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

Last Updated on August 1, 2021

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 (T_m), Constant that depends on Metal Crystal Structure (K_o) and Normal Valence in Metal (v).

The formula for calculating activation energy of diffusion:

Q = RT_m(K_o + v)

Where:

Q = Activation Energy of Diffusion
R = Gas Constant
T_m = Melting Temperature of Metal
K_o = 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
T_m = Melting Temperature of Metal = 4
K_o = Constant that depends on Metal Crystal Structure = 8
v = Normal Valence in Metal = 2

Q = RT_m(K_o + 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
T_m = Melting Temperature of Metal
K_o = 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
T_m = Melting Temperature of Metal = 5
K_o = 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.

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

T_m = ^Q / _{R (Ko + v)}

Where;

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

Let’s solve an example;
Find the melting temperature of metal when the activation energy of diffusion is 44, the gas constant is 12, the constant that depends on metal crystal structure is 6 and the normal valence in metal is 2.

This implies that;

Q = Activation Energy of Diffusion = 44
R = Gas Constant = 12
K_o = Constant that depends on Metal Crystal Structure = 6
v = Normal Valence in Metal = 2

T_m = ^Q / _{R (Ko + v)}
T_m = ⁴⁴ / _{12 (6 + 2)}
T_m = ⁴⁴ / _{12 (8)}
T_m = ⁴⁴ / ₉₆
T_m = 0.458

Therefore, the melting temperature of metal is 0.458.

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

K_o = (^Q / _RTm) – v

Where;

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

Let’s solve an example;
Find the constant that depends on metal crystal structure when the activation energy of diffusion is 20, the gas constant is 14, the melting temperature of metal is 11 and the normal valence in metal is 4.

This implies that;

Q = Activation Energy of Diffusion = 20
R = Gas Constant = 14
T_m = Melting Temperature of Metal = 11
v = Normal Valence in Metal = 4

K_o = (^Q / _RTm) – v
K_o = (²⁰ / _(14)(11)) – 4
K_o = (²⁰ / ₁₅₄) – 4
K_o = 0.129 – 4
K_o = -3.87

Therefore, the constant that depends on metal crystal structure is -3.87.

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

v = (^Q / _RTm) – K_o

Where;

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

Let’s solve an example;
Find the normal valence in metal when the activation energy of diffusion is 24, the gas constant is 10, the melting temperature of metal is 8 and the constant that depends on metal crystal structure is 12.

This implies that;

Q = Activation Energy of Diffusion = 24
R = Gas Constant = 10
T_m = Melting Temperature of Metal = 8
K_o = Constant that depends on Metal Crystal Structure = 12

v = (^Q / _RTm) – K_o
v = (²⁴ / _(10)(8)) – 12
v = (²⁴ / ₈₀) – 12
v = 0.3 – 12
v = -11.7

Therefore, the normal valence in metal is -11.7.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the activation energy of diffusion.

Now, Click on Mass Transport under Materials and Metallurgical

Now, Click on Activation Energy of Diffusion under Fuel and Furnaces

The screenshot below displays the page or activity to enter your values, to get the answer for the activation energy of diffusion according to the respective parameter which is the Gas Constant (R), Melting Temperature of Metal (T_m), Constant that depends on Metal Crystal Structure (K_o) and Normal Valence in Metal (v).

Now, enter the values appropriately and accordingly for the parameters as required by the Gas Constant (R) is 24, Melting Temperature of Metal (T_m) is 4, Constant that depends on Metal Crystal Structure (K_o) is 8 and Normal Valence in Metal (v) is 2.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the activation energy of diffusion and presents the formula, workings and steps too.