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 atm is cooled to solid propanol at \(-150^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).

Short Answer

Expert verified
The qualitative sketch of how the entropy changes as propanol goes from vapor at \(150^{\circ}\mathrm{C}\) to solid at \(-150^{\circ}\mathrm{C}\) will show a general continuous decreasing trend with steeper slopes during the points of phase transition, which are at \(97.4^{\circ}\mathrm{C}\) and \(-126.5^{\circ}\mathrm{C}\). The sketch will have the following features: 1) Initial decrease of entropy as vapor cools down, 2) A more dramatic decrease in entropy at the vapor to liquid phase transition, 3) Decrease of entropy as liquid cools down, 4) Another dramatic decrease in entropy at the liquid to solid phase transition, and 5) Decrease of entropy as solid cools down to its final temperature.

Step by step solution

01

Identify phase transitions

From the given information, we know that propanol melts at \(-126.5^{\circ}\mathrm{C}\) and boils at \(97.4^{\circ}\mathrm{C}\). Therefore, the phase transitions are as follows: 1. Cooling from vapor to liquid occurs at \(97.4{ }^{\circ} \mathrm{C}\). 2. Cooling from liquid to solid occurs at \(-126.5^{\circ} \mathrm{C}\).
02

Cooling from vapor to liquid

When cooling the propanol vapor from \(150^{\circ} \mathrm{C}\) to \(97.4^{\circ} \mathrm{C}\), the entropy decreases as the molecules lose energy and come closer together. As the temperature reaches the boiling point, the entropy of the system will decrease more dramatically due to the phase transition from vapor to liquid.
03

Cooling from liquid to solid

After the phase transition from vapor to liquid, the entropy continues to decrease as the liquid cools down to \(-126.5^{\circ}\mathrm{C}\). At the melting point, the liquid changes into a solid. Just like in the previous case, the entropy of the system decreases more dramatically due to the phase transition.
04

Cooling the solid

Once the propanol has changed into a solid, the entropy continues to decrease as it cools down to \(-150^{\circ}\mathrm{C}\). In the solid phase, the entropy decreases at a slower rate compared to the phase transitions.
05

Drawing the qualitative sketch

Combine the information from the previous steps to draw a qualitative sketch of how the entropy changes during the cooling process of propanol from \(150^{\circ}\mathrm{C}\) vapor to \(-150^{\circ}\mathrm{C}\) solid. The sketch should show the following major features: 1. Initial decrease of entropy as vapor cools down. 2. A more dramatic decrease in entropy at the vapor to liquid phase transition. 3. Decrease of entropy as liquid cools down. 4. Another dramatic decrease in entropy at the liquid to solid phase transition. 5. Decrease of entropy as solid cools down to its final temperature. The entropy will have a general continuous decreasing trend with steeper slopes during the points of phase transition.

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Most popular questions from this chapter

(a) What sign for \(\Delta S\) do you expect when the pressure on 0.600 mol of an ideal gas at \(350 \mathrm{~K}\) is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change? Explain.

Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly? (b) If the ice cube melts reversibly, is \(\Delta E\) zero for the process? Explain.

For each of the following pairs, indicate which substance possesses the larger standard entropy: (a) \(1 \mathrm{~mol}\) of \(\mathrm{P}_{4}(g)\) at \(300^{\circ} \mathrm{C}, 0.01 \mathrm{~atm},\) or \(1 \mathrm{~mol}\) of \(\mathrm{As}_{4}(g)\) at \(300^{\circ} \mathrm{C}, 0.01 \mathrm{~atm} ;\) (b) \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}(g)\) at \(100^{\circ} \mathrm{C}, 1 \mathrm{~atm},\) or \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(100^{\circ} \mathrm{C}, 1 \mathrm{~atm} ;\) (c) \(0.5 \mathrm{~mol}\) of \(\mathrm{N}_{2}(g)\) at \(298 \mathrm{~K}, 20-\mathrm{L}\) volume, or \(0.5 \mathrm{~mol} \mathrm{CH}_{4}(g)\) at \(298 \mathrm{~K}, 20-\mathrm{L}\) volume; (d) \(100 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}(s)\) at \(30^{\circ} \mathrm{C}\) or \(100 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)\) at \(30^{\circ} \mathrm{C}\)

In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) or \(\mathrm{C}_{2} \mathrm{H}_{6}(g),(\mathbf{b}) \mathrm{CO}_{2}(g)\) or \(\mathrm{CO}(g) ?\) Explain.

Octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) is a liquid hydrocarbon at room temperature that is the primary constituent of gasoline. (a) Write a balanced equation for the combustion of \(\mathrm{C}_{8} \mathrm{H}_{18}(l)\) to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) (b) Without using thermochemical data, predict whether \(\Delta G^{\circ}\) for this reaction is more negative or less negative than \(\Delta H^{\circ}\).

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