Chemical Thermodynamics: Real-World Scenarios (8)

Question

When 1 mole of ice melts at 0°C and 1 atm, it absorbs 6.01 kJ of heat. Find $\Delta H$, $\Delta S$, and $\Delta G$ for this process. Then determine if ice will spontaneously melt at 263 K (−10°C), assuming $\Delta H$ and $\Delta S$ are temperature-independent.

Solution — Step by Step

Why This Works

The Gibbs equation $\Delta G = \Delta H - T \Delta S$ is the master criterion for spontaneity at constant temperature and pressure. When $\Delta G < 0$, the process is spontaneous; when $\Delta G > 0$, the reverse process is spontaneous; at $\Delta G = 0$, the system is at equilibrium.

For phase transitions, $\Delta H$ and $\Delta S$ are roughly constant (we assume them so), and the transition temperature is the unique $T$ at which they balance: $T_{\text{transition}} = \Delta H / \Delta S$.

Alternative Method

Estimate $\Delta G$ using the formula directly without finding the transition temperature first. At any $T$:

$\Delta G(T) = \Delta H - T \Delta S$

Plug $T = 263$: get $+224$ J. Plug $T = 273$: get 0. Plug $T = 283$: get $-220$ J. The sign change happens at 273 K.

Final answer: $\Delta H = +6.01$ kJ/mol, $\Delta S = +22.0$ J/(mol·K). At 263 K, $\Delta G = +224$ J/mol > 0, so melting is non-spontaneous (ice stays ice).