Question

The number of vacancies in some hypothetical metal increases by a factor of 5 when the temperature is increased from 1080 K to 1170 K. Calculate the energy (in kJ/mol) for vacancy formation assuming that the density of the metal remains the same over this temperature range.

Answer 1

Answer:

E = 15.7 KJ/mol

Explanation:

The number of vacancies in a metal is given by

      n = n₀ $e^{-E/KT}$

They tell us that

     n = 5 no

We replace

      5 n₀ = n₀   e^{-E/KT}

      -E / KT = ln 5

       E = KT ln 5

       E = 1,381 10⁻²³  1170 ln 5

        E = 2.6 10⁻²⁰ J

To take (J / mol) we multiply between Avogadro's number

        E = 2.6 10⁻²⁰ 6.022 10²³

        E = 1.57 10⁴ J / mol

        E = 15.7 KJ/mol