Question

For a liquid, enthalpy of fusion is\[1.435\;kcal\;mo{l^{ - 1}}\], and molar entropy change is\[5.26\;cal\;mo{l^{ - 1}}{K^{ - 1}}\]. The melting point of the liquid is:
$
  A.{\text{ }}0^\circ C \\
  B.{\text{ }} - 273^\circ C \\
  C.{\text{ }}173^\circ C \\
  D.{\text{ }}100^\circ C \\
 $

Answer 1

Hint: We have to find the melting point of unknown liquid. They give enthalpy of fusion and molar entropy change of unknown liquid. We can use the fusion formula to solve the question.

Complete step by step solution:
\[\Delta Sfusion = {\text{ }}\dfrac{{\Delta Hfusion}}{{Tmp}}\]
Where,
\[\Delta {S_{fusion}}\] = molar entropy change
\[\Delta {H_{fusion}}\]​​= enthalpy of fusion
${T_{mp}}$ = melting point temperature of a liquid
Given:
Enthalpy of fusion of liquid = \[\Delta {H_{fusion}} = 1.435{\text{ }}kcal/mole\]= \[1.435{\text{ }} \times {10^3}cal/mole\]
The molar entropy change of liquid = \[\Delta {S_{fusion}} = 5.26{\text{ }}calmo{l^{ - 1}}{K^{ - 1}}\]
Complete step by step answer:
We can find the melting point of liquid by putting the given values in a fusion formula.
Therefore, we get
\[\Delta Sfusion = {\text{ }}\dfrac{{\Delta Hfusion}}{{Tmp}}\]
\[{\text{5}}{\text{.26 cal mo}}{{\text{l}}^{{\text{ - 1}}}}{{\text{K}}^{{\text{ - 1}}}}{\text{ = }}\dfrac{{{\text{1}}{\text{.435 \times 1}}{{\text{0}}^{\text{3}}}{\text{cal/mole}}}}{{{\text{Tmp}}}}\]
\[{\text{Tmp = }}\dfrac{{{\text{1}}{\text{.435 \times 1}}{{\text{0}}^{\text{3}}}{\text{cal/mole}}}}{{{\text{5}}{\text{.26 cal mo}}{{\text{l}}^{{\text{ - 1}}}}{{\text{K}}^{{\text{ - 1}}}}}}\]
\[{T_{mp}}_{\;} = {\text{ }}0.00027{\text{ }}K{\text{ }} = {\text{ }}{0^o}C\]
Therefore, the melting point of a liquid is \[{0^o}C\]
Hence, we can conclude that the option A is the correct option.

Note: We must know that the melting point of a substance is determined by measuring the temperature. And the entropy of fusion \[\left( {\Delta {S_{fusion}}} \right)\] is usually calculated by dividing the enthalpy of fusion \[\left( {\Delta {H_{fusion}}} \right)\] by the melting point temperature of a given liquid.
Usually for a given chemical reaction, we can find the change in the standard molar entropy of a reaction by the difference between the sum of the molar entropy of the products and the sum of the molar entropy of the reactants. The change of entropy on melting or fusion of a given liquid is a measure of the change in the structure when melting occurs, so change in entropy is dependent upon the chemical structure of a substance.