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dimaraw [331]
3 years ago
13

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 .
Chemistry
2 answers:
____ [38]3 years ago
5 0

Answer:

The energy for vacancy formation in silver is 1.1 ev/atom

Explanation:

The total number of sites is equal to:

N=\frac{N_{A} \rho }{A}

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:

N=\frac{6.023x10^{23}*9.5 }{107.9} =5.3x10^{22} atom/cm^{3} =5.3x10^{28} m^{-3}

The energy for vacancy is equal:

Q=-RTln(\frac{N_{v} }{N} )

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:

Q=-8.614x10^{-5} *1073*ln(\frac{3.6x10^{23} }{5.3x10^{28} } )=1.1ev/atom

krek1111 [17]3 years ago
4 0

Answer : The energy for vacancy formation in silver is, 1.762\times 10^{-19}J

Explanation :

Formula used :

N_v=N\times e^{(\frac{-E}{K\times T})}

or,

N=\frac{N_A\times \rho}{M}

So,

N_v=[\frac{N_A\times \rho}{M}]\times e^{(\frac{-E}{K\times T})}

where,

N_v = equilibrium number of vacancies = 3.6\times 10^{23}m^{-3}=3.6\times 10^{20}L^{-1}

E = energy = ?

M = atomic weight = 107.9 g/mole

N_A = Avogadro's number = 6.022\times 10^{23}mol^{-1}

\rho = density = 9.5g/cm^3=9.5g/ml=9500g/L

T = temperature = 800^oC=273+800=1073K

K = Boltzmann constant = 1.38\times 10^{-23}J/K

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}]}

E=1.762\times 10^{-19}J

Therefore, the energy for vacancy formation in silver is, 1.762\times 10^{-19}J

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