Consider the reaction, H₂+C₂H₄ → C₂H₆ The molecular diamesters of H₂ and C₂H₄ are 1.8 Å and 3.6 Å… · ABC26PH0361

Subject: Physical Chemistry · Chapter: Chemical Kinetics · Topic: Chemical Kinetics – General · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Hard

Consider the reaction, $\mathrm{H}_{2}+\mathrm{C}_{2}\mathrm{H}_{4} \rightarrow \mathrm{C}_{2}\mathrm{H}_{6}$ The molecular diamesters of $\mathrm{H}_{2}$ and $\mathrm{C}_{2}\mathrm{H}_{4}$ are $1.8\,\mathrm{\AA}$ and $3.6\,\mathrm{\AA}$ respectively. The pre-exponential factor in the rate constant calculated using collision theory in $\mathrm{m^{3}\,mol^{-1}\,s^{-1}}$ is approximately. (For this reaction at 300 K,)
\[ \left(\dfrac{8\mathrm{k}_{\mathrm{B}}\mathrm{T}}{\pi\mu}\right)^{1/2} \mathrm{N}_{\mathrm{A}} = 1.11\times 10^{27}\,\mathrm{m\,mol^{-1}\,s^{-1}} \]
, where the symbols have their usual meanings)
(a)$2.5 \times 10^{8}$
(b)$2.5 \times 10^{14}$
(c)$9.4 \times 10^{17}$
(d)$9.4 \times 10^{23}$
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
d = (1.8 + 3.6)/2 = 2.7 Å, so σ = πd² = 2.29 × 10⁻¹⁹ m². A = σ × 1.11 × 10²⁷ ≈ 2.5 × 10⁸ m³ mol⁻¹ s⁻¹ (a).

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