Chemistry
Phase Diagram of Water
The phase diagram of water illustrates the relationship between temperature, pressure, and the physical states of water: solid, liquid, and gas. At low temperatures and high pressures, water exists as a solid (ice), while at higher temperatures and lower pressures, it exists as a gas (water vapor). The diagram provides a visual representation of these phase transitions under different conditions.
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eBook - PDFThe Atmospheric Environment
Effects of Human Activity
- Michael B. Mcelroy(Author)
- 2021(Publication Date)
- Princeton University Press(Publisher)
4.2 Phase Diagrams The conditions for equilibrium between the three phases of a substance can be represented simultaneously on a graph known as a phase diagram. The phase diagram for water is illustrated by Figure 4.3a. Equilibrium between phases ex- Phase Diagrams 33 ists only for temperatures and pressures indicated by the lines separating the areas labeled “ice,” “liquid,” and “vapor.” The curves for the three phases intersect for pure water at a temperature of 273.0098 K (0.0098°C) at a pres- sure of 6.1 mb. For this unique configuration, known as the triple point, all three phases (ice, liquid, and vapor) are si- multaneously in equilibrium. Ice is unstable at temperatures higher than the triple point; it melts. Liquid is unstable at temperatures below the triple point; it freezes. The melting-point temperature (the solid line separating the liquid and solid phases) decreases slightly as the value of the total pressure applied to the ice increases; meaning, it is affected by the presence of other gases in addition to H 2 O. It is equal to 273 K (0°C) at a pressure of 1 atm (Figure 4.3b): it is this property of water that was initially used to set the zero point for the Celsius scale of temperature. We can un- derstand the shift in the melting point by recalling that the density of water ice is less than the density of its liquid: ap- plication of pressure to an ice crystal causes it to more easily revert to the more dense liquid form. The pressure effect on melting is relatively modest under atmospheric conditions; the melting point line in Figure 4.3a is nearly vertical.
- John Reisel(Author)
- 2021(Publication Date)
- Cengage Learning EMEA(Publisher)
All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 71 3.2 Phase Diagrams volume or specific internal energy is. Those quantities depend on the relative amount of the water that is in liquid and in vapor form. Although P-v-T diagrams are useful in helping understand phases of a substance, they are often more cumbersome than nec- essary for illustrating a process that the sub- stance is undergoing. As such, we usually will rely on two-dimensional projections of this surface to illustrate thermodynamic processes. A P-T projection of water (such that the volume is into the page) is shown in Figure 3.3, and a P-T projection that is indicative of the behavior of most other sub- stances is shown in Figure 3.4. As can be seen in Figures 3.3 and 3.4, the diagrams are similar, with the exception being the slope of the line dividing the solid and liquid phases: this is a consequence of the feature of water expanding upon freezing, whereas most substances contract upon freezing. The lines between two phases represent states where both states exist. At the intersection of all three phases, there is a pressure and temperature where all three phases coexist. On a P-T diagram, this is called the triple point; however, it should be noted that this state exists at a range of specific volumes and FIGURE 3.2 A P-v-T surface for substances that contract upon freezing (most substances).
eBook - PDF- Arieh Ben-naim, Roberta Ben-naim(Authors)
- 2011(Publication Date)
- World Scientific(Publisher)
These are used to describe systems with several compo-nents, say water and ethanol. But now we are only interested in pure water, and the phase diagram can be described in a two-dimensional space.” The professor pointed at the Phase Diagram of Water again. “Likewise, in the phase diagram, we can imagine ourselves moving from a cold to a hot region or from low to high pressures.” “Imagine,” said the professor, aiming his laser pointer at the region denoted ‘vapor’ in the diagram, “that you are at point A in the diagram. This point is characterized by low pressure, P , and high temperature, T ” (Fig. 2.1). “Walking within the phase diagram, up or down from point A is like tread-ing into nothingness. The water molecules are so dispersed that it almost seems like you are walking in empty space. We shall, however, have a chance to ‘see’ the vapor phase from the microscopic point of view later on.” “For instance, suppose we start at point A and walk either right or left (i.e., increasing or decreasing the temperature), or up and down (increasing or decreasing the pressure). In the real world, we shall not see much of a change — but you will see quite a lot of changes on the microscopic level.” “You should realize that the resemblance of the phase diagram to a real map is not to be taken seriously. On a map, going to the right actually means moving east, whereas there is no real movement in the phase diagram. Going to the right signifies increasing the temperature of the system, not moving in the real world. Likewise, going up means increasing the pressure on the system.” Pointing to a point in A, in the ‘vapor’ region (Fig. 2.1), he continued: “Scientists say that we have two degrees of freedom in this area.
eBook - PDFThermodynamics and Statistical Mechanics
An Integrated Approach
- M. Scott Shell(Author)
- 2015(Publication Date)
- Cambridge University Press(Publisher)
A schematic representation of the Phase Diagram of Water. At greatly elevated pressures, several crystallographically distinct ice phases are seen, beyond the usual ice Ih formed at ambient pressure. Adapted from www1.lsbu.ac.uk/water/phase. html. 177 10.1 Conditions for phase equilibrium Recognizing that dE α , dV α , and dN α can all vary independently, the conditions for equilibrium between two phases must then be given by T α ¼ T β , P α ¼ P β , μ α ¼ μ β ð10:4Þ It will be helpful to take the following viewpoint: imagine that we can manipulate each phase independently by changing its temperature, pressure, or chemical potential while retaining the same phase identity (e.g., liquid or vapor). As an example, consider liquid water and ice phases, each of which might be varied in temperature and pressure. To find the conditions of solid–liquid equilibrium, we must search (T, P) space for states satisfying the equalities in (10.4). The points at which these are satisfied then correspond to the melting line. If the equalities are not satisfied, just one phase will exist at those state conditions. In fact, one of the variables in (10.4) is redundant. Recall that only two intensive variables are required in order to completely specify the thermodynamic state and hence all intensive properties of a single-component system. Therefore, if we choose T and P then μ for either phase is uniquely specified, and generally we can write μ ¼ μ(T, P). So, if we are looking for T and P combinations that enable equilibrium between liquid water and ice, we can simply solve the equation μ α (T, P) ¼ μ β (T, P) (10.5) where the superscripts indicate each phase. Notice that we have already accounted for the thermal and mechanical equilibrium conditions by assuming that the temperatures and pressures are constant. This equality of chemical potentials constitutes an equation with two unknowns, T and P.
eBook - PDF- Patrick M. Woodward, Pavel Karen, John S. O. Evans, Thomas Vogt(Authors)
- 2021(Publication Date)
- Cambridge University Press(Publisher)
This is an example of an invariant point; one with no degrees of freedom. A line on the H 2 O phase diagram thus represents the presence of two phases, and a point where three lines intersect represents three phases. The final point to mention on the water phase diagram is the critical point, which occurs at the critical temperature and critical pressure. Beyond this point, liquid and vapor have the same density and can’t be distinguished—a supercritical fluid is the only phase present. A practical consequence is that above the critical temperature, gas can’t be liquefied by application of pressure alone. As the focus of this text is on solid state materials, the majority of the chemical systems that we’ll consider will be condensed systems, i.e. ones in which the vapor pressures of the substances involved are negligible compared to atmospheric pressure. The pressure can therefore be considered as constant, and one degree of freedom is removed from the system. The phase rule for a condensed system becomes: 4 Note that this is not the case in a phase diagram with two or more components. In a two-component diagram, a single solid phase is represented by a line and in a three-component diagram by a point. 5 In practice, remaining at equilibrium means using a slow cooling rate. With more rapid cooling, one may not allow time for crystallites of ice to nucleate and thus obtains a supercooled state. This, however, is not an equilibrium state of the system. 122 Phase Diagrams and Phase Transitions P þ F ¼ C þ 1 (4.2) This is the form of the phase rule that will apply for the rest of this chapter. 4.2 Two-Component Phase Diagrams 4.2.1 Without Compound Formation Figure 4.2 shows one of the simplest phase diagrams for a two-component (A and B) or binary condensed system, a system in which A and B form no compounds A m B n . Components A and B form no solid solutions (x is either zero or one in A 1−x B x ) but are completely miscible when molten.
eBook - PDFPhysical Chemistry
A Modern Introduction, Second Edition
- William M. Davis(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
phaseboundarylinemeansthatonedegreeoffreedomiseliminated�Iftemperaturewere varied,pressurewouldhavetochangeaccordingtothephaseboundarylineinorderfor thetwophasestocontinuetocoexist� Letusconsidertheformofthephasediagramofwater,showninFigure4�1,andthe information that is incorporated into it� There are three phase equilibrium lines corre-spondingtothecoexistenceofliquidandsolid,ofliquidandvapor,andofsolidandvapor� Thesecurvesmeetatasinglepointwhereallthreephasescoexist,anditiscalledthe triple point �Thispointistheonespecificpressure,temperature,and(implicitly)volumeatwhich thisoccurs�Forwater,thetriplepointoccursataverylowpressure�Wewillseethatphase diagraminformationisrelatedtoequationsofstate,whichinturnarerelatedtointer-molecular interactions� Thus, laboratory measurement of phase behavior data provides informationoncertainintrinsicmolecularpropertiesrelatedtointermolecularinteraction� Normal phase transition temperatures (i�e�,freezingpoint,boilingpoint)arethosetem-peraturesatwhichtwophasescoexistwiththepressureat1bar�Ahorizontallinedrawn onaphasediagramcorrespondingtoapressureof1barcrossesthephaseequilibrium curvesatthenormalphasetransitiontemperatures� Thepressure–volume( P – V )isothermsofagasthatcanliquefyshowcertainqualitative differencesfromthoseofanidealgas,whichcannotbeliquefied�Generally,thevolume ofaliquidchangesveryslowlywithpressure�Thus, P–V isothermsofaliquidtendtobe almostverticallines�Atsometemperatureandpressure,thishastochangetothe P–V isothermbehaviorwehavealreadyconsideredforgases�Thechangemustbecontinuous sinceourexperienceindicatesnopressureandtemperaturewhereasubstanceinstanta-neouslychangesitsvolume�Volumeisacontinuous,ratherthandiscontinuous,function oftemperatureandpressureregardlessofthenumberofphases�Asaresult,thereisone P–V isothermwithaninflectionpoint,andthisisillustratedinFigure4�2�Attheinflection
eBook - PDFNatural Gas Hydrates
A Guide for Engineers
- John Carroll(Author)
- 2003(Publication Date)
- Gulf Professional Publishing(Publisher)
Water has many different solid forms (e.g., denoted ice I, ice II), but most of these occur at extreme conditions (i.e., at very high pressures). 212 Natural Gas Hydrates: A Guide for Engineers Single-Component Systems For a pure component system, we are interested only in the pressure-temperature diagram. Actually, we are primarily concerned with how the single-component information relates to the two-component systems. The first rule about phase diagrams pertains to a one-component system existing as a single phase. The phase rule (N = 1 and p = 1) says that there are two degrees of freedom. Therefore: 1. A single-component system in a single phase occupies a region in the temperature-pressure plane . This leads to the second rule. The phase rule for a single-component system (N = 1) and two phases in equilibrium (p = 2) indicates that there is one degree of freedom. 2. For a single-component system, the location where two phases are in equilibrium corresponds to a curve in the temperature-pressure plane . The curve where vapor and liquid are in equilibrium is called the vapor pressure curve . If the component does not decompose, then this curve ends in a critical point. The solid-liquid curve is called the melting curve and the gas-solid the sublimation curve . These curves bound the various single-phase regions. For example, the vapor region lies at pressures less than and temperatures greater than the vapor pressure curve and at temperatures greater than and pressures less than the sublimation curve. The next rule arises when there are three phases in equilibrium. In this case, the phase rule says there are zero degrees of freedom. Thus, this is a fixed point in the pressure-temperature plane and is called a triple point . The location of the triple point is at the intersection of the two-phase loci. 3. Three two-phase loci intersect at a triple point, a point where three phases are in equilibrium .
eBook - PDF- Stanley M. Walas(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
The pressures employed in these and the few other investigations of this type that have been made are somewhat out of the range of ordinary processing of condensed phases, but it is nevertheless interesting to have the information. 5.4.6. Equilibrium and Reality A phase diagram represents conditions of equilibrium. Trans- formations in the solid phase at lower temperatures may be particularly slow and unless some way can be found to speed up attainment of equilibrium, the investigation may not be practicable. Figures 5.25(d) and (e) are two of the few cases that have been investigated of solid-phase equilibria. Temper- atures should be made as high as possible and the necessary time allowed. Some solid-phase transformations can be accelerated by introducing a melting step. For instance, with a system like that of Figure 5.23(g), the solid solution con- taining 25% thallium nitrate could not be prepared by an impatient individual by mixing the ingredients at room temperature in the proper proportions. If the mixture were melted at 300 C, however, and then cooled slowly below 285 C, the solid solution would be obtained. Below eutectic temperatures, unfortunately, such tricks are not applicable. Also, since rates of solid transformations are predominantly diffusion-controlled, it is unlikely that they can be catalyzed by traces of foreign materials. Thus time and temperature are the only controls available. 5.5. TERNARY SYSTEMS Planar diagrams of ternary systems at constant T and P are composition diagrams showing regions, lines, and points at which different phases exist. Compositions of phases in equilibrium may be connected with tie-lines (connodals), but for interpolation purposes and to reduce the clutter on a small diagram some kind of continuous tie-line correlation is preferred.
eBook - PDF- Sam Miller(Author)
- 2015(Publication Date)
- Cambridge University Press(Publisher)
The numerical value of the slope ( β 1 ) is −3.6670 × 10 9 Pa, and the numerical value of the intercept ( β 0 ) is 2.0572 × 10 10 Pa. A few sample calculations show that a very large change in melting pressure is associated with a very small change in melting temperature. Put another way, the melting temperature is nearly constant over the ordinary range of pressures in Earth’s troposphere. 7.4. Phase Diagram of Evaporation, Sublimation, and Melting for Water We’ll adapt the thermodynamic diagrams used throughout this book to show the phases of water as functions of temperature and pressure. By computing all possi-ble values of e s (using 7.45 and 7.47 ) and p m (using 7.54 ) in the temperature range between absolute zero and several hundred Kelvins above zero, we can generate curves for the liquid-vapor, the solid-vapor, and the solid-liquid equilibrium states. These are shown in Figure 7.3 . T T 0 e 0 T C p C Ice Liquid Vapor Superfluid Gas Triple point Critical point E M S 0 0 p Figure 7.3. Phase diagram for water substance. Heavy lines labeled S, M, and E are the sublimation, melting, and evaporation lines, computed using ( 7.47 ), ( 7.54 ), and ( 7.45 ), respectively. All three lines meet at the reference point, corresponding to p = 611.12 Pa, and T = 273.16 K, meaning that all three phases can coexist in equilibrium at this temperature and pressure. The three ordinary states of water (ice, liquid, and vapor) occur at relatively low pressures and temperatures. At very high temperatures, but relatively low pressures, water vapor is sometimes called a “gas,” although this distinction is somewhat subjective. At very high temperatures and very high pressures (above the critical point corresponding to p c and T c ), the distinction between liquid and gas disappears, and the substance enters a superfluid (or simply fluid ) state. 7.5. Additional Functions for Expressing Vapor Pressure above Liquid and Ice 157 Some important points illustrated by Figure 7.3 .
eBook - PDF- Donald Olander(Author)
- 2007(Publication Date)
- CRC Press(Publisher)
The simpler appearance of the p -T projection is due to the elimination of the volume as a represented variable in the diagram. The line labeled L/V in the p -T projection gives the temperature dependence of the vapor pressure of liquid water, also called the vaporization curve . The S/V line is the sublimation curve . It represents the equilibrium pressure of water vapor over ice. The S/L line is called the melting line and gives the combinations of pressure and temperature for which solid and liquid water coexist at equilibrium. Water is unusual among pure substances because its melting temperature is lowered as the pressure is increased. Most other substances behave in the opposite way; their melting * The line AB in the T -v plot of Figure 2.9 is hidden in the saturated-liquid curve. BZ BC v v v v xv x v v v v x f g f g f f g f = − − = + − − − = ( ) 1 Equations of State 67 curves tilt to the right from the triple point rather than to the left. The unusual behavior of water is due to the higher density of the liquid compared to that of the solid. Detailed analyses of the vaporization curve and the melting line are presented in Chapter 5. 2.7 THE STEAM TABLES The graphical representations of Figures 2.8 and 2.9 are valuable for understanding the general features of the p -v -T properties of water but are of little use for quantitative analysis. For this purpose, extensive tables of the thermodynamic properties of water have been compiled. Such tabular information is available for many condensable substances in addition to water. For the latter, the property listings are called the steam tables , although they contain data for liquid water and ice as well as for the vapor phase. The steam considered in the tables is pure, undiluted by other gases such as air. Mixtures of water vapor and noncondensible gases are considered in Chapter 5.
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