## How to Calculate and Solve for Mobility of an Ionic Specie | Electrical Properties

The image of mobility of an ionic specie is shown below.

To compute for mobility of an ionic specie, five essential parameters are needed and these parameters are Valence (nI), Electrical Charge (e), Diffusion Coefficient (DI), Boltzmann’s Constant (K) and Temperature (T).

The formula for calculating the mobility of an ionic specie:

μI = nIeDI/KT

Where:

μI = Mobility of an Ionic Specie
nI = Valence
e = Electrical Charge
DI = Diffusion Coefficient
K = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the mobility of an ionic specie when the valence is 18, the electrical charge is 9, the diffusion coefficient is 12, the boltzmann’s constant is 6 and the temperature is 3.

This implies that;

nI = Valence = 18
e = Electrical Charge = 9
DI = Diffusion Coefficient = 12
K = Boltzmann’s Constant = 6
T = Temperature = 3

μI = nIeDI/KT
μI = (18)(9)(12)/(6)(3)
μI = 1944/18
μI = 108

Therefore, the mobility of an ionic specie is 108 m²/(V. s).

## How to Calculate and Solve for Diffusion Coefficient | Mass Transfer

The image above represents diffusion coefficient.

To compute for diffusion coefficient, three essential parameters are needed and these parameters are Constant (BA), Boltzmann’s Constant (KB) and Temperature (T).

The formula for calculating diffusion coefficient:

DA = BAKBT

Where:

DA = Diffusion Coefficient | Nernst-Einstein Equation
BA = Constant
KB = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the diffusion coefficient when the constant is 21, the boltzmann’ s constant is 1.39e-23 and temperature is 12.

This implies that;

BA = Constant = 21
KB = Boltzmann’s Constant = 1.3806e-23
T = Temperature = 12

DA = BAKBT
DA = (21)(1.38e-23)(12)
DA = 3.47

Therefore, the diffusion coefficient is 3.47e-21 cm²/s.

Calculating the Constant when the Diffusion Coefficient and the Temperature is Given.

BA = DA / KB x T

Where;

BA = Constant
DA = Diffusion Coefficient | Nernst-Einstein Equation
KB = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the constant when the diffusion coefficient is 10 and the temperature is 3.

This implies that;

DA = Diffusion Coefficient | Nernst-Einstein Equation = 10
KB = Boltzmann’s Constant = 1.3806e-23
T = Temperature = 12

BA = DA / KB x T
BA = 10 / 1.3806e-23 x 12
BA = 10 / 1.70e-9
BA = 5.88e+9

Therefore, the constant is 5.88e+9.