# Phase diagrams - Chemistry (2023)

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liquid and solid

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### learning goals

At the end of this section, you can:

• Explain the construction and use of a typical phase diagram.
• Use phase diagrams to identify stable phases at specific temperatures and pressures and to describe phase transitions that result from changes in these properties.
• Describe the supercritical fluid phase of matter.

The previous module described the change in equilibrium vapor pressure of a liquid with temperature. Given the definition of boiling point, the graphs of vapor pressure vs. temperature represent how the boiling point of the liquid changes with pressure. The use of heating and cooling curves to determine the melting (or freezing) point of a substance has also been described. Making these measurements over a wide range of pressures produces data that can be plotted as a phase diagram. TOphase diagramcombines pressure-temperature diagrams for the liquid-gas, solid-liquid, and solid-gas phase transition equilibria of a substance. These diagrams indicate the physical states that prevail under certain conditions of pressure and temperature and also give the pressure dependence of the phase transition temperatures (melting points, sublimation points, boiling points). A typical phase diagram for a pure substance is shown in[Shortcut].

The physical state of a substance and its phase transition temperatures are shown graphically on a phase diagram.

To illustrate the utility of these diagrams, consider the phase diagram for water shown in the figure.[Shortcut].

The pressure and temperature axes in this phase diagram of water are not drawn on a constant scale to illustrate several important properties.

We can use the phase diagram to identify the physical state of a water sample under specific conditions of pressure and temperature. For example, a pressure of 50 kPa and a temperature of -10 °C correspond to the area of ​​the diagram labeled "Ice". Under these conditions, water only exists in solid form (ice). A pressure of 50 kPa and a temperature of 50 °C correspond to the realm of "water"; here water only exists as a liquid. At 25 kPa and 200 °C, water is only in a gaseous state. Note that in the H2On the O-phase diagram, the pressure and temperature axes are not drawn on a constant scale to allow you to see several important features described here.

The BC curve in[Shortcut]is the graph of vapor pressure versus temperature as described in the previous module of this chapter. This "liquid-vapor" curve separates the liquid and gas regions of the phase diagram and gives the boiling point of water at any pressure. For example, at 1 atm, the boiling point is 100 °C. Note that the liquid-vapor curve ends at a temperature of 374 °C and a pressure of 218 atm, indicating that water cannot exist as a liquid above this temperature, regardless of pressure. Under these conditions, the physical properties of water are between those of its liquid and gas phase. This unique state of matter is called a supercritical fluid, a topic that is discussed in the next section of this module.

The solid vapor curve, called AB in[Shortcut], indicates the temperatures and pressures at which ice and water vapor are in equilibrium. These pairs of temperature and pressure data correspond to the points of sublimation or deposition of water. If we could extend the solid gas line[Shortcut]we would see that ice at -10 °C has a vapor pressure of about 0.20 kPa. Therefore, if we place a frozen sample in a vacuum with a pressure lower than 0.20 kPa, the ice will sublime. This is the basis of the "freeze-drying" process often used to preserve foods like the pictured ice cream.[Shortcut].

Freeze-dried foods like this ice cream are dehydrated by sublimation at pressures below the triple point of water. (Credit: ʺlwaoʺ/Flickr)

The solid-liquid curve labeled BD shows the temperatures and pressures at which ice and liquid water are in equilibrium, representing the melting/freezing points of water. Note that this curve has a slightly negative slope (heavily exaggerated for clarity), indicating that the melting point of water decreases slightly with increasing pressure. Water is an unusual substance in this regard, as most substances exhibit an increase in melting point with increasing pressure. This behavior is partially responsible for the movement of glaciers, as shown in[Shortcut]. The bottom of a glacier is under immense pressure due to its weight, which can melt some of the ice and create a layer of liquid water over which the glacier can slide more easily.

The immense pressure under the glaciers results in partial melting, creating a layer of water that provides lubrication to support glacial movement. This satellite photo shows the advance of the edge of the Perito Moreno Glacier in Argentina. (Image credit: NASA)

The intersection of the three curves is denoted by B in[Shortcut]. At the pressure and temperature represented by this point, the three aqueous phases coexist in equilibrium. This pair of temperature-pressure data is denoted astriple point. At pressures below the triple point, water cannot exist as a liquid, regardless of temperature.

Determination of the state of the water.
Using the phase diagram given for water[Shortcut], determine the condition of the water at the following temperatures and pressures:

(a) –10 °C y 50 kPa

(b) 25°C y 90 kPa

(Video) Phase Diagrams of Water & CO2 Explained - Chemistry - Melting, Boiling & Critical Point

(c) 50°C y 40 kPa

(d) 80°C y 5kPa

(e) -10°C y 0,3 kPa

(f) 50 °C y 0,3 kPa

Solution
Using the phase diagram of water, we can determine that the state of water at any temperature and pressure is: (a) solid; (b) liquid; (c) liquid; (d) gasoline; (e) solid; (f) gasoline.

What phase changes might the water undergo with changes in temperature if the pressure is maintained at 0.3 kPa? Is the pressure maintained at 50 kPa?

Respondedor:

Bei 0,3 kPa: $$\text{s}\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{g}$$bei −58 ° C. Bei 50 kPa: $$\text{s}\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{l}$$ bei 0 °C, l ⟶ g hasta 78 °C

Consider the phase diagram for carbon dioxide shown in[Shortcut]as another example. The solid-liquid curve slopes upward, indicating that the melting point of CO2it increases with pressure, as is the case with most substances (water is a notable exception, as described above). Note that the triple point is well above 1 atm, indicating that carbon dioxide cannot exist as a liquid under ambient pressure conditions. Instead, cooling carbon dioxide gas to 1 atm leads to its separation into a solid state. Similarly, solid carbon dioxide does not melt at 1 atm pressure, but sublimes into CO gas.2. Finally, note that the critical point for carbon dioxide is observed at a relatively modest temperature and pressure compared to water.

The pressure and temperature axes in this carbon dioxide phase diagram are not drawn on a constant scale to illustrate several important properties.

Determination of the state of carbon dioxide.
Using the phase diagram for carbon dioxide shown in FIG.[Shortcut], determine the state of CO2at the following temperatures and pressures:

(a) –30 °C y 2000 kPa

(b) –60 °C y 1000 kPa

(c) –60 °C y 100 kPa

(d) 20°C y 1500kPa

(e) 0°C y 100kPa

(f) 20 °C y 100 kPa

Solution
Using the phase diagram provided for carbon dioxide, we can determine the state of CO2at each specified temperature and pressure are as follows: (a) liquid; (b) solid; c) gasoline; (d) liquid; (e) gasoline; (f) gasoline.

Determine the phase changes that carbon dioxide undergoes when its temperature is varied while its pressure is held constant at 1500 kPa. At 500 kPa? At what approximate temperatures do these phase changes occur?

Respondedor:

bei 1500 kPa: $$\text{s}\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{l}$$ bei −45 °C , $$\text{l}\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{g}$$ bei −10 °C;

bei 500 kPa: $$\text{s}\phantom{\rule{0.2em}{0ex}}⟶\phantom{\rule{0.2em}{0ex}}\text{g}$$ bei −58 °C

If we place a sample of water in a closed container at 25°C, remove the air, and allow the evaporation-condensation equilibrium to settle, we are left with a mixture of liquid water and water vapor at a pressure of 0.03 atm. A clear boundary between the more dense liquid and the less dense gas is clearly observed. As we increase the temperature, the vapor pressure of water increases as described by the liquid-gas curve in the phase diagram of water ([Shortcut]) and a biphasic equilibrium of liquid and gas phase is maintained. At a temperature of 374 °C, the vapor pressure has increased to 218 atm, and any further increase in temperature leads to the disappearance of the boundary between the liquid and vapor phases. All the water in the tank is now in a single phase, with physical properties intermediate between the gaseous and liquid states. This phase of matter is calledsupercritical fluid, and the temperature and pressure above which this phase exists is thecritical point([Shortcut]). Above its critical temperature, a gas cannot be liquefied, no matter how much pressure is applied. The pressure required to liquefy a gas at its critical temperature is called the critical pressure. The critical temperatures and pressures of some common substances are given[Shortcut].

substanceCritical temperature (K)Critical pressure (atm)
hydrogen33.212.8
Nitrogen126,033,5
oxygen154,349,7
carbon dioxide304.273,0
Ammonia405,5111,5
sulfur dioxide430,377,7
Agua647,1217,7

(a) A sealed container of liquid carbon dioxide is heated slightly below its critical point, resulting in (b) the formation of the supercritical fluid phase. Cooling of the supercritical fluid reduces its temperature and pressure below the critical point, resulting in the re-establishment of the separate liquid and gas phases (c and d). The colored floats illustrate the density differences between liquid, gas, and supercritical fluid states. (Credit: modified work by "mrmrobin"/YouTube)

Like a gas, a supercritical fluid expands and fills a container, but its density is much greater than the typical densities of gases and is often similar to that of liquids. Like liquids, these liquids have the ability to dissolve non-volatile solutes. However, they have essentially no surface tension and very low viscosities, which allows them to more effectively penetrate very small openings in a solid mixture and remove soluble components. These properties make supercritical fluids extremely useful solvents for a variety of applications. For example, supercritical carbon dioxide has become a very popular solvent in the food industry, used to decaffeinate coffee, defat potato chips, and extract flavors and fragrances from citrus oils. It is non-toxic, relatively inexpensive, and not considered a pollutant. After use, CO2it can be easily recovered by reducing the pressure and collecting the resulting gas.

The critical temperature of carbon dioxide.
If we wave a carbon dioxide fire extinguisher on a cold day (18°C), we can hear liquid CO2splashing in the cylinder. However, the same cylinder appears to contain no liquid on a hot summer day (35°C). Explain these observations.

Solution
On cold days, the temperature of the CO2is below the critical temperature of CO2, 304 K o 31 °C ([Shortcut]), that is, liquid CO2is present in the cylinder. On hot days, the CO temperature decreases2is greater than its critical temperature of 31°C. Above this temperature, no amount of pressure can liquefy CO.2then there is no net CO2is present in the fire extinguisher.

Ammonia can be liquefied by compression at room temperature; Oxygen cannot be liquefied under these conditions. Why do the two gases behave differently?

Respondedor:

The critical temperature of ammonia is 405.5 K, which is above room temperature. The critical temperature of oxygen is below room temperature; therefore, oxygen cannot be liquefied at room temperature.

Decaffeination of coffee with supercritical CO2

Coffee is the second most traded commodity in the world after oil. All over the world, people love the aroma and taste of coffee. Many of us also rely on an ingredient in coffee, caffeine, to get us going in the morning or keep us awake in the afternoon. But at the end of the day, the stimulant effects of coffee can keep you from sleeping, so you may want to drink decaf at night.

Many methods of decaffeinating coffee have been used since the early 20th century. They all have advantages and disadvantages, and they all depend on the physical and chemical properties of the caffeine. Since caffeine is a somewhat polar molecule, it dissolves well in water, a polar liquid. However, since many of the more than 400 compounds that contribute to the flavor and aroma of coffee are also found in H2Hot water decaffeination processes can also remove some of these compounds, negatively affecting the odor and taste of decaffeinated coffee. dichloromethane (CH2Kl2) and ethyl acetate (CH3CO2C2H5) have a similar polarity to caffeine and are therefore very effective solvents for caffeine extraction, but both also remove some flavor and aroma components, and require long extraction and purification times to use. Because both of these solvents are toxic, health concerns have been raised about the effects of residual solvents left in decaffeinated coffee.

Supercritical liquid extraction with carbon dioxide is now widely used as a more effective and environmentally friendly decaffeination method.[Shortcut]). At temperatures above 304.2 K and pressures above 7376 kPa, CO2It is a supercritical fluid with gaseous and liquid properties. As a gas, it penetrates deep into the coffee beans; As a liquid, it effectively dissolves certain substances. Supercritical carbon dioxide extraction of steamed coffee beans removes 97-99% of the caffeine, leaving the flavor and aroma of the coffee intact. because CO2is a gas under standard conditions, its removal from the extracted coffee beans is easily accomplished, as is the recovery of the caffeine from the extract. The caffeine obtained from coffee beans through this process is a valuable product that can be used later as an additive in other foods or medicines.

(a) Caffeine molecules have polar and nonpolar regions, making them soluble in solvents of different polarities. (b) The schematic shows a typical decaffeination process using supercritical carbon dioxide.

(Video) Phase Changes, Heats of Fusion and Vaporization, and Phase Diagrams

The conditions of temperature and pressure under which a substance exists as a solid, liquid, and gas are summarized in a phase diagram for that substance. Phase diagrams are combined representations of three pressure and temperature equilibrium curves: solid-liquid, liquid-gas, and solid-gas. These curves represent the relationships between phase transition temperatures and pressures. The intersection of the three curves represents the triple point of the substance: the temperature and pressure at which the three phases are in equilibrium. At pressures below the triple point, a substance cannot exist in a liquid state, regardless of its temperature. The end point of the liquid-gas curve represents the critical point of the substance, the pressure and temperature above which a liquid phase cannot exist.

From the phase diagram for water ([Shortcut]), determine the condition of the water in:

(a) 35°C y 85 kPa

(b) –15 °C y 40 kPa

(c) –15 °C y 0,1 kPa

(d) 75°C y 3kPa

(e) 40°C y 0,1 kPa

(f) 60 °C y 50 kPa

(Video) Phase Diagrams

What phase changes occur when water is subjected to different pressures at a constant temperature of 0.005°C? 40 degrees? At -40°C?

At low pressures and 0.005 °C, water is a gas. When the pressure increases to 4.6 torr, the water solidifies; If the pressure increases further, it becomes liquid. At 40°C, water is steam at low pressure; at pressures above about 75 torr it becomes a liquid. At -40 °C, water changes from a gas to a solid when the pressure increases above very low values.

Pressure cookers allow food to cook faster because the higher pressure in the pressure cooker increases the boiling temperature of the water. A certain pressure cooker has a safety valve that releases steam when the pressure exceeds 3.4 atm. What is the approximate maximum temperature that can be reached in this pressure cooker? Explain your reasoning.

From the phase diagram of carbon dioxide in[Shortcut], determine the state of CO2No:

(a) 20 °C y 1000 kPa

(b) 10°C y 2000 kPa

(c) 10°C y 100 kPa

(d) -40°C y 500 kPa

(e) -80°C y 1500 kPa

(f) –80 °C y 10 kPa

(a liquid; (b) solid; (c) gas; (d) gas; (e) gas; (f) gasoline

Determine the phase changes that carbon dioxide undergoes when the pressure changes when the temperature is maintained at -50 °C. If the temperature stays at -40 °C? 20 degrees? (See the phase diagram in[Shortcut].)

Consider a cylinder containing a mixture of liquid carbon dioxide in equilibrium with gaseous carbon dioxide at an initial pressure of 65 atm and a temperature of 20°C. Draw a graph showing the change in cylinder pressure with time as carbon dioxide is released at constant temperature.

(Video) Phase diagrams | States of matter and intermolecular forces | Chemistry | Khan Academy

Trockeneis, Colorado2(S), does not melt at atmospheric pressure. It sublimes at a temperature of -78 °C. What is the lowest pressure at which CO2(S) melts into CO2(UE)? At approximately what temperature does this occur? (To see[Shortcut]for the phase diagram.)

If a severe storm causes a power outage, you may need to use a clothesline to dry your clothes. In many parts of the country, in the dead of winter, clothes freeze quickly when hung on a clothesline. If it doesn't snow, do they still dry? Explain your answer

Yes, the ice will sublime, although it can take several days. Ice has low vapor pressure and some ice molecules gasify and escape from ice crystals. Over time, more and more solids turn into gases until the clothes are finally dry.

Can nitrogen liquefy at room temperature (approx. 25°C)? Can sulfur dioxide be liquefied at room temperature? Justify your answers.

Elemental carbon has a gas phase, a liquid phase, and two distinct solid phases, as shown in the phase diagram:

(a) On the phase diagram, identify the gas and liquid regions.

(b) Graphite is the most stable carbon phase under normal conditions. Label the graphite phase on the phase diagram.

(c) When graphite is heated to 2500 K under standard conditions while increasing the pressure to 1010Pa, it will turn into a diamond. Label the diamond stage.

(d) Circle each triple point on the phase diagram.

(e) In what phase does carbon exist at 5000 K and 108Pai?

(f) When the temperature of a carbon sample increases from 3000 K to 5000 K at a constant pressure of 10°C6Pa, what phase transition can occur?

(A)

(B)

(C)

(D)

(e) liquid phase (f) sublimation

## glossary

critical point
Temperature and pressure above which a gas cannot condense into a liquid
phase diagram
Pressure-temperature diagram summarizing the conditions under which the phases of a substance can exist
supercritical fluid
substance at a temperature and pressure above its critical point; exhibits properties that lie between those of the gaseous and liquid states
triple point
Temperature and pressure at which the vapor, liquid, and solid phases of a substance are in equilibrium
(Video) Phase Diagram Explained, Examples, Practice Problems (Triple Point, Critical Point, Phase Changes)

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