Calculate the energy for vacancy formation in silver, given that the equilibrium number of vacancies at 800˚C (1073 K) is 3.6 ×
1023 m-3 . The atomic weight and density (at 800˚C) for silver are, respectively, 107.9 g/mol and 9.5 g/cm3 .
2 answers:
Answer:
The energy for vacancy formation in silver is 1.1 ev/atom
Explanation:
The total number of sites is equal to:

Where
NA = Avogadro´s number = 6.023x10²³atom/mol
A = atomic weight of silver = 107.9 g/mol
ρ = density of silver = 9.5 g/cm³
Replacing:

The energy for vacancy is equal:

Where
R = 8.314 J/mol K = 8.614x10⁻⁵ev/atom K
T = 800°C = 1073 K
Nv = number of vacancy = 3.6x10²³m⁻³
Replacing:

Answer : The energy for vacancy formation in silver is, 
Explanation :
Formula used :

or,

So,
![N_v=[\frac{N_A\times \rho}{M}]\times e^{(\frac{-E}{K\times T})}](https://tex.z-dn.net/?f=N_v%3D%5B%5Cfrac%7BN_A%5Ctimes%20%5Crho%7D%7BM%7D%5D%5Ctimes%20e%5E%7B%28%5Cfrac%7B-E%7D%7BK%5Ctimes%20T%7D%29%7D)
where,
= equilibrium number of vacancies = 
E = energy = ?
M = atomic weight = 107.9 g/mole
= Avogadro's number = 
= density = 
T = temperature = 
K = Boltzmann constant = 
Now put all the given values in the above formula, we get:
![3.6\times 10^{20}L^{-1}=[\frac{(6.022\times 10^{23}mol^{-1})\times 9500g/L}{107.9g/mol}]\times e^{[\frac{-E}{(1.38\times 10^{-23}J/K)\times 1073K}]}](https://tex.z-dn.net/?f=3.6%5Ctimes%2010%5E%7B20%7DL%5E%7B-1%7D%3D%5B%5Cfrac%7B%286.022%5Ctimes%2010%5E%7B23%7Dmol%5E%7B-1%7D%29%5Ctimes%209500g%2FL%7D%7B107.9g%2Fmol%7D%5D%5Ctimes%20e%5E%7B%5B%5Cfrac%7B-E%7D%7B%281.38%5Ctimes%2010%5E%7B-23%7DJ%2FK%29%5Ctimes%201073K%7D%5D%7D)

Therefore, the energy for vacancy formation in silver is, 
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