Calculate the energy for vacancy formation in nickel (ni), given that the equilibrium number of vacancies at 850°c (1123 k) is 4.7 × 1022 m–3. the atomic weight and density (at 850°c) for ni are, respectively, 58.69 g/mol and 8.80 g/cm3.

litzyguzman13   ·   11.07.2019 11:30
ANSWER(S): 1 Show answers 1 Сomment
ANSWER(S)
answered: baptistatm51976
12.07.2019 03:00
What do you not know about it
answered: duncanswart1558
09.07.2019 18:20

you gotta add the following molecules so we can give u an answer

explanation:

answered: penajay
27.06.2019 09:00

the answer is true.

this statement is true.
12.03.2022 12:48

The energy for vacancy formationE_{v} can be calculated as:

N_{v}=Ne^{-\frac{E_{v}}{kT}}

Here, N_{v} is equilibrium number of vacancies, N is number of atomic sites per unit vacancies, k is Boltzmann constant, T is temperature.

Here, number of atomic sites per unit vacancies can be calculated as follows:

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

Here, ρ is density, N_{A} is Avogadro's number and A is atomic weight.

Putting the values,

N=\frac{8.80 g/cm^{3}(6.023\times 10^{23} mol^{-1})}{58.69 g/mol}=9.03\times 10^{22} cm^{-3}

Converting cm^{-3} to m^{-3}

Since, 1 cm^{-3} =10^{-6} m^{3}

Thus, 9.03\times 10^{22} cm^{-3}=9.03\times 10^{28} m^{-3}

Now, the energy for vacancy formationE_{v} at 850 °C or 1123 K can be calculated using the following equation:

N_{v}=Ne^{-\frac{E_{v}}{kT}}

Rearranging,

E_{v}=kTln\frac{N}{N_{v}}

Putting the values,

E_{v}=(1.38\times 10^{-23} J/K)(1123 K)ln\frac{(9.03\times 10^{28} m^{-3})}{(4.7\times 10^{22}m^{-3})}=2.23\times 10^{-19}J

Therefore, energy for vacancy formation in nickel is 2.23\times 10^{-19}J

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