RTln(kP)/P.
(3)
The corrected volume of activation (V
=
corr
= –31.0 1.1 cm3 mol–1) was calculated with allowance for the
compressibility of toluene under pressure (4).
Vcorr = –RTln(kP)/P + (n – 1)RT ,
(4)
500
1000
1500
2000
P/bar
T
Fig. 3. Plot of ln(kp/kp=1) vs. P for the reaction (see Scheme 2) in
toluene at 25 C.
where kP is the reaction rate constant at pressure P while considꢀ
ering the solvent incompressible, (n – 1)RT is the correction
T
for the compressibility of the solvent, n is the order of the reacꢀ
tion, and = ln(d)/P is the compressibility of the solvent
T
The enthalpy of the reaction (see Scheme 2) in 1,2ꢀdichloꢀ
roethane at 25 C was measured by calorimetry as described earꢀ
lier.8 Crystals of compound 1 (25—35 mg) were added to a solution
of hexꢀ1ꢀene in 1,2ꢀdichloroethane (150 mL, C2 = 1.0 mol L–1).
Three successive measurements of the heat effect gave –136.1,
–135.1, and –137.8 kJ mol–1. The enthalpy of dissolution of
a solid sample of 1 in 1,2ꢀdichloroethane makes a contribution of
21.9 kJ mol–1, so the average enthalpy of the reaction (see
Scheme 2) in solution is –158.2 1.0 kJ mol–1. This exothermic
effect is appreciably greater than those obtained for the Diels—Alꢀ
(90•10–6 bar–1 for toluene at 25 C).16
d
–1/cm3 g–1
1.1631
1.1630
1.1629
1.1628
1.1627
1.1626
1.1625
1.1624
2
1
der reactions of compound 1 with anthracene (–97 kJ mol–1
)
and cyclopentadiene (–134 kJ mol–1), yet being lower than
the enthalpy of a reaction of compound 1 with butaꢀ1,3ꢀdiene
(–201 kJ mol–1).8
3
This work was financially supported by the Russian
Foundation for Basic Research (Project No. 12ꢀ03ꢀ00029a).
0.001 0.002 0.003 0.004 0.005
C3/mol L–1
Fig. 1. Plots of d–1 vs. C3 (see Eq. (1)) for the reaction (see
Scheme 2) in toluene at 25 0.002 C: (1) d–1 = –0.030935C3 +
References
+ 1.162857, R2 = 0.9997, C01 = 6.986•10–3 mol L–1, C02
=
= 0.12495 mol L–1, Vr–n = –26.6 cm3 mol–1 (for clarity, straight
line 1 is shifted down the Y axis by 0.0002); (2) d–1 = –0.031638C3 +
1. H. M. R. Hoffmann, Angew. Chem., Int. Ed. Engl., 1969,
8, 556.
2. K. Mikami, M. Shimizu, Chem. Rev., 1992, 92, 1021.
3. K. Zheng, J. Shi, X. Liu, X. Feng, J. Am. Chem. Soc., 2008,
130, 15770.
+ 1.163056, R2 = 0.9997, C01 = 7.172•10–3 mol L–1, C02
= 0.1246 mol L–1, Vr–n = –27.2 cm3 mol–1; (3) d–1
=
=
,
= –0.030409C3 + 1.162612, R2 = 0.9994, C01 = 6.90•10–3 mol L–1
C
02 = 0.1114 mol L–1, Vr–n = –26.2 cm3 mol–1
.