UPSC Combined Geo-Scientist, Mains · 2023 · Mains Paper II
Q1(g). Activation energy of 2HI → H₂ + I₂
Question
The rate constant for the reaction 2HI(g) → H₂(g) + I₂(g) is 1.33 × 10⁻⁶ dm³ mol⁻¹ s⁻¹ at 575 K and 2.50 × 10⁻³ dm³ mol⁻¹ s⁻¹ at 716 K. Calculate the value of activation energy of the reaction.
Answer in brief
Ea = 1.83 × 10⁵ J mol⁻¹ = 183 kJ mol⁻¹.
Key points
- ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂).
- k₂/k₁ = 2.50 × 10⁻³/1.33 × 10⁻⁶ = 1879.7, ln(k₂/k₁) = 7.539.
- 1/575 − 1/716 = 3.4248 × 10⁻⁴ K⁻¹; Ea = 8.314 × 7.539/3.4248 × 10⁻⁴ = 1.830 × 10⁵ J mol⁻¹.
- Pre-exponential factor A = 5.6 × 10¹⁰ dm³ mol⁻¹ s⁻¹; the units of k show a second-order (bimolecular) reaction.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
CoversArrhenius equationactivation energyHI decompositionrate constanttemperature dependence
All parts of Question 1
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