Question

The enthalpy of fusion of water is 1.435 kcal \[mo{l^{ - 1}}\]. The molar entropy change for the melting of ice at 0 is:
a.) 5.260 \[\dfrac{{cal}}{{mol\,K}}\]
b.) 0.526 \[\dfrac{{cal}}{{mol\,K}}\]
c.) 10.52 \[\dfrac{{cal}}{{mol\,K}}\]
d.) 21.04 \[\dfrac{{cal}}{{mol\,K}}\]

Answer 1

Hint: The change of entropy for phase change of a substance is equal to the ratio of change of enthalpy and the temperature at which the change is taking place. This is into consideration that the surrounding pressure remains constant during the phase change.

Complete step by step answer:
Entropy is the measure of the system's thermal energy per unit temperature that is unavailable for doing useful work. As the work is obtained from ordered molecular motion, the amount of entropy is also a measure of the molecular disorderness, or the measure of randomness of a system. The idea of entropy provides a mathematical way to check which processes are not feasible, even if they do not violate the fundamental law of conservation of energy.
Now, in the given question:
The enthalpy of fusion of ice = 1.435 kcal \[mo{l^{ - 1}}\]
The reaction involved is:
\[{H_2}{O_{(s)}} \to {H_2}{O_{(l)}}\]
Now, we know that
The change in entropy in a phase change reaction = \[\dfrac{{The\,enthalpy\,change\,in\,the\,reaction}}{{Temperature}}\]
\[ \Rightarrow \Delta S = \dfrac{{\Delta H}}{T}\]
\[ \Rightarrow \Delta S = \dfrac{{1.435 \times 1000}}{{273}}\dfrac{{cal}}{{mol\,K}}\]
\[ \Rightarrow \Delta S = 5.260\dfrac{{cal}}{{mol\,K}}\]
Therefore, the molar entropy change for the melting of ice at 0 is \[5.260\dfrac{{cal}}{{mol\,K}}\].
Hence, the correct answer is (A) \[5.260\dfrac{{cal}}{{mol\,K}}\].

Note: Make sure to check the units in the option. One can give the options in some other units as well to confuse the student. As in this question, kcal was to be converted to calories and Celsius was to be converted to Kelvins.