The mass transfer co-efficient for a solid sphere of radius 'a' dissolving in a large volume of quiescent liquid, in which D is the diffusivity of solute, is

Answer: Option A

For a solid sphere dissolving in a large volume of quiescent (stationary) liquid, the system is governed by diffusion alone since there is no convective flow.

Under these conditions, the mass transfer process is described by a steady-state diffusion model.

According to the solution of Fick’s second law for a stationary medium around a dissolving sphere, the mass transfer coefficient (k_c) is given by:

k_c = D/a, where
D = diffusivity of the solute in the liquid
a = radius of the solid sphere

This expression assumes that the diffusion is radial and the concentration at the surface of the sphere remains constant.

Option B (D/2a) is incorrect because it does not match the standard solution for diffusion from a sphere.

Option C (Proportional to √D) applies in some unsteady-state or film-type approximations, not for steady diffusion from a sphere.

Option D (Dependent on Reynolds number) is incorrect here, since the liquid is quiescent and there is no bulk motion, making Reynolds number irrelevant.

Therefore, the correct answer is D/a.

Correct Answer: Option A: D/a