The number of vacancies in some hypothetical metal increases by a factor of 6 when the temperature is increased from 1070 K to 1160 K. Calculate the energy (in kJ/mol) for vacancy formation assuming that the density of the metal remains the same over this temperature range.

The answer to the question is

The energy (in kJ/mol) for vacancy formation assuming that the density of the metal remains the same over this temperature range is 3.41165×10⁻²² kJ/mol

Explanation:

To solve the question, we note that the Boltzmann equation for vibrational states is

Where

N₀ = Population of the lower energy state

N₁ = Population of the upper energy state

ΔE = dE = The energy difference between the two states

k = the Boltzmann constant and

T  = Kelvin temperature

Therefore we have

From which

Therefore

= 3.41165×10⁻²² kJ/mol

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