Question

What is the activation energy (Q) for a vacancy formation if 10 moles of a metal have 2.3 X 10^13 vacancies at 425°C?

Answer 1

`Activation\ Energy=2.5* 10^(-19)\ J`

Step-by-step explanation:

Using the expression shown below as:

`N_v=N* e^{-\frac {Q_v}{k* T}`

Where,

`N_v` is the number of vacancies

N is the number of defective sites

k is Boltzmann's constant =
`1.38* 10^(-23)\ J/K`

`{Q_v}` is the activation energy

T is the temperature

Given that:

`N_v=2.3* 10^(13)`

N = 10 moles

1 mole =
`6.023* 10^(23)`

So,

N =
`10* 6.023* 10^(23)=6.023* 10^(24)`

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

Applying the values as:

`2.3* 10^(13)=6.023* 10^(24)* e^{-\frac {Q_v}{1.38* 10^(-23)* 698.15}`

`ln[\frac {2.3}{6.023}* 10^(-11)]=-\frac {Q_v}{1.38* 10^(-23)* 698.15}`

`Q_v=2.5* 10^(-19)\ J`