How to Calculate and Solve for Permeation | Mass Transfer

The image above represents permeation.

To compute for permeation, six essential parameters are needed and these parameters are Length of Vessel (L), Diameter (D), Initial Concentration (c1), Final Concentration (c2), Inlet Radius of Pipe (r1and Exit Radius of Pipe (r2).

The formula for calculating permeation:

j = -2πLD (c1 – c2 / In(r1/r2))

Where:

j = Permeation
L = Length of Vessel
D = Diameter
c1 = Initial Concentration
c2 = Final Concentration
r1 = Inlet Radius of Pipe
r2 = Exit Radius of Pipe

Let’s solve an example;
Find the permeation when the length of vessel is 8, the diameter is 2, the initial concentration is 4, the final concentration is 9, the inlet radius of pipe is 13 and the exit radius of pipe is 11.

This implies that;

L = Length of Vessel = 8
D = Diameter = 2
c1 = Initial Concentration = 4
c2 = Final Concentration = 9
r1 = Inlet Radius of Pipe = 13
r2 = Exit Radius of Pipe = 11

j = -2πLD (c1 – c2 / In(r1/r2))
j = -2π(8)(2) (4 – 9/In(13/11))
j = (-100.53) (-5/In(1.18))
j = (-100.53) (-5/0.167)
j = (-100.53) (-29.93)
j = 3008.9

Therefore, the permeation is 3008.9 m².

Continue reading How to Calculate and Solve for Permeation | Mass Transfer

How to Calculate and Solve for Knudsen Diffusion of Moulding Sand | Mass Transfer

The image above represents knudsen diffusion of moulding sand.

To compute for knudsen diffusion of moulding sand, three essential parameters are needed and these parameters are Pore Radius (r), Temperature (T) and Molecular Weight (M).

The formula for calculating knudsen diffusion of moulding sand:

Dk = 9700r√(T/M)

Where:

Dk = Knudsen Diffusion of Moulding Sand
r = Pore Radius
T = Temperature
M = Molecular Weight

Let’s solve an example;
Find the knudsen diffusion of moulding sand when the pore radius is 24, the temperature is 18 and the molecular weight is 12.

This implies that;

r = Pore Radius = 24
T = Temperature = 18
M = Molecular Weight = 12

Dk = 9700r√(T/M)
Dk = 9700(24)√(18/12)
Dk = 9700(24)√(1.5)
Dk = 9700(24)(1.22)
Dk = 285120.6

Therefore, the knudsen diffusion of moulding sand is 285120.6 cm²/s.

Calculating the Pore Radius when the Knudsen Diffusion of Moulding Sand, the Temperature and the Molecular Weight is Given.

r = Dk / 9700 √(T / M)

Where:

r = Pore Radius
Dk = Knudsen Diffusion of Moulding Sand
T = Temperature
M = Molecular Weight

Let’s solve an example;
Find the pore radius when the knudsen diffusion of moulding sand is 20, the temperature is 14 and the molecular weight is 10.

This implies that;

Dk = Knudsen Diffusion of Moulding Sand = 20
T = Temperature = 14
M = Molecular Weight = 10

r = Dk / 9700 √(T / M)
r = 20 / 9700 √(14 / 10)
r = 20 / 9700 √(1.4)
r = 20 / 11446
r = 0.00174

Therefore, the pore radius is 0.00174.

Continue reading How to Calculate and Solve for Knudsen Diffusion of Moulding Sand | Mass Transfer

How to Calculate and Solve for Permeability due to Partial Pressure | Mass Transfer

The image above represents permeability due to partial pressure.

To compute for permeability due to partial pressure, three essential parameters are needed and these parameters are Diffusion Coefficient (D), Constant (K) and Partial Pressure (Po).

The formula for calculating permeability due to partial pressure:

P = DK / √(Po)

Where:

P = Permeability due to Partial Pressure
D = Diffusion Coefficient
K = Constant
Po = Partial Pressure

Let’s solve an example;
Find the permeability due to partial pressure when the diffusion coefficient is 12, the constant is 14 and the partial pressure is 17.

This implies that;

D = Diffusion Coefficient = 12
K = Constant = 14
Po = Partial Pressure = 17

P = DK / √(Po)
P = (12)(14) / √(17)
P = 168 / 4.12
P = 40.74

Therefore, the permeability due to partial pressure is 40.74.

Calculating the Diffusion Coefficient when the Permeability due to Partial Pressure, the Constant and the Partial Pressure is Given.

D = P x √(Po) / K

Where;

D = Diffusion Coefficient
P = Permeability due to Partial Pressure
K = Constant
Po = Partial Pressure

Let’s solve an example;
Find the diffusion coefficient when the permeability due to partial pressure is 12, the constant is 8 and the partial pressure is 16.

This implies that;

P = Permeability due to Partial Pressure = 12
K = Constant = 8
Po = Partial Pressure = 16

D = P x √(Po) / K
D = 12 x √(16) / 8
D = 12 x 4 / 8
D = 48 / 8
D = 6

Therefore, the diffusion constant is 6.

Continue reading How to Calculate and Solve for Permeability due to Partial Pressure | Mass Transfer

How to Calculate and Solve for Stokes-Einstein Equation of Diffusivity | Mass Transfer

The image above represents strokes-einstein equation of diffusivity.

To compute for strokes-einstein equation of diffusivity, four essential parameters are needed and these parameters are Boltzmann’s Constant (KB), Temperature (T), Radius of Sphere (R) and Viscosity (η).

The formula for calculating strokes-einstein equation of diffusivity:

D = KBT / 6πRη

Where:

D = Diffusivity
KB = Boltzmann’s Constant
T = Temperature
R = Radius of Sphere
η = Viscosity

Let’s solve an example;
Find the diffusivity when the boltzmann’s constant is 1.3806E-23, the temperature is 22, the radius of sphere is 12 and the viscosity is 10.

This implies that;

KB = Boltzmann’s Constant = 1.3806E-23
T = Temperature = 22
R = Radius of Sphere = 12
η = Viscosity = 10

D = KBT / 6πRη
D = (1.3806e-23)(22) / 6π(12)(10)
D = 3.037e-22 / 2261.94
D = 1.342

Therefore, the diffusivity is 1.342e-25 cm²/s.

Continue reading How to Calculate and Solve for Stokes-Einstein Equation of Diffusivity | Mass Transfer

How to Calculate and Solve for Mobility | Mass Transfer

The image above represents mobility.

To compute for mobility, two essential parameters are needed and these parameters are Steady State Velocity (v) and Drag Force (F).

The formula for calculating mobility:

B = v / F

Where:

B = Mobility
v = Steady State Velocity
F = Drag Force

Let’s solve an example;
Find the mobility when the steady state velocity is 22 and the drag force is 11.

This implies that;

v = Steady State Velocity = 22
F = Drag Force = 11

B = v / F
B = 22 / 11
B = 2

Therefore, the mobility is 2 m/Ns.

Calculating the Steady State Velocity when the Mobility and the Drag Force is Given.

v = B x F

Where;

v = Steady State Velocity
B = Mobility
F = Drag Force

Let’s solve an example;
Find the steady state velocity when the mobility is 14 and the drag force is 2.

This implies that;

B = Mobility = 14
F = Drag Force = 2

v = B x F
v = 14 x 2
v = 28

Therefore, the steady state velocity is 28 m/s.

Continue reading How to Calculate and Solve for Mobility | Mass Transfer

How to Calculate and Solve for Relationship between Electrical Conductivity and Diffusivity | Mass Transfer

The image above represents relationship between electrical conductivity and diffusivity.

To compute for relationship between electrical conductivity and diffusivity, five essential parameters are needed and these parameters are Electrical conductivity (σ ), Coordination Number (Z), Electron Charge (e), Boltzmann’s Constant (KB) and Temperature (T).

The formula for calculating relationship between electrical conductivity and diffusivity:

σ/D = n(Ze)² / KBT

Where:

σ/D = Relationship between Electrical Conductivity and Diffusivity
σ = Electrical Conductivity
D = Diffusivity
Z = Coordination Number
e = Electron Charge
KB = Boltzmann’s Constant
T = Temperature

Let’s solve an example;
Find the relationship between electrical conductivity and diffusivity when the electrical conductivity is 2, the coordination number is 3, the electron charge is 4, the boltzmann’s constant is 1.3806e-23 and the temperature is 7.

This implies that;

σ = Electrical Conductivity = 2
Z = Coordination Number = 3
e = Electron Charge = 4
KB = Boltzmann’s Constant = 1.3806e-23
T = Temperature = 7

σ/D = n(Ze)² / KBT
σ/D = 2(3(4))² / 1.3806e-23(7)
σ/D = 2(12)² / 9.66e-23
σ/D = 2(144) / 9.66e-23
σ/D = 288 / 9.66e-23
σ/D = 2.97

Therefore, the relationship between electrical conductivity and diffusivity is 2.97e+24.

Continue reading How to Calculate and Solve for Relationship between Electrical Conductivity and Diffusivity | Mass Transfer

How to Calculate and Solve for Activation Energy of Diffusion | Mass Transfer

The image above represents activation energy of diffusion.

To compute for activation energy of diffusion, four essential parameters are needed and these parameters are Gas Constant (R), Melting Temperature of Metal (Tm), Constant that depends on Metal Crystal Structure (Ko) and Normal Valence in Metal (v).

The formula for calculating activation energy of diffusion:

Q = RTm(Ko + v)

Where:

Q = Activation Energy of Diffusion
R = Gas Constant
Tm = Melting Temperature of Metal
Ko = Constant that depends on Metal Crystal Structure
v = Normal Valence in Metal

Let’s solve an example;
Find the activation energy of diffusion when the gas constant is 24, the melting temperature of metal is 4, the constant that depends on metal crystal structure is 8 and the normal valence in metal is 2.

This implies that;

R = Gas Constant = 24
Tm = Melting Temperature of Metal = 4
Ko = Constant that depends on Metal Crystal Structure = 8
v = Normal Valence in Metal = 2

Q = RTm(Ko + v)
Q = 24(4)(8 + 2)
Q = 24(4)(10)
Q = 960

Therefore, the activation energy of diffusion is 960 J.

Calculating the Gas Constant when the Activation Energy of Diffusion, the Melting Temperature of Metal, the Constant that depends on Metal Crystal Structure and the Normal Valence in Metal is Given.

R = Q / Tm (Ko + v)

Where;

R = Gas Constant
Q = Activation Energy of Diffusion
Tm = Melting Temperature of Metal
Ko = Constant that depends on Metal Crystal Structure
v = Normal Valence in Metal

Let’s solve an example;
Given that the activation energy of diffusion is 9, the melting temperature is 5, the constant that depends on metal crystal structure is 14 and the normal valence in metal is 7.

This implies that;

Q = Activation Energy of Diffusion = 9
Tm = Melting Temperature of Metal = 5
Ko = Constant that depends on Metal Crystal Structure = 14
v = Normal Valence in Metal = 7

R = Q / Tm (Ko + v)
R = 9 / 5 (14 + 7)
R = 9 / 5 (21)
R = 9 / 105
R = 0.085

Therefore, the gas constant is 0.085.
Continue reading How to Calculate and Solve for Activation Energy of Diffusion | Mass Transfer

How to Calculate and Solve for Frequency Factor of Diffusion | Mass Transfer

The image above represents frequency factor of diffusion.

To compute for frequency factor of diffusion, five essential parameters are needed and these parameters are Interatomic Distance (σ), Jump Frequency (vo), Coordination Number (z), Gas Constant (R) and Entropy Change (ΔS).

The image above represents frequency factor of diffusion:

Do = σ²voz/6 . eΔS/R

Where:

Do = Frequency Factor of Diffusion
σ = Interatomic Distance
vo = Jump Frequency
z = Coordination Number
R = Gas Constant
ΔS = Entropy Change

Let’s solve an example;
Find the frequency factor of diffusion when the interatomic distance is 11, the jump frequency is 22, the coordination number is 14, the gas constant is 17 and the entropy change is 10.

This implies that;

σ = Interatomic Distance = 11
vo = Jump Frequency = 22
z = Coordination Number = 14
R = Gas Constant = 17
ΔS = Entropy Change = 10

Do = σ²voz/6 . eΔS/R
Do = (11)²(22)(14)/6 . e10/17
Do = (121)(22)(14)/6 . e0.588
Do = 37268/6 . 1.80
Do = 6211.33 . 1.80
Do = 11185.41

Therefore, the frequency factor of diffusion is 11185.41.

Continue reading How to Calculate and Solve for Frequency Factor of Diffusion | Mass Transfer

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.

Continue reading How to Calculate and Solve for Diffusion Coefficient | Mass Transfer