Chapter 12: Problem 34
Draw the general shape of the temperature-energy graph for the cooling of acetone from \(100^{\circ} \mathrm{C}\) to \(-100{ }^{\circ} \mathrm{C}\). (Given: .\(\left.\mathrm{Mp}=-95.4^{\circ} \mathrm{C} ; \mathrm{Bp}=56.2^{\circ} \mathrm{C}\right)\)
Short Answer
Expert verified
The graph shows a diagonal drop, a plateau at \(56.2^{\circ} \mathrm{C}\), another drop, a plateau at \(-95.4^{\circ} \mathrm{C}\), and a final drop.
Step by step solution
01
Understand the States of Acetone
Acetone begins at a temperature of \(100^{\circ} \mathrm{C}\), which is above its boiling point (\(56.2^{\circ} \mathrm{C}\)). Initially, acetone will be in the gaseous state. It cools down from here to \(-100^{\circ} \mathrm{C}\), past both its boiling and melting points.
02
Identify Phase Transitions
As acetone cools from \(100^{\circ} \mathrm{C}\), the first phase transition occurs at its boiling point \(56.2^{\circ} \mathrm{C}\), where it changes from a gas to a liquid. The second phase transition is at the melting point \(-95.4^{\circ} \mathrm{C}\), where acetone solidifies from liquid to solid.
03
Plot Temperature vs Energy for Gas to Liquid
Start the graph with a downward sloping line from \(100^{\circ} \mathrm{C}\) until \(56.2^{\circ} \mathrm{C}\), indicating cooling as a gas. Then, draw a horizontal line at \(56.2^{\circ} \mathrm{C}\) representing the energy release as acetone condenses -- the temperature remains constant during this phase change.
04
Plot Temperature vs Energy for Liquid to Solid
Continue the graph with a downward slope from \(56.2^{\circ} \mathrm{C}\) to \(-95.4^{\circ} \mathrm{C}\), showing continued cooling as a liquid. At \(-95.4^{\circ} \mathrm{C}\), draw another horizontal line, indicating the phase transition from liquid to solid.
05
Plot Temperature vs Energy for Cooling Solid
After the phase change, draw another downward sloping line from \(-95.4^{\circ} \mathrm{C}\) to \(-100^{\circ} \mathrm{C}\) to show the cooling of solid acetone. This final section of the graph completes the cooling process.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Temperature-Energy Graph
A temperature-energy graph is a way to visually represent the changes in temperature and energy of a substance as it undergoes phase transitions. It generally displays how temperature changes as the system either absorbs or releases energy. For acetone, as it cools from a high temperature to a low temperature, this graph becomes a handy tool to understand its behavior at various states.
Initially, you have acetone starting in its gaseous state. As energy is released and temperature drops from 100°C, the graph shows a downward slope until it hits 56.2°C, acetone's boiling point. At this point, instead of continuing to drop, the graph becomes a horizontal line. This occurrence signals that the energy is not changing the temperature but is being used to convert gas into liquid.
As the temperature continues to lower after this phase change, you'll notice another slope on the graph until it reaches -95.4°C, where acetone melts into a solid. Graphically, this is represented with another flat line. Below -95.4°C, the graph resumes a downward slope as solid acetone continues to cool to -100°C.
Initially, you have acetone starting in its gaseous state. As energy is released and temperature drops from 100°C, the graph shows a downward slope until it hits 56.2°C, acetone's boiling point. At this point, instead of continuing to drop, the graph becomes a horizontal line. This occurrence signals that the energy is not changing the temperature but is being used to convert gas into liquid.
As the temperature continues to lower after this phase change, you'll notice another slope on the graph until it reaches -95.4°C, where acetone melts into a solid. Graphically, this is represented with another flat line. Below -95.4°C, the graph resumes a downward slope as solid acetone continues to cool to -100°C.
Cooling Curves
Cooling curves are graphs that depict how a substance’s temperature changes over time as it loses heat, often through the energy exchange with its environment. They are essential for illustrating phase changes and the periods where energy is used to alter the state of the substance rather than its temperature.
For acetone, the cooling curve starts at 100°C with the substance in a gaseous state. The downward slope from 100°C to 56.2°C shows the cooling process of the gas. Once acetone reaches 56.2°C, the energy released does not drop the temperature further but achieves the condensation of gas into a liquid. This is represented by a flat, horizontal line in the cooling curve.
From 56.2°C to -95.4°C, another downward line is observed, indicating the cooling of liquid acetone until it starts to solidify. At its melting point, -95.4°C, a second flat line is seen, where the remaining energy focuses on solidifying the liquid into a solid. Finally, a downward slope resumes as solid acetone continues to release energy down to -100°C.
For acetone, the cooling curve starts at 100°C with the substance in a gaseous state. The downward slope from 100°C to 56.2°C shows the cooling process of the gas. Once acetone reaches 56.2°C, the energy released does not drop the temperature further but achieves the condensation of gas into a liquid. This is represented by a flat, horizontal line in the cooling curve.
From 56.2°C to -95.4°C, another downward line is observed, indicating the cooling of liquid acetone until it starts to solidify. At its melting point, -95.4°C, a second flat line is seen, where the remaining energy focuses on solidifying the liquid into a solid. Finally, a downward slope resumes as solid acetone continues to release energy down to -100°C.
Acetone Properties
Acetone, known by its chemical formula \(\text{C}_3\text{H}_6\text{O}\), is a small organic molecule with distinct physical properties due to its simple structure. It’s characterized by having a relatively low boiling point and a typical ketone odor often associated with nail polish remover and paint thinners.
One of the noteworthy properties of acetone is its boiling point at 56.2°C, which is lower than water. This low boiling point makes it quite volatile and easy to evaporate. Additionally, the melting point is crucial for understanding its cooling curve; at -95.4°C, acetone transitions from a liquid to a solid. These properties affect how it undergoes phase changes when energy is released or absorbed.
Acetone also dissolves in water and many other organic solvents, which is why it’s so extensively used in industry and laboratories. Its balancing act of easily transitioning between phases gives it importance in various temperature-dependent processes.
One of the noteworthy properties of acetone is its boiling point at 56.2°C, which is lower than water. This low boiling point makes it quite volatile and easy to evaporate. Additionally, the melting point is crucial for understanding its cooling curve; at -95.4°C, acetone transitions from a liquid to a solid. These properties affect how it undergoes phase changes when energy is released or absorbed.
Acetone also dissolves in water and many other organic solvents, which is why it’s so extensively used in industry and laboratories. Its balancing act of easily transitioning between phases gives it importance in various temperature-dependent processes.
Phase Change
Phase change is the process during which a substance transitions between different states of matter: solid, liquid, and gas. These changes occur due to energy exchange, where energy is either absorbed or released by the substance. Phase changes do not alter the chemical composition of a substance, but they do affect its physical properties.
When acetone is cooled, it undergoes phase transitions at defined temperatures known as its boiling and melting points. At 56.2°C, acetone condenses from gas to liquid, this is known as condensation, a phase change involving energy release. Contrary to lowering temperature, the energy is harnessed to facilitate the phase shift.
When acetone reaches -95.4°C, it solidifies – a process termed freezing. Again, energy is focused on the transformation instead of temperature change. Understanding these transitions is crucial for predicting how substances will react in varied environmental conditions and for practical applications in cooling and heating systems.
When acetone is cooled, it undergoes phase transitions at defined temperatures known as its boiling and melting points. At 56.2°C, acetone condenses from gas to liquid, this is known as condensation, a phase change involving energy release. Contrary to lowering temperature, the energy is harnessed to facilitate the phase shift.
When acetone reaches -95.4°C, it solidifies – a process termed freezing. Again, energy is focused on the transformation instead of temperature change. Understanding these transitions is crucial for predicting how substances will react in varied environmental conditions and for practical applications in cooling and heating systems.
