What is the Difference between diffusivity and mass transfer coefficient?

The rate of transfer of a process is equal to the driving force divided by the resistance.

The mass transfer coefficient is the resistance to mass transfer. In mass transfer the driving force is the concentration gradient. The mass transfer coefficient is considered anything that contributes to resistance to mass transfer: thermal and eddy diffusivity, distance, etc.

Fick's law of diffusion describes convective mass transfer as:

N=-c*D*(ca2-ca1)/(z2-z1)

where:

-c is some constant multiplier (unitless)
-The quantity (z2-z1) is the distance between two points. (length i.e. meters)
-D is the mass diffusivity or the diffusion coefficient and is dependent on properties of the substance (such as particle size etc.) and temperature. (units: length2/time i.e. m2/s)
-The quantity (ca2-ca1) is the concentration gradient between the same two points (the driving force) (units: amount/length3 i.e. mol/m3)
-N is the rate of mass transfer (units: mass/(length2*time) i.e. mol/m2*s) )

Putting Fick's law in terms of the mass transfer coefficient kc', yields:

N=-kc'*(ca2-ca1)

where kc'= -c*D/(z2-z1).

You can see that the mass transfer coefficient is in fact a function of the diffusivity.