Diffusivity ‘D’ is defined as the ratio of the molar flux to the corresponding concentration gradient and its units are m^{2}/s. The diffusivity of a component mean it tells about the mobility characteristic of the component and it is a function of temperature, pressure, nature, and concentration of the other components. Diffusivity of gases at atmospheric pressure in cm^{2}/s is in the range less than 1 and for liquids is of the order 1 x 10^{5}.^{ }Diffusivity of a gas generally varies with temperature and pressure according to the relation DµT^{1.5}/P and for liquids it varies by D µT. Diffusivity of liquids can be estimated by Wilke–Chang equation.
Mass transfer coefficient ‘k’ is defined as molar flux = (mass transfer coefficient) X (concentration difference). We consider concentration difference not concentration gradient and the units will change according to the choice of the concentration selection, which we take into consideration. If mole/ volume is used then the units are cm/s and if mole fraction is choosed then the unit will be the units of flux, (mole/ cm^{2} s) due to the reason that mole fractions are dimensionless. The ratio of mass flux for diffusion of A to the mass flux through nondiffusing B for equimolar counterdiffusion is greater than one. The mass transfer coefficients, k_{g} and k_{y} are related according to the relation k_{G}/P = k_{Y}/P^{2}. According to the film theory, the mass transfer coefficient, k_{l}, and diffusivity are related as k_{l }µ D as boundary layer theory predicts that k_{l} α D ^{0.67}. For mass transfer of a solute A present in a dilute mixture of A and B, the term P_{B,M} tends to total pressure P.
Relation between diffusivity and mass transfer coefficient:
Mass transfer coefficient is the ratio of molecular diffusivity to the thickness of stagnant layer (given by film theory)
Theories which explain about mass transfer coefficient calculation are:
1. Film Theory: considered as steady state model
2. Boundary Layer Theory
3. Penetration Theory
4. Surface Renewal Theory
5. Surface Stretch Theory
6. Combination of Film and Surface Renewal Theory
Some dimensionless groups
Corresponding to Prandtl number in heat transfer, the dimensionless group in mass transfer is Schmidt number (μ/ρD_{v}).
According to Danckwerts surface renewal theory, the mass transfer coefficient, k_{l}’ is given by (D_{AB} .S)^{0.5}."S" in Danckwerts surface renewal theory is fraction of the surface renewed per unit time.
According to the penetration theory, the average mass transfer coefficient k_{L},av is given by
2 (D_{AB} / p t)^{0.5}.
For example let a certain mass transfer process, k_{l} = 1 x 10 ^{ 3 }cm/s and D_{AB} = 1 x 10^{5} cm^{2}/s the film thickness in cm is 0.01cm.
The Knudsen diffusivity is dependent on the molecular velocity and pore radius of the catalyst. A gaseous solute having mass diffusivity equal to 0.5cm^{2}/s diffuses into a porous solid having a porosity of 0.5 and a porosity of 2 then the effective diffusivity in the porous solid is 0.125 cm^{2}/s. Knudsen diffusion occurs when the ratio of mean free path to the pore diameter is much greater than one. In Knudsen diffusion molecule – pore wall collision is important. Knudsen diffusivity is independent of total pressure it increases with the square root of temperature and inversely with the square root of molecular weight, it falls in the range of 10 ^{–1} to 10 ^{– 4} cm^{2}/s.
The term permeability is defined as permeability=solubility X diffusivity
Approximate Diffusivities of gases at standard atmospheric pressure, 101.325 KPa:
s.no

System

Temperature, ^{0}C

Diffusivity,m^{2}/s X 10^{5}

Reference

1

H_{2 } CH_{4}

0

6.25

Chapman,s.&T.G. Cowling

2

O_{2 } N_{2}

0

1.81

,,

3

CO – O_{2}

0

1.85

,,

4

CO_{2} – O_{2}

0

1.39

,,

5

Air – NH_{3}

0

1.98

Wintergeist

6

Air – H_{2}O

25.9
59.0

2.58
3.05

Gilliland

7

Air – C_{2}H_{5}OH

25.9

1.02

Gilliland

8

Air – nButanol

25.9
59.0

0.87
1.04

International critical table

9

Air – Ethyl Acetate

25.9
59.0

0.87
1.06

Gilliland

10

Air – Aniline

25.9
59.0

0.74
0.90

Gilliland

11

Air – Chlorobenzene

25.9
59.0

0.74
0.90

Gilliland

12

Air  Toluene

25.9
59.0

0.86
0.92

Gilliland

Approximate Diffusivities of Liquids at 1 atm, pressure:
s.no

System

Temperature,
^{0}C

Solute con:
Kmole/m^{3}

Diffusivity,
m^{2}/s X 10^{9}
 
solute

solvent
 
1

Cl_{2}

Water

16

0.12

1.26

2

HCl

Water

0
,,
10
,,
16

9
2
9
2.5
0.5

2.7
1.8
3.3
2.5
2.44

3

NH3

Water

5
15

3.5
1.0

1.24
1.77

4

CO2

Water

10
20

0
0

1.26
1.21

5

NaCl

Water

18
,,
,,
,,
,,

0.05
0.2
1.0
3.0
5.4

1.24
1.36
1.54
1.28
0.82

6

Methanol

Water

15

0

0.91
0.96

7

Acetic acid

Water

12.5
,,
18

1.0
0.01
1.0

0.50
0.83
0.90

8

Ethanol

Water

10
,,
16

3.75
0.05
2.0

0.50
0.83
0.90

9

nbutanol

Water

15

0

0.77

10

Co2

Ethanol

17

0

3.2

11

chloroform

ethanol

20

2.0

1.25
