Question

Propanol \(\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\right)\) melts at \(-126.5^{\circ} \mathrm{C}\) and boils at \(97.4^{\circ} \mathrm{C}\). Draw a qualitative sketch of how the entropy changes as propanol vapor at \(150^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) is cooled to solid propanol at \(-150^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).

Short answer

A qualitative sketch of entropy vs. temperature for the cooling of propanol vapor can be divided into five steps: 1. Cooling of propanol vapor from \(150^{\circ} \mathrm{C}\) to \(97.4^{\circ} \mathrm{C}\), where the entropy decreases with a negative slope. 2. Phase change - condensation at \(97.4^{\circ} \mathrm{C}\), where entropy abruptly decreases. 3. Cooling of propanol liquid from \(97.4^{\circ} \mathrm{C}\) to \(-126.5^{\circ} \mathrm{C}\), where the entropy decreases with a less negative slope than the vapor phase. 4. Phase change - freezing at \(-126.5^{\circ} \mathrm{C}\), where entropy abruptly decreases again. 5. Cooling of propanol solid from \(-126.5^{\circ} \mathrm{C}\) to \(-150^{\circ} \mathrm{C}\), where the entropy decreases with a smaller slope than the liquid phase.

Step-by-step solution

Cooling of Propanol Vapor

As the propanol vapor cools down from \(150^{\circ} \mathrm{C}\) to its boiling point, \(97.4^{\circ} \mathrm{C}\), the particles lose energy and become more ordered. As a result, the entropy of propanol vapor will decrease with a negative slope.

Phase Change - Condensation

Propanol vapor will undergo a phase change and become a liquid at its boiling point, \(97.4^{\circ} \mathrm{C}\). During this phase change, the propanol particles become even more ordered due to stronger intermolecular forces. Entropy will abruptly decrease at this point.

Cooling of Propanol Liquid

As the liquid propanol cools down from the boiling point to its melting point, \(-126.5^{\circ} \mathrm{C}\), the particles continue to lose energy. As a result, the entropy will continue to decrease, but with a less negative slope than the vapor phase.

Phase Change - Freezing

Propanol will undergo another phase change and become a solid at its melting point, \(-126.5^{\circ} \mathrm{C}\). During this change, the particles will become highly ordered and fixed in their positions within the solid crystal lattice. The entropy will again abruptly decrease at this point.

Cooling of Propanol Solid

Finally, as the solid propanol cools down from its melting point, \(-126.5^{\circ} \mathrm{C}\), to \(-150^{\circ} \mathrm{C}\), the particles continue to lose energy and slight movement. Therefore, the entropy will continue to decrease but with a smaller slope than the liquid phase. Based on these entropy changes, a qualitative sketch of entropy vs. temperature can be drawn with decreasing slopes during cooling phases, abrupt drops during phase changes, and different slopes for each type of phase (vapor, liquid, and solid).