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10.5: Los diagramas de fase

  • Page ID
    1880
  • habilidades para desarrollar 

    • Explicar la construcción y el uso de un diagrama de fase típico.

    • Use diagramas de fase para identificar fases estables a temperaturas y presiones dadas, y para describir las transiciones de fase resultantes de cambios en estas propiedades

    • Describir la fase fluida supercrítica de la materia.

    En el módulo anterior, se describió la variación de la presión de vapor de equilibrio de un líquido con la temperatura. Considerando la definición del punto de ebullición, los gráficos de presión de vapor versus temperatura representan cómo el punto de ebullición del líquido varía con la presión. También se describió el uso de curvas de calentamiento y enfriamiento para determinar el punto de fusión (o congelación) de una sustancia. Hacer tales mediciones en un amplio rango de presiones produce datos que se pueden presentar gráficamente como un diagrama de fase. Un diagrama de fase combina gráficos de presión versus temperatura para los equilibrios de transición de fase líquido-gas, sólido-líquido y sólido-gas de una sustancia. Estos diagramas indican los estados físicos que existen bajo condiciones específicas de presión y temperatura, y también proporcionan la dependencia de la presión de las temperaturas de transición de fase (puntos de fusión, puntos de sublimación, puntos de ebullición). Un diagrama de fase típico para una sustancia pura se muestra en la Figura \(\PageIndex{1}\).

    A graph is shown where the x-axis is labeled “Temperature” and the y-axis is labeled “Pressure.” A line extends from the lower left bottom of the graph sharply upward to a point that is a third across the x-axis. A second line begins at the lower third of the first line at a point labeled “triple point” and extends to the upper right corner of the graph where it is labeled “critical point.” The two lines bisect the graph area to create three sections, labeled “solid” near the top left, “liquid” in the top middle and “gas” near the bottom right. A pair of horizontal arrows, one left-facing and labeled “deposition” and one right-facing and labeled” sublimation,” are drawn on top of the bottom section of the first line. A second pair of horizontal arrows, one left-facing and labeled “freezing” and one right-facing and labeled “melting”, are drawn on top of the upper section of the first line. A third pair of horizontal arrows, one left-facing and labeled “condensation” and one right-facing and labeled ”vaporization,” are drawn on top of the middle section of the second line.

    Figura \(\PageIndex{1}\): El estado físico de una sustancia y sus temperaturas de transición de fase se representan gráficamente en un diagrama de fase.

    Para ilustrar la utilidad de estos gráficos, considere el diagrama de fase para el agua que se muestra en la Figura \(\PageIndex{2}\).

    A graph is shown where the x-axis is labeled “Temperature in degrees Celsius” and the y-axis is labeled “Pressure ( k P a ).” A line extends from the origin of the graph which is labeled “A” sharply upward to a point in the bottom third of the diagram labeled “B” where it branches into a line that slants slightly backward until it hits the highest point on the y-axis labeled “D” and a second line that extends to the upper right corner of the graph labeled “C”. C is labeled “Critical point, with a dotted line extending downward to the x-axis labeled 374 degrees Celsius, and another dotted line extending to the y-axis labeled 22,089 k P a. The two lines bisect the graph area to create three sections, labeled “Ice (solid)” near the middle left, “Water (liquid)” in the top middle and “Water vapor (gas)” near the bottom middle. Point B is labeled “Triple point” and has a dotted line extending downward to the x-axis labeled 0.01, and another dotted line extending to the y-axis labeled 0.6. Halfway between points B and C a dotted line extends from the originally discussed line downward to the point 100 degrees Celsius on the x-axis, and another dotted line extends to the y-axis at 101 k P a. Another dotted line extends from this dotted line downward at 0 degrees Celsius.

    Figura \(\PageIndex{2}\): Los ejes de la presión y la temperatura en este diagrama de fase del agua no están dibujados a escala constante para ilustrar varias propiedades importantes.

    Podemos usar el diagrama de fases para identificar el estado físico de una muestra de agua en condiciones específicas de presión y temperatura. Por ejemplo, una presión de 50 kPa y una temperatura de −10 °C corresponden a la región del diagrama etiquetada como "hielo". En estas condiciones, el agua existe solo como un sólido (hielo). Una presión de 50 kPa y una temperatura de 50 °C corresponden a la región "agua"; aquí, el agua existe solo como un líquido. A 25 kPa y 200 °C, el agua existe solo en estado gaseoso. Tenga en cuenta que en el diagrama de fase H2O, los ejes de presión y temperatura no están dibujados a una escala constante para permitir la ilustración de varias características importantes como se describe aquí.

    La curva BC en la Figura \(\PageIndex{2}\) es la gráfica de presión de vapor versus temperatura como se describe en el módulo anterior de este capítulo. Esta curva de "líquido-vapor" separa las regiones líquida y gaseosa del diagrama de fases y proporciona el punto de ebullición del agua a cualquier presión. Por ejemplo, a 1 atm, el punto de ebullición es de 100 °C. Observe que la curva de líquido-vapor termina a una temperatura de 374 °C y una presión de 218 atm, lo que indica que el agua no puede existir como líquido por encima de esta temperatura, independientemente de la presión. Las propiedades físicas del agua en estas condiciones son intermedias entre las de sus fases líquida y gaseosa. Este estado único de la materia se llama el fluido supercrítico, un tema que se describirá en la siguiente sección de este módulo.

    La curva de vapor sólido, etiquetada AB en la Figura \(\PageIndex{2}\), indica las temperaturas y presiones a las cuales el hielo y el vapor de agua están en equilibrio. Estos pares de datos de temperatura-presión corresponden a los puntos de sublimación o deposición del agua. Si pudiéramos acercarnos a la línea de gas sólido en la Figura \(\PageIndex{2}\), veríamos que el hielo tiene una presión de vapor de aproximadamente 0.20 kPa a -10 °C. Por lo tanto, si colocamos una muestra congelada en el vacío con una presión inferior a 0.20 kPa, el hielo sublimará. Esta es la base del proceso de "liofilización" que se usa a menudo para conservar alimentos, como el helado que se muestra en la Figura \(\PageIndex{3}\).

    >A photograph shows a package with a rocket being launched on the front and a block of pink, white and brown striped solid in a wrapper next to it.

    Figura \(\PageIndex{3}\): Los alimentos liofilizados, como este helado, se deshidratan por la sublimación a presiones por debajo del punto triple para el agua. (crédito: ʺlwaoʺ/Flickr)

    La curva sólido-líquido etiquetada BD muestra las temperaturas y presiones a las que el hielo y el agua líquida están en equilibrio, representando los puntos de fusión/congelación del agua. Tenga en cuenta que esta curva exhibe un poco de una pendiente negativa (muy exagerada para mayor claridad), lo que indica que el punto de fusión del agua disminuye un poco a medida que aumenta la presión. El agua es una sustancia inusual a este respecto, ya que la mayoría de las sustancias exhiben un aumento en el punto de fusión al aumentar la presión. Este comportamiento es en parte responsable del movimiento de los glaciares, como el que se muestra en la Figura \(\PageIndex{4}\). El fondo de un glaciar experimenta una presión inmensa debido a su peso que puede derretir parte del hielo, formando una capa de agua líquida sobre la cual el glaciar puede deslizarse más fácilmente.

    A photograph shows an aerial view of a land mass. The white mass of a glacier is shown near the top left quadrant of the photo and leads to two branching blue rivers. The open land is shown in brown.

    Figura \(\PageIndex{4}\): Las inmensas presiones debajo de los glaciares resultan en una fusión parcial para producir una capa de agua que proporciona lubricación para ayudar al movimiento glacial. Esta fotografía satelital muestra el avance del glaciar Perito Moreno en Argentina. (crédito: NASA)

    El punto de intersección de las tres curvas se etiqueta B en la Figura \(\PageIndex{2}\). A la presión y temperatura representadas por este punto, las tres fases del agua coexisten en equilibrio. Este par de datos de temperatura-presión se llama el punto triple. A presiones inferiores al punto triple, el agua no puede existir como líquido, independientemente de la temperatura.

    Ejemplo \(\PageIndex{1}\): Determinando el Estado De fase Del Agua

     Usando el diagrama de fase para el agua dado en la Figura 10.4.2, determine el estado del agua a las siguientes temperaturas y presiones:temperatures and pressures:

    1. −10 °C y 50 kPa
    2. 25 °C y 90 kPa
    3. 50 °C y 40 kPa
    4. 80 °C y 5 kPa
    5. −10 °C y 0.3 kPa
    6. 50 °C y 0.3 kPa

    Solución

    Usando el diagrama de fase para el agua, podemos determinar que el estado del agua a cada temperatura y presión dada es la siguiente: (a) sólido; (b) líquido; (c) líquido; (d) gas; (e) sólido; (f) gas.

    Ejercicio \(\PageIndex{1}\)

    ¿Qué cambios de fase puede experimentar el agua a medida que cambia la temperatura si la presión se mantiene a 0.3 kPa? Si la presión se mantiene a 50 kPa?

    Respuesta:

    A 0.3 kPa: s⟶ g a −58 °C. A 50 kPa: s⟶ l a 0 °C, l ⟶ g a 78 °C

    Considere el diagrama de fase para el dióxido de carbono que se muestra en la Figura \(\PageIndex{5}\) como otro ejemplo. La curva sólido-líquido exhibe una pendiente positiva, lo que indica que el punto de fusión del CO2 aumenta con la presión como lo hace con la mayoría de las sustancias (el agua es una notable excepción como se describió anteriormente). Observe que el punto triple está muy por encima de 1 atm, lo que indica que el dióxido de carbono no puede existir como líquido en condiciones de presión ambiente. En cambio, enfriando el dióxido de carbono gaseoso a 1 atm resulta en su deposición en el estado sólido. Del mismo modo, el dióxido de carbono sólido no se funde a una presión de 1 atm sino que se sublima para producir CO2 gaseoso. Finalmente, observe que el punto crítico para el dióxido de carbono se observa a una temperatura y presión relativamente moderadas en comparación con el agua.

    A graph is shown where the x-axis is labeled “Temperature ( degree sign, C )” and has values of negative 100 to 100 in increments of 25 and the y-axis is labeled “Pressure ( k P a )” and has values of 10 to 1,000,000. A line extends from the lower left bottom of the graph upward to a point around“27, 9000,” where it ends. The space under this curve is labeled “Gas.” A second line extends in a curve from point around “-73, 100” to “27, 1,000,000.” The area to the left of this line and above the first line is labeled “Solid” while the area to the right is labeled “Liquid.” A section on the graph under the second line and past the point “28” on the x-axis is labeled “S C F.”

    Figura\(\PageIndex{5}\): Los ejes de presión y temperatura en este diagrama de fase de dióxido de carbono no están dibujados a escala constante para ilustrar varias propiedades importantes.​​​​​​​

    Ejemplo \(\PageIndex{2}\): Determinando el estado de fase del dióxido de carbono 

    Using the phase diagram for carbon dioxide shown in Figure 10.4.5, determine the state of CO2 at the following temperatures and pressures:

    1. −30 °C and 2000 kPa
    2. −60 °C and 1000 kPa
    3. −60 °C and 100 kPa
    4. 20 °C and 1500 kPa
    5. 0 °C and 100 kPa
    6. 20 °C and 100 kPa

    Solución

    Using the phase diagram for carbon dioxide provided, we can determine that the state of CO2 at each temperature and pressure given are as follows: (a) liquid; (b) solid; (c) gas; (d) liquid; (e) gas; (f) gas.

    Ejercicio \(\PageIndex{2}\)

    Determine the phase changes carbon dioxide undergoes when its temperature is varied, thus holding its pressure constant at 1500 kPa? At 500 kPa? At what approximate temperatures do these phase changes occur?

    Respuesta

    at 1500 kPa: s⟶ l at −45 °C, l⟶ g at −10 °C; at 500 kPa: s⟶ g at −58 °C 

    Supercritical Fluids

    If we place a sample of water in a sealed container at 25 °C, remove the air, and let the vaporization-condensation equilibrium establish itself, we are left with a mixture of liquid water and water vapor at a pressure of 0.03 atm. A distinct boundary between the more dense liquid and the less dense gas is clearly observed. As we increase the temperature, the pressure of the water vapor increases, as described by the liquid-gas curve in the phase diagram for water (Figure \(\PageIndex{2}\)), and a two-phase equilibrium of liquid and gaseous phases remains. At a temperature of 374 °C, the vapor pressure has risen to 218 atm, and any further increase in temperature results in the disappearance of the boundary between liquid and vapor phases. All of the water in the container is now present in a single phase whose physical properties are intermediate between those of the gaseous and liquid states. This phase of matter is called a supercritical fluid, and the temperature and pressure above which this phase exists is the critical point (Figure \(\PageIndex{5}\)). 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 critical pressures of some common substances are given in Table \(\PageIndex{1}\).

    Table \(\PageIndex{1}\): Critical Temperatures and Critical Pressures of select substances
    Substance Critical Temperature (K) Critical Pressure (atm)
    hydrogen 33.2 12.8
    nitrogen 126.0 33.5
    oxygen 154.3 49.7
    carbon dioxide 304.2 73.0
    ammonia 405.5 111.5
    sulfur dioxide 430.3 77.7
    water 647.1 217.7

    Like a gas, a supercritical fluid will expand and fill a container, but its density is much greater than typical gas densities, typically being close to those for liquids. Similar to liquids, these fluids are capable of dissolving nonvolatile solutes. They exhibit essentially no surface tension and very low viscosities, however, so they can more effectively penetrate very small openings in a solid mixture and remove soluble components. These properties make supercritical fluids extremely useful solvents for a wide range of applications. For example, supercritical carbon dioxide has become a very popular solvent in the food industry, being used to decaffeinate coffee, remove fats from potato chips, and extract flavor and fragrance compounds from citrus oils. It is nontoxic, relatively inexpensive, and not considered to be a pollutant. After use, the CO2 can be easily recovered by reducing the pressure and collecting the resulting gas.

    Four photographs are shown where each shows a circular container with a green and red float in each. In the left diagram, the container is half filled with a colorless liquid and the floats sit on the surface of the liquid. In the second photo, the green float is near the top and the red float lies near the bottom of the container. In the third photo, the fluid is darker and the green float sits halfway up the container while the red is sitting at the bottom. In the right photo, the liquid is colorless again and the two floats sit on the surface.

    Figura \(\PageIndex{6}\): (a) A sealed container of liquid carbon dioxide slightly below its critical point is heated, resulting in (b) the formation of the supercritical fluid phase. Cooling the supercritical fluid lowers its temperature and pressure below the critical point, resulting in the reestablishment of separate liquid and gaseous phases (c and d). Colored floats illustrate differences in density between the liquid, gaseous, and supercritical fluid states. (credit: modification of work by “mrmrobin”/YouTube)

    Ejemplo \(\PageIndex{3}\): The Critical Temperature of Carbon Dioxide

    If we shake a carbon dioxide fire extinguisher on a cool day (18 °C), we can hear liquid CO2 sloshing around inside the cylinder. However, the same cylinder appears to contain no liquid on a hot summer day (35 °C). Explain these observations.

    Solución

    On the cool day, the temperature of the CO2 is below the critical temperature of CO2, 304 K or 31 °C (Table \(\PageIndex{1}\)), so liquid CO2 is present in the cylinder. On the hot day, the temperature of the CO2 is greater than its critical temperature of 31 °C. Above this temperature no amount of pressure can liquefy CO2 so no liquid CO2 exists in the fire extinguisher.

    Ejercico \(\PageIndex{3}\)

     Ammonia can be liquefied by compression at room temperature; oxygen cannot be liquefied under these conditions. Why do the two gases exhibit different behavior?

    Respuesta

    The critical temperature of ammonia is 405.5 K, which is higher than room temperature. The critical temperature of oxygen is below room temperature; thus oxygen cannot be liquefied at room temperature.

    Decaffeinating Coffee Using Supercritical CO2

    Coffee is the world’s second most widely traded commodity, following only petroleum. Across the globe, people love coffee’s aroma and taste. Many of us also depend on one component of coffee—caffeine—to help us get going in the morning or stay alert in the afternoon. But late in the day, coffee’s stimulant effect can keep you from sleeping, so you may choose to drink decaffeinated coffee in the evening.

    Since the early 1900s, many methods have been used to decaffeinate coffee. All have advantages and disadvantages, and all depend on the physical and chemical properties of caffeine. Because caffeine is a somewhat polar molecule, it dissolves well in water, a polar liquid. However, since many of the other 400-plus compounds that contribute to coffee’s taste and aroma also dissolve in H2O, hot water decaffeination processes can also remove some of these compounds, adversely affecting the smell and taste of the decaffeinated coffee. Dichloromethane (CH2Cl2) and ethyl acetate (CH3CO2C2H5) have similar polarity to caffeine, and are therefore very effective solvents for caffeine extraction, but both also remove some flavor and aroma components, and their use requires long extraction and cleanup times. Because both of these solvents are toxic, health concerns have been raised regarding the effect of residual solvent remaining in the decaffeinated coffee.

    Two images are shown and labeled “a” and “b.” Image a shows a molecule composed of a five member ring composed of two blue spheres and three black spheres. One of the blue spheres is bonded to a black sphere bonded to three white spheres and one of the black spheres is bonded to a white sphere. The other two black spheres are double bonded together and make up one side of a six-membered ring that is also composed of two more black spheres and two blue spheres, both of which are bonded to a black sphere bonded to three white spheres. The black spheres are each double bonded to red spheres. Image b shows a diagram of two vertical tubes that lie next to one another. The left-hand tube is labeled “Extraction vessel.” A small tube labeled “Soaked beans” leads into the top of the tube and a label at the bottom of the tube reads “Decaffeinated beans.” The right tube is labeled “Absorption vessel.” A tube near the top of this tube is labeled “Water” and another tube leads from the right tube to the left. This tube is labeled with a left-facing arrow and the phrase “supercritical carbon dioxide.” There is a tube leading away from the bottom which is labeled, “Caffeine and water.” There is another tube that leads from the extraction vessel to the absorption vessel which is labeled, “supercritical C O subscript 2 plus caffeine.”

    Figura \(\PageIndex{7}\): (a) Caffeine molecules have both polar and nonpolar regions, making it soluble in solvents of varying polarities. (b) The schematic shows a typical decaffeination process involving supercritical carbon dioxide.

    Supercritical fluid extraction using carbon dioxide is now being widely used as a more effective and environmentally friendly decaffeination method (Figure \(\PageIndex{7}\)). At temperatures above 304.2 K and pressures above 7376 kPa, CO2 is a supercritical fluid, with properties of both gas and liquid. Like a gas, it penetrates deep into the coffee beans; like a liquid, it effectively dissolves certain substances. Supercritical carbon dioxide extraction of steamed coffee beans removes 97−99% of the caffeine, leaving coffee’s flavor and aroma compounds intact. Because CO2 is 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 recovered from coffee beans via this process is a valuable product that can be used subsequently as an additive to other foods or drugs.

    Resumen

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

    Glosario

    critical point
    temperature and pressure above which a gas cannot be condensed into a liquid
    phase diagram
    pressure-temperature graph summarizing conditions under which the phases of a substance can exist
    supercritical fluid
    substance at a temperature and pressure higher than its critical point; exhibits properties intermediate between those of gaseous and liquid states
    triple point
    temperature and pressure at which the vapor, liquid, and solid phases of a substance are in equilibrium

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