A first-order heterogeneous reaction A → B is carried out using a porous spherical catalyst. Assume isothermal conditions, and that intraphase diffusion controls the reaction rate. At a bulk A concentration of 0.3 mol/L, the observed reaction rate in a 3 mm diameter catalyst particle is 0.2 mol/(s·L catalyst volume). At a bulk A concentration of 0.1 mol/L, the observed reaction rate, in mol/(s·L catalyst volume), in a 6 mm diameter catalyst particle, is

Question

Accepted Answer

The correct answer is B, 0.033. GATE 2024 official key: (B). For strong intraparticle diffusion limitation, the effectiveness factor η ∝ 1/d_p, so the observed rate ∝ C_Ab/d_p. Rate₂ = Rate₁×(C_Ab2/C_Ab1)×(d_p1/d_p2) = 0.2×(0.1/0.3)×(3/6) ≈ 0.033 mol/(s·L).