What is the molar entropy change for melting of ice at 0℃, if ΔH𝒻 = 1.435 kcal/mol?

The correct option is 5.26 cal/(mol K).

To find the molar entropy change for the melting of ice (fusion), we use the thermodynamic relation for a phase change at constant temperature and pressure:
$$\Delta S_{\text{fus}}=\frac{\Delta H_{\text{fus}}}{T}$$
where:
- $\Delta S_{\text{fus}}$ is the molar entropy of fusion,
- $\Delta H_{\text{fus}}$ is the molar enthalpy of fusion (given as $1.435\text{kcal/mol}$),
- $T$ is the absolute temperature in Kelvin.

Step 1: Convert the temperature to Kelvin.
The melting point of ice is given as $0\text{℃}$.
$$T=0+273.15=273.15\text{K}$$
(We can approximate this as $273\text{K}$ for calculation purposes).

Step 2: Convert the enthalpy of fusion from kcal/mol to cal/mol.
Since $1\text{kcal}=1000\text{cal}$:
$$\Delta H_{\text{fus}}=1.435\times 1000=1435\text{cal/mol}$$

Step 3: Calculate the molar entropy change ($\Delta S_{\text{fus}}$).
Substitute the values into the entropy formula:
$$\Delta S_{\text{fus}}=\frac{1435\text{cal/mol}}{273\text{K}}$$
$$\Delta S_{\text{fus}}\approx 5.256\text{cal/(mol K)}$$
Rounding to three significant figures gives $5.26\text{cal/(mol K)}$.