For propane, the ∆H° of vaporization is 22.90 kJ/mol and the ∆S° of vaporization is 99.0 J/mol･K. At 1.00 atm and 220.5 K, what is the ∆G° of vaporization for propane, in kJ/mol?

To calculate the standard Gibbs free energy change (\(\Delta G^\circ\)) for the vaporization of propane, we use the following equation:

\[
\Delta G^\circ = \Delta H^\circ - T \Delta S^\circ
\]

Where:
- \(\Delta G^\circ\) is the Gibbs free energy change,
- \(\Delta H^\circ\) is the enthalpy change,
- \(T\) is the temperature in Kelvin (220.5 K in this case),
- \(\Delta S^\circ\) is the entropy change.

Given:
- \(\Delta H^\circ = 22.90 \, \text{kJ/mol}\),
- \(\Delta S^\circ = 99.0 \, \text{J/mol} \cdot \text{K} = 0.0990 \, \text{kJ/mol} \cdot \text{K}\) (since we need the units to match, convert J to kJ by dividing by 1000),
- \(T = 220.5 \, \text{K}\).

Now, applying the values to the equation:

\[
\Delta G^\circ = 22.90 \, \text{kJ/mol} - (220.5 \, \text{K} \times 0.0990 \, \text{kJ/mol} \cdot \text{K})
\]

\[
\Delta G^\circ = 22.90 \, \text{kJ/mol} - 21.835 \, \text{kJ/mol}
\]

\[
\Delta G^\circ = 1.065 \, \text{kJ/mol}
\]

Therefore, the standard Gibbs free energy change for the vaporization of propane at 220.5 K and 1.00 atm is \(\Delta G^\circ = 1.065 \, \text{kJ/mol}\).

Would you like to explore the concepts of Gibbs free energy or related thermodynamic principles further? 

Here are 5 related questions:
1. How does the sign of \(\Delta G^\circ\) determine spontaneity in chemical processes?
2. Why do we convert entropy from J/mol·K to kJ/mol·K in Gibbs free energy calculations?
3. How would increasing the temperature affect \(\Delta G^\circ\) for propane vaporization?
4. Can \(\Delta G^\circ\) ever be zero for a phase change? If so, under what conditions?
5. What is the physical significance of enthalpy and entropy in phase transitions?

**Tip:** Always ensure the units of enthalpy (\(\Delta H\)) and entropy (\(\Delta S\)) match when applying them in the Gibbs free energy formula.

Learn how to calculate the standard Gibbs free energy change (ΔG°) for the vaporization of propane at 220.5 K and 1.00 atm. This problem involves thermodynamic concepts such as enthalpy, entropy, and the Gibbs free energy equation. Suitable for undergraduate chemistry and physics students.

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