Answer to Question #121703 in Molecular Physics | Thermodynamics for Dheeraj

Question

For the same diffusion time, the depth of penetration at 500 degree celcius and 850 degree celcius is in the ratio 1:6. The activation process for the above diffusion process is?

Answer 1

The diffusion coefficient is

$$D=D_0e^{-\frac{E_a}{2RT}}.$$

We have

$$\frac{D_1}{D_2}=\frac{1}{6}=\frac{e^{-\frac{E_a}{2RT_1}}}{e^{-\frac{E_a}{2RT_2}}}.$$

Solve for $E_a$:

$$E_a=\frac{2T_1T_2R\text{ ln}(D_1/D_2)}{T_1-T_2}=36\text{ kJ/mol}.$$

The activation energy for the diffusion process is 36 kJ/mol.