Pyrolysis is an important industrial process for conversion of coal to liquid fuels and chemical fee — Organic Chemistry Chemistry Question
Kinetics of a free radical reaction
Pyrolysis is an important industrial process for conversion of coal to liquid fuels and chemical feedstocks. The structure of coal can be viewed as a three-dimensional network of polycyclic aromatic building blocks joined together by short aliphatic bridges. In model pyrolysis studies, α,ω-diphenylalkanes are sometimes used as model compounds for coal.
Thermal decomposition of 1,3-diphenylpropane gives toluene and styrene as the major products and ethylbenzene and other hydrocarbons as byproducts. The following mechanism of decomposition has been proposed (the first step is the slowest):
Applying the steady-state approximation for the radical 2, derive the rate equation for the side reaction of ethylbenzene formation.
Model Answer
d/dt = 0 = k1[S] - k2[S]
r = k2[S] = k1[S]
What is the ratio between the steady-state concentrations of the radicals 1 and 3?
Model Answer
d/dt = 0 = k1[S] - k3[S] + k4
d/dt = 0 = k2[S] + k3[S] - k4 = k1[S] + k3[S] - k4
The first step is the slowest, therefore k1[S] << k3[S], by neglecting k1[S] term, we get:
k3[S] = k4/ = k4 / (k3[S])
Additionally, two free radicals can recombine. The rate constant of recombination kR is supposed to be the same for all radicals.
1 R1• + R2• → R1-R2
Why could we neglect these reactions in the steady-state equations in questions 9.1 and 9.2?
Model Answer
Since the rate of radicals generation is small, the concentrations of radicals is low, and the rate of chain propagation which is proportional to the radical concentration is much higher than the rate of recombination which is proportional to the square of the radical concentration. This approximation is known as the long-chain approximation (many chain propagation steps occur before the radical recombinates).
One of the radicals is present in the reaction mixture at much higher concentration than others. This radical is:
a) PhCHCH2CH2Ph•, because it is the most stable one;
b) PhCH2•, because the rate constant of β-scission reaction (4) is higher than the rate constant of chain propagation reaction (3);
c) PhCH2CH2•, because it accumulates in the system.
Model Answer
The correct answer is (b).
Obtain the rate equation for toluene formation. Determine the reaction order. Express the effective activation energy via the activation energies of elementary steps.
Model Answer
The rate of free radicals generation must be equal to their recombination rate. Since the concentration of PhCH2• is much higher than those of other radicals, only the rate of two benzyl radicals recombination should be taken into account:
d[R]/dt = 0 = 2 k1[S] - 2 kR^2 ⇒ = (k1[S] / kR)^(1/2)
r = k3[S] = k3 (k1/kR)^(1/2) [S]^(3/2)
The total order is 1.5.
The effective rate constant:
keff = k3 (k1/kR)^(1/2)
The activation energy is:
EA = E3 + 1/2 E1 - 1/2 ER ≈ E3 + 1/2 E1
because activation energy of free radical recombination is close to zero.