Question

Free energy, $G=H-T\Delta S$, is a state function that indicates whether a reaction is spontaneous or non-spontaneous. If you think of $TS$ as the part of the system`s energy that is disordered already, then $(H-TS)$ is the part of the system`s energy that is still ordered and therefore free to cause spontaneous change by becoming disordered.
Also, $\Delta G=\Delta H-T\Delta S$
From the second law of Thermodynamics, a reaction is spontaneous if ${\Delta }_{total}S$ is positive, non-spontaneous if ${\Delta }_{total}S$ is negative, and at equilibrium if ${\Delta }_{total}S$ is zero.
Since, $-T\Delta S=\Delta G$ and since $\Delta G$ and $\Delta S$ have opposite signs, we can restate the Thermodynamic criterion for the spontaneity of a reaction carried out at a constant temperature and pressure.
If $\Delta G<0$, the reaction is spontaneous
If $\Delta G>0$, the reaction is non-spontaneous
If $\Delta G=0$, the reaction is at equilibrium
Read the above paragraph carefully and answer the following questions based on the above comprehension.

One mol of ice is converted to liquid at $273K$; $H_{2}O\left(s\right)$ and $H_{2}O\left(l\right)$ have entropies $38.20$ and $60.03Jmo{l}^{-1}d{g}^{-1}$. Enthalpy change in the conversion will be:

• A. $59.59Jmo{l}^{-1}$
• B. $593.95Jmo{l}^{-1}$
• C. $5959.5Jmo{l}^{-1}$
• D. $59595Jmo{l}^{-1}$

Answer 1

Answer: (C)

$5959.5Jmo{l}^{-1}$

The conversion of ice to liquid water is an equilibrium process where $G$=0.

Therefore, $\Delta H$ = $T\Delta S$

Now, $S$ = ($S_2-S_1$) = 60.03-38.2 = 21.83 J/mol dg or J/mol K

Thus, $\Delta H$ = 273 x 21.83 = 5959.5 J/mol.