GATE 2020 CH – Question 34

Chemical Reaction Engineering · Reaction rates and kinetics of homogeneous reactions · 1 mark · Numerical answer

Acetaldehyde X decomposes through a four-step radical mechanism with overall rate $-r_X=k_2[k_1/(2k_3)]^{1/2}C_X^{3/2}=k_{overall}C_X^{3/2}$. Elementary activation energies for k₁,k₂,k₃ are 320,40,0 kJ/mol. All rate constants follow Arrhenius laws. Find overall activation energy in kJ/mol, rounded to the nearest integer.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 199 to 201

Explanation

Taking logarithms gives $\ln k_{overall}=\ln k_2+\frac12\ln k_1-\frac12\ln k_3-\frac12\ln2$. The coefficient of $-1/(RT)$ is therefore $E_{overall}=E_2+E_1/2-E_3/2$. Substituting gives 40 + 160 − 0 = 200 kJ/mol. The constant factor 2 affects the pre-exponential factor, not the activation energy.

More Reaction rates and kinetics of homogeneous reactions questions

GATE 2026 CH Q31 – Consider a homogeneous gas phase reaction, A + 2B 2C + 3D, occurring at constant…
GATE 2026 CH Q43 – The reaction rate constants of two reactions follow Arrhenius' law. The activation…
GATE 2024 CH Q19 – The ratio of the activation energy of a chemical reaction to the universal gas constant is…
GATE 2024 CH Q20 – The rate of a reaction A B is 0.2 mol m-3 s-1 at a particular concentration C A1. The rate…
GATE 2022 CH Q64 – An elementary irreversible gas-phase reaction, A B + C, is carried out at fixed…
GATE 2021 CH Q34 – The following homogeneous liquid phase reactions are at equilibrium. The values of rate…

All Reaction rates and kinetics of homogeneous reactions questions →