Entropy Change During Vaporization of Methanol

Q4. What is the change in entropy that occurs in the system when 1.00 mol of methanol (CH3OH) vaporizes from a liquid to a gas at its boiling point (64.6°C)? For methanol, ΔHvap = 35.2 kJ/mol.

Background

Topic: Thermodynamics – Entropy Change During Phase Transitions

This question tests your understanding of how to calculate the entropy change ($\Delta S$) for a substance undergoing a phase change (liquid to gas) at its boiling point. The process is isothermal, and the heat absorbed is equal to the enthalpy of vaporization.

Key Terms and Formulas

• Entropy ($\Delta S$): A measure of disorder or randomness in a system.

• Enthalpy of vaporization ($\Delta H_{vap}$): The energy required to convert 1 mole of a liquid to a gas at constant temperature and pressure.

• Boiling point: The temperature at which the liquid turns into gas (here, 64.6°C).

• Formula for entropy change during a phase transition:

$\Delta S = \frac{q_{\text{rev}}}{T}$

Where $q_{\text{rev}}$ is the heat absorbed in a reversible process (here, $\Delta H_{vap}$), and $T$ is the absolute temperature in Kelvin.

Step-by-Step Guidance

1. Convert the boiling point from Celsius to Kelvin:

   $T = 64.6^\circ \text{C} + 273.15$

2. Express the enthalpy of vaporization in joules (since entropy is typically in J/K):

   $\Delta H_{vap} = 35.2 \text{ kJ/mol} \times 1000 \text{ J/kJ}$

3. Plug the values into the entropy change formula:

   $\Delta S = \frac{\Delta H_{vap}}{T}$

4. Set up the calculation with your converted values, but do not solve yet:

   $\Delta S = \frac{35,200 \text{ J/mol}}{T}$

Try solving on your own before revealing the answer!

Final Answer: 98.2 J/mol·K

$\Delta S = \frac{35,200 \text{ J/mol}}{337.75 \text{ K}} = 104.2 \text{ J/mol·K}$

The entropy change is positive, reflecting increased disorder as methanol vaporizes.