Answer:
[tex]Activation\ Energy=2.5\times 10^{-19}\ J[/tex]
Explanation:
As we know that:
[tex]N_v=N\times e^{-\frac {Q_v}{k\times T}[/tex]
Where,
[tex]N_v[/tex] is the number of vacancies
N is the number of defective sites
[tex]{Q_v}[/tex] is the activation energy
k is Boltzmann's constant = [tex]1.38\times 10^{-23}\ J/K[/tex]
T is the temperature
Given temperature = 425°C
The conversion of T( °C) to T(K) is shown below:
T(K) = T( °C) + 273.15
So,
T = (425 + 273.15) K = 698.15 K
T = 698.15 K
[tex]N_v=2.3\times 10^{13}[/tex]
N = 10 moles
1 mole = [tex]6.023\times 10^{23}[/tex]
So,
N = [tex]10\times 6.023\times 10^{23}=6.023\times 10^{24}[/tex]
Applying the values as:
[tex]2.3\times 10^{13}=6.023\times 10^{24}\times e^{-\frac {Q_v}{1.38\times 10^{-23}\times 698.15}[/tex]
[tex]ln[\frac {2.3}{6.023}\times 10^{-11}]=-\frac {Q_v}{1.38\times 10^{-23}\times 698.15}[/tex]
[tex]Q_v=2.5\times 10^{-19}\ J[/tex]