according to the collision theory, the ratio of squares of pre-exponential factors of reactions $2\left(\mathrm{A}_{2}\right)$ and 1 $\left(\mathrm{A}_{1}\right)$ at the same temperature $\left(\frac{\mathrm{A}_{2}}{\mathrm{A}_{1}}\right)^{2}$
Species
Mass (g/mol)
Diameter (mm)
X
5
0.3
Y
20
0.5
M
10
0.4
N
10
0.4
(a)4/5
(b)$5 / 5$
(c)$5 / 3$
(d)$3 / 5$
Answer
Answer: A ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
Collision theory: A ∝ σ√(8k_BT/πμ) with σ = πd², d = (d_X + d_Y)/2. Both pairs have d = 0.4 mm, so (A₂/A₁)² = μ₁/μ₂; μ₁ = 5×20/25 = 4, μ₂ = 10×10/20 = 5 → 4/5.