Question

If a solid has a heat of fusion of 17.02 kJ/mol and an entropy of fusion of 38.98 J/mol- K, what is the melting point in °C) of this pure solid? Type your answer rounded to 1 decimal place without units (i.e. NN.N).

Answer 1

Explanation:

Melting point is defined as the point at which a solid substance starts to change into liquid state.

Whereas entropy is the degree of randomness of molecules present in a substance.

Heat of fusion is defined as the amount of heat energy necessary to melt a solid substance at its melting point.

Relation between entropy and heat of fusion is as follows.

                  $\Delta S = \frac{\Delta H}{T}$

where,          $\Delta S$ = 38.98 J/mol K

                     $\Delta H$ = 17.02 kJ/mol

                                    = $17.02 kJ/mol \times \frac{1000 J}{1 kJ}$

                                    = 17020 J/mol

Therefore, calculate the melting point as follows.

                   $\Delta S = \frac{\Delta H}{T}$

                           38.98 J/mol K = $\frac{17020 J/mol}{T}$

                              T = 436.63 K

Change the temperature into degree celsius as follows.

                             $(436.63 - 273)^{o}C$

                                 = $163.63^{o}C$

Thus, we can conclude that the melting point in $^{o}C$ is $163.63^{o}C$.