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qaws [65]
3 years ago
10

Calculate the equilibrium number of vacancies per cubic meter for copper at 1000K. The energy for vacancy formation is 0.9eV/ato

m; the atomic weight and density at 1000K for copper are 63.5g/mol and 8.45g/cm3, respectively.
Chemistry
1 answer:
nexus9112 [7]3 years ago
3 0

Answer:

Therefore the equilibrium number of vacancies per unit cubic meter =2.34×10²⁴ vacancies/ mole

Explanation:

The equilibrium number of of vacancies is denoted by N_v.

It is depends on

  • total no. of atomic number(N)
  • energy required for vacancy
  • Boltzmann's constant (k)= 8.62×10⁻⁵ev K⁻¹
  • temperature (T).

N_v=Ne^{-\frac{Q_v}{kT} }

To find  equilibrium number of of vacancies we have find N.

N=\frac{N_A\ \rho}{A_{cu}}

Here ρ= 8.45 g/cm³  =8.45 ×10⁶m³

N_A= Avogadro Number = 6.023×10²³

A_{Cu}= 63.5 g/mole

N=\frac{6.023\times 10^{23}\times 8.45\times 10^{6}}{63.5}

   =8.01\times 10^{28 g/mole

Here Q_v=0.9 ev/atom , T= 1000k

Therefore the equilibrium number of vacancies per unit cubic meter,

N_v=( 8.01\times 10^{28}) e^{-(\frac{0.9}{8.62\times10^{-5}\times 1000})

   =2.34×10²⁴ vacancies/ mole

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