Question

The standard molar entropies of water ice, liquid, and vapor are $37.99, 69.91$, and $188.83 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, respectively. On a single graph, show how the Gibbs energies of each of these phases vary with temperature.

Answer 1

Solution:

We know that $\Delta T$ (ice water) $<\Delta T_{\text {(liquid)}}<\Delta T$ (vapor)

by formula: $\Delta G_m = -S_m \Delta T$

We have $S_{m}^{\circ}$ is positive, $T>0 \Rightarrow G_m<0$

 

Phase	$S_{m}^{\circ}$ (J molK-1)	$G_m$ (J/mol)
Ice Water	37.99	-37.99
Liquid	69.91	-69.91
Vapor	188.83	-188.83

 

Therefore, $\Delta G_m$ (Ice Water) $< \Delta G_m($Liquid$) < \Delta G_m$ (Vapor)

Therefore, $\Delta G_m$ (Ice Water) $< \Delta G_m($Liquid$) < \Delta G_m$ (Vapor)