Entropy Calculations: Phase Changes in Liquids

Entropy of Liquids

Entropy Calculations During Phase Changes

When a substance undergoes a phase change, such as fusion (melting) or vaporization (boiling), there is a change in entropy (ΔS). Entropy is a measure of the disorder or randomness in a system. The entropy change associated with these phase transitions can be calculated using the enthalpy change (ΔH) and the temperature at which the phase change occurs (Tmp for melting point, Tbp for boiling point).

• Entropy of Fusion (ΔSfus): The entropy change when a solid melts to become a liquid at its melting point.

• Entropy of Vaporization (ΔSvap): The entropy change when a liquid becomes a gas at its boiling point.

Key Formulas

• Entropy of Fusion:

$\Delta S_{fus} = \frac{\Delta H_{fus}}{T_{mp}}$

• Entropy of Vaporization:

$\Delta S_{vap} = \frac{\Delta H_{vap}}{T_{bp}}$

Where:

• $\Delta H_{fus}$ = enthalpy of fusion (energy required to melt 1 mole of substance)

• $\Delta H_{vap}$ = enthalpy of vaporization (energy required to vaporize 1 mole of substance)

• $T_{mp}$ = melting point (in Kelvin)

• $T_{bp}$ = boiling point (in Kelvin)

Example: Calculating Entropy of Fusion

Problem: Methanol has a normal melting point of 64.7°C and an entropy of fusion of 9.36 J/K. Determine its enthalpy of fusion.

• Solution: Rearranging the formula for entropy of fusion:

$\Delta H_{fus} = \Delta S_{fus} \times T_{mp}$

• Convert melting point to Kelvin: $T_{mp} = 64.7 + 273.15 = 337.85\ \text{K}$

• Calculate enthalpy of fusion:

$\Delta H_{fus} = 9.36\ \text{J/K} \times 337.85\ \text{K} = 3162.2\ \text{J}$

• Final Answer: 3162 joules or 3.16 kJ

Practice Problem

Problem: Calculate entropy of vaporization of 8.4 g of acetic acid (CH3COOH) with a boiling point of 118°C. $\Delta H_{vap} = 21.7$ kJ/mol.

• Solution Steps:

• Convert boiling point to Kelvin: $T_{bp} = 118 + 273.15 = 391.15\ \text{K}$

• Calculate entropy of vaporization per mole:

$\Delta S_{vap} = \frac{21,700\ \text{J/mol}}{391.15\ \text{K}} = 55.5\ \text{J/(mol·K)}$

• To find the entropy change for 8.4 g, first calculate moles of acetic acid (molar mass = 60.05 g/mol):

$\text{Moles} = \frac{8.4\ \text{g}}{60.05\ \text{g/mol}} = 0.14\ \text{mol}$

$\Delta S_{vap,\ total} = 0.14\ \text{mol} \times 55.5\ \text{J/(mol·K)} = 7.77\ \text{J/K}$

• Final Answer: 7.77 J/K

Additional info: The practice problem answer is inferred based on standard calculation steps for entropy of vaporization.