Discussion
For gas film control in the shrinking core model, the time for complete conversion varies with particle radius as
Answer: A
Correct answer: the radius to the first power only
With the mass transfer coefficient taken as constant, \[ \tau = \frac{\rho_B R}{3bk_gC_{Ag}}, \] so the time varies directly with the radius - the weakest dependence of the three regimes, since ash layer control gives \( R^{2} \) and reaction control gives \( R \) as well but with a different constant. In practice the coefficient itself depends on particle size, which steepens the observed dependence somewhat.
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