What is the difference between the diffusivity or diffusion coefficient ($\mathrm{m^2\,s^{-1}}$) and the mass transfer coefficient?

Prove that for equimolecular counter diffusion from a sphere to a surrounding stationary infinite medium, the Sherwood number based on the diameter $d$ of the sphere is equal to 2. (Data: the Sherwood number is defined as $\mathrm{Sh} = k_cd/D_{AB}$, where $k_c$ is the mass transfer coefficient based on concentration ($\mathrm{m\,s^{-1}}$) and $D_{AB}$ is the diffusivity of component A in the medium B ($\mathrm{m^2\,s^{-1}}$).)

Ammonia gas is diffusing at a constant rate through a layer of 1 mm thickness of stagnant air. Conditions are fixed so that the gas contains 50 % by volume of ammonia at one boundary of the stagnant layer. The ammonia diffusing to the other boundary is quickly absorbed and the concentration is then negligible. The temperature is 295 K and the pressure is atmospheric, and under these conditions the diffusivity of ammonia in air is $0.18\ \mathrm{cm^2\,s^{-1}}$. Calculate the flux of mass transfer of ammonia ($\mathrm{mol\,m^{-2}\,s^{-1}}$).

Assuming that the non-diffusing gas (air) is replaced by a mixture of methane (B) and hydrogen (C) in volume ratio 2:1, re-calculate the flux of mass transfer of ammonia, if the diffusivity of ammonia in methane and the diffusivity of ammonia in hydrogen are $0.184\ \mathrm{cm^2\,s^{-1}}$ and $0.690\ \mathrm{cm^2\,s^{-1}}$, respectively. (Data: the diffusivity of a component $i$ in a multicomponent mixture follows the Stefan-Maxwell model $D_{i,mix} = 1/\sum_{j \ne i} (y'_j/D_{ij})$, $y'_j = y_j/\sum_{j \ne i} y_j$.)