$30.4 \mathrm{~kJ}$ of heat is required to melt one mole of sodium chloride and the entropy change at the melting point is $28.4 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ at 1 atm. The melting point of sodium chloride is _______________ K (Nearest Integer)

The heat required to melt one mole of a substance is known as its molar enthalpy of fusion, denoted as $\Delta H_\mathrm{fus}$. For sodium chloride, $\Delta H_\mathrm{fus}$ is $30.4\ \mathrm{kJ/mol}$. <br/><br/> The entropy change at the melting point is given by $\Delta S = \frac{\Delta H_\mathrm{fus}}{T_\mathrm{m}}$, where $T_\mathrm{m}$ is the melting point in Kelvin. Substituting the given values, we get: <br/><br/> $28.4\ \mathrm{J/K/mol} = \frac{30.4\ \mathrm{kJ/mol}}{T_\mathrm{m}}$ <br/><br/> Solving for $T_\mathrm{m}$, we get: <br/><br/> $$T_\mathrm{m} = \frac{30.4\ \mathrm{kJ/mol}}{28.4\ \mathrm{J/K/mol}} = 1070.4\ \mathrm{K}$$ <br/><br/> Rounding off to the nearest integer, the melting point of sodium chloride is $\boxed{1070\ \mathrm{K}}$.