Project ForgeChemical Reaction Engineering
Reaction Kinetics
GATE 2013
Hard
The overall rates of an isothermal catalytic reaction using spherical catalyst particles of diameters 1 mm and 2 mm are rA1 and rA2 (in mol (kg-catalyst)⁻¹ h⁻¹), respectively. The other physical properties of the catalyst particles are identical. If pore diffusion resistance is very high, the ratio rA2/rA1 is _____
0.5(± 0.03 accepted)
Explanation
Under strong pore-diffusion limitation (large Thiele modulus φ), the effectiveness factor for a sphere approaches η≈3/φ, and since φ∝R (particle radius), η∝1/R — so the observed rate per unit catalyst mass scales as 1/R. With R1=0.5mm and R2=1mm: rA2/rA1=R1/R2=0.5/1=0.5.
Source: GATE CH 2013 (2013)
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