In a crystal at 827°C one out of 1010 lattice site is found to be vacant but at 927°C, one out of 2

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In a crystal at 827°C one out of 1010 lattice site is found to be vacant but at 927°C, one out of 2 × 109 lattice sites is found to be vacant. The enthalpy of vacancy formation in kJ/mol is

Accepted Answer

$\ln\frac{f_{2}}{f_{1}} = \frac{\Delta H}{R}\left( \frac{1}{T_{1}} - \frac{1}{T_{2}} \right)$

Or, $\ln\frac{1/\left( 2 \times 10^{9} \right)}{1/\left( 10^{10} \right)} = \frac{\Delta H}{R}\left( \frac{1}{1100} - \frac{1}{1200} \right) \Rightarrow \Delta H = 176.8\text{KJ/mol}$

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