Calculate the molal entropy of fusion and vaporisation of ethyl alcohol which melts at 158.8 K and boils at 351.5 K. The latent heat of fusion and vaporisation are 108 kJ/kg and 855 kJ/kg respectively.
The correct answer and explanation is :
To calculate the molal entropy changes of fusion and vaporization for ethyl alcohol (ethanol), we can use the following formula:
[ \Delta S = \frac{\Delta H}{T} ]
Where:
- ( \Delta S ) is the entropy change (J/mol·K)
- ( \Delta H ) is the enthalpy change (heat of fusion or vaporization) in joules
- ( T ) is the absolute temperature (K) at which the phase transition occurs
Given Data:
- Melting Point (Fusion):
- Melting temperature: 158.8 K
- Latent heat of fusion: 108 kJ/kg
- Molar mass of ethanol: 46.07 g/mol
- Boiling Point (Vaporization):
- Boiling temperature: 351.5 K
- Latent heat of vaporization: 855 kJ/kg
Calculations:
- Entropy Change for Fusion:
- Convert the latent heat of fusion to J/mol:
[ \Delta H_{\text{fusion}} = 108\, \text{kJ/kg} \times 46.07\, \text{g/mol} = 4,981.56\, \text{J/mol} ] - Calculate the entropy change:
[ \Delta S_{\text{fusion}} = \frac{\Delta H_{\text{fusion}}}{T_{\text{fusion}}} = \frac{4,981.56\, \text{J/mol}}{158.8\, \text{K}} \approx 31.3\, \text{J/mol·K} ]
- Entropy Change for Vaporization:
- Convert the latent heat of vaporization to J/mol:
[ \Delta H_{\text{vaporization}} = 855\, \text{kJ/kg} \times 46.07\, \text{g/mol} = 39,357.85\, \text{J/mol} ] - Calculate the entropy change:
[ \Delta S_{\text{vaporization}} = \frac{\Delta H_{\text{vaporization}}}{T_{\text{vaporization}}} = \frac{39,357.85\, \text{J/mol}}{351.5\, \text{K}} \approx 112.9\, \text{J/mol·K} ]
Explanation:
Entropy is a measure of the disorder or randomness of a system. During phase transitions, such as melting and boiling, the entropy of the system changes due to the rearrangement of molecules.
- Fusion (Melting): When ethanol transitions from solid to liquid at its melting point (158.8 K), the entropy increases because the structured arrangement of molecules in the solid state becomes more disordered in the liquid state. The calculated entropy change for fusion is approximately 31.3 J/mol·K.
- Vaporization (Boiling): When ethanol transitions from liquid to gas at its boiling point (351.5 K), there is a significant increase in entropy. The molecules in the gas phase are much more disordered and have greater freedom of movement compared to the liquid phase. The calculated entropy change for vaporization is approximately 112.9 J/mol·K.
These entropy changes are consistent with the expectations for phase transitions, where the disorder increases from solid to liquid and further from liquid to gas. The larger entropy change during vaporization compared to fusion reflects the greater degree of disorder associated with the transition from liquid to gas.