Answer : The Activation energy, Ea = 201.820 KJ/mol
The Pre-exponential constant,
= 1.7658 ×
![m^{2}/s](https://tex.z-dn.net/?f=m%5E%7B2%7D%2Fs)
Solution : Given,
Diffusivity of Ni at
,
= 1.23 ×
![m^{2}/s](https://tex.z-dn.net/?f=m%5E%7B2%7D%2Fs)
Diffusivity of Ni at
,
= 1.45 ×
![m^{2}/s](https://tex.z-dn.net/?f=m%5E%7B2%7D%2Fs)
Temperature,
=
= 1200 + 273 = 1473 K
Temperature,
=
= 1800 + 273 = 2073 K
Value of R = 8.314 J/mol/K
Formula used :
..........(1)
This formula convert into logarithm term for the calculation of activation energy. So the formula is,
........(2)
Now put all the values in above formula (2), we get
![ln\frac{1.23\times 10^{-16}}{1.45\times 10^{-14}}=\frac{Ea}{8.314}\left [\frac{1}{2073}-\frac{1}{1473} \right ]](https://tex.z-dn.net/?f=ln%5Cfrac%7B1.23%5Ctimes%2010%5E%7B-16%7D%7D%7B1.45%5Ctimes%2010%5E%7B-14%7D%7D%3D%5Cfrac%7BEa%7D%7B8.314%7D%5Cleft%20%5B%5Cfrac%7B1%7D%7B2073%7D-%5Cfrac%7B1%7D%7B1473%7D%20%5Cright%20%5D)
Rearranging the terms, we get the value of Activation energy, (Ea) as
Ea = 201.820 KJ/mol
Now, we have to calculate the value of Pre-exponential constant,
bye using formula (1)
![D=D_{0}\times\text{exp}\left (\frac{-Ea}{RT} \right )](https://tex.z-dn.net/?f=D%3DD_%7B0%7D%5Ctimes%5Ctext%7Bexp%7D%5Cleft%20%28%5Cfrac%7B-Ea%7D%7BRT%7D%20%5Cright%20%29)
now put all the values in formula,we get
![1.23\times10^{-16}m^{2}/s =D_{0}\times\text{exp}\left (\frac{-201820J/mol} {8.314J/mol/K\times1473K} \right )](https://tex.z-dn.net/?f=1.23%5Ctimes10%5E%7B-16%7Dm%5E%7B2%7D%2Fs%20%3DD_%7B0%7D%5Ctimes%5Ctext%7Bexp%7D%5Cleft%20%28%5Cfrac%7B-201820J%2Fmol%7D%20%7B8.314J%2Fmol%2FK%5Ctimes1473K%7D%20%5Cright%20%29)
Rearranging the terms, we get the value of Pre-exponential constant,
as
= 1.7658 × ![10^{-9} m^{2}/s](https://tex.z-dn.net/?f=10%5E%7B-9%7D%20m%5E%7B2%7D%2Fs)