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Chapter 11: Problem 57

(a) What is the significance of the critical point in a phase diagram? (b) Why does the line that separates the gas and liquid phases end at the critical point?

Short Answer

Expert verified
(a) In a phase diagram, the critical point is the unique temperature and pressure at which the gas and liquid phases of a substance have identical densities and become indistinguishable. It signifies the highest temperature and pressure at which a gas can be liquefied and marks the transition of a substance into a supercritical fluid that exhibits properties of both gas and liquid phases. (b) The gas-liquid phase boundary ends at the critical point because, beyond this point, the gas and liquid phases become indistinguishable and the substance exists as a supercritical fluid. Thus, it is not possible to separate the gas and liquid phases beyond the critical point.

Step by step solution

01

(a) Significance of the critical point

In a phase diagram, the critical point refers to the unique temperature and pressure at which the gas and liquid phases of a substance have identical densities and become indistinguishable from each other. This point denotes the end of the gas-liquid phase boundary and signifies the highest temperature and pressure at which a gas can be liquefied by an increase in pressure. Beyond the critical point, the substance is referred to as a supercritical fluid that exhibits properties of both gas and liquid phases. The critical point is significant as it provides information on the conditions under which a substance can transition between the gas and liquid phase.
02

(b) Gas-Liquid phase boundary ending at the critical point

The line that separates the gas and liquid phases in a phase diagram is known as the phase boundary. This boundary represents the set of conditions (temperature and pressure) under which the substance can coexist in both gas and liquid phases. The phase boundary ends at the critical point because this is the point at which the gas and liquid phases become indistinguishable from each other. Beyond the critical point, there are no distinct gas and liquid phases, and the substance exists as a supercritical fluid. As a result, it isn't possible to separate the gas and liquid phases beyond the critical point, which is why the gas-liquid phase boundary ends at this point.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Critical Point
The critical point on a phase diagram is crucial because it marks the specific temperature and pressure where a gas and liquid become indistinguishable. Imagine heating water in a closed container; as temperature and pressure increase, a state is eventually reached where no matter how much pressure is added, the substance cannot become a separate liquid form.
At this unique critical point, the densities of the gas and liquid are the same, making them indistinguishable.
  • This is the highest temperature and pressure combination where liquid can still form from gas by compressing it.
  • Beyond this point, both states blend, and the result is called a "supercritical fluid."
Understanding this concept gives insight into how substances behave under extreme conditions, important for various scientific and industrial applications.
What is a Supercritical Fluid?
A supercritical fluid is a state of matter that forms beyond the critical point. It happens when a substance is subjected to both temperatures and pressures higher than their respective critical values. In this state, the substance doesn鈥檛 fit neatly into a liquid or gas category, displaying unique characteristics.
For example, a supercritical fluid can effuse through solids like a gas but can dissolve materials similar to a liquid.
  • This unique behavior makes them highly useful, such as in supercritical fluid extraction, where it's used to decaffeinate coffee or to extract essential oils.
  • They can be environmentally friendly solvents, offering an alternative to organic solvents that are harmful to the environment.
Supercritical fluids combine the expanding force of gas and the dissolving power of liquids.
Gas-Liquid Phase Boundary Demystified
In a phase diagram, the gas-liquid phase boundary represents conditions under which a substance can exist as both a gas and a liquid simultaneously. This line or boundary is crucial for predicting the phase behavior of the material.
It ends at the critical point because beyond that, the clear distinctions between gas and liquid cease to exist, and the substance becomes a supercritical fluid.
  • The phase boundary guides scientists in understanding how to manipulate temperature and pressure to achieve desired phases for industrial processes.
  • It's important when designing equipment that uses gas or liquid phases, ensuring proper function under set temperature and pressure ranges.
Beyond the critical point, the phase transition becomes irrelevant as no distinct phases are present, making the gas-liquid phase boundary an essential feature of phase diagrams.

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Most popular questions from this chapter

Propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) is pressurized into liquid and stored in cylinders to be used as a fuel. The normal boiling point of propane is listed as \(-42^{\circ} \mathrm{C}\). (a) When converting propane into liquid at room temperature of \(25^{\circ} \mathrm{C},\) would you expect the pressure in the tank to be greater or less than atmospheric pressure? How does the pressure within the tank depend on how much liquid propane is in it? (b) Suppose the fuel tank leaks and a few liters of propane escape rapidly. What do you expect would happen to the temperature of the remaining liquid propane in the tank? Explain. (c) How much heat must be added to vaporize \(20 \mathrm{~g}\) of propane if its heat of vaporization is \(18.8 \mathrm{~kJ} / \mathrm{mol} ?\) What volume does this amount of propane occupy at \(100 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C} ?\)

(a) What is the significance of the triple point in a phase diagram? (b) Could you measure the triple point of water by measuring the temperature in a vessel in which water vapor, liquid water, and ice are in equilibrium under \(101.32 \mathrm{kPa}\) of air? Explain.

You are high up in the mountains and boil water to make some tea. However, when you drink your tea, it is not as hot as it should be. You try again and again, but the water is just not hot enough to make a hot cup of tea. Which is the best explanation for this result? (a) High in the mountains, it is probably very dry, and so the water is rapidly evaporating from your cup and cooling it. (b) High in the mountains, it is probably very windy, and so the water is rapidly evaporating from your cup and cooling it. (c) High in the mountains, the air pressure is significantly less than \(101.3 \mathrm{kPa}\), so the boiling point of water is much lower than at sea level. (d) High in the mountains, the air pressure is significantly less than \(101.3 \mathrm{kPa}\), so the boiling point of water is much higher than at sea level.

(a) What atoms must a molecule contain to participate in hydrogen bonding with other molecules of the same kind? (b) Which of the following molecules can form hydrogen bonds with other molecules of the same kind: \(\mathrm{CH}_{3} \mathrm{~F}, \mathrm{CH}_{3} \mathrm{NH}_{2}, \mathrm{CH}_{3} \mathrm{OH}, \mathrm{CH}_{3} \mathrm{Br} ?\)

Which member in each pair has the stronger intermolecu- lar dispersion forces? (a) \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{CH}_{3} \mathrm{OH},\) (b) \(\mathrm{CBr}_{3} \mathrm{CBr}_{3}\) or (c) \(\mathrm{C}\left(\mathrm{CH}_{3}\right)_{4}\) or \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\) \(\mathrm{CCl}_{3} \mathrm{CCl}_{3}\)
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