Project ForgeChemical Reaction Engineering
Reaction Kinetics
GATE 2020
Hard
Acetaldehyde (X) decomposes via a four-step free radical mechanism with overall rate −rX=k2(k1/2k3)^0.5·CX^1.5=koverall·CX^1.5, where the elementary-step activation energies (kJ/mol) are Ea1=320, Ea2=40, Ea3=0. The activation energy for the overall reaction (kJ/mol) is (round off to nearest integer)
200 kJ/mol(± 2 accepted)
Explanation
Since ln(koverall)=ln(k2)+0.5[ln(k1)−ln(k3)]+const, the activation energies combine the same way: Ea,overall=Ea2+0.5(Ea1−Ea3)=40+0.5×(320−0)=40+160=200 kJ/mol.
Source: GATE CH 2020 (2020)
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