Water vapor Phase diagram of water

Application of the Gibbs phase rule to one-component systems. Phase diagrams of water and sulfur

For one-component system TO=1 and the phase rule is written as:

C = 3– F

If F= 1, then WITH=2, they say that the system bivariant;
F= 2, then WITH=1 , system monovariant;
F= 3, then WITH = 0, system invariant.

The relationship between pressure ( R), temperature ( T) and volume ( V) phases can be represented in three dimensions phase diagram. Each point (called figurative point) on such a diagram depicts some equilibrium state. It is usually more convenient to work with sections of this diagram using a plane R – T(at V = const) or plane P–V(at T = const). In what follows we will consider only the case of a section by a plane R – T(at V = const).

The state of water has been studied over a wide range of temperatures and pressures. At high pressures, the existence of at least ten crystalline modifications of ice has been established. The most studied is ice I - the only modification of ice found in nature.

The presence of various modifications of a substance - polymorphism - leads to complication of state diagrams.

Phase diagram of water in coordinates R – T is presented in Fig. 15. It consists of 3 phase fields- areas of various R, T- values at which water exists in the form of a certain phase - ice, liquid water or steam (indicated in the figure by the letters L, F and P, respectively). These phase fields are separated by 3 boundary curves.

Liquid water ↔ steam, and the number of degrees of freedom calculated by the phase rule is WITH= 3 – 2 = 1. This equilibrium is called monovariant. This means that for a complete description of the system it is enough to determine only one variable- either temperature or pressure, since for a given temperature there is only one equilibrium pressure and for a given pressure there is only one equilibrium temperature.

At pressures and temperatures corresponding to points below line AB, the liquid will completely evaporate, and this region is the region of vapor. To describe a system in a given single-phase region, two independent variables are needed: temperature and pressure ( WITH = 3 – 1 = 2).

At pressures and temperatures corresponding to points above line AB, the vapor is completely condensed into liquid ( WITH= 2). The upper limit of the evaporation curve AB is at point B, which is called the critical point (for water 374.2ºС and 218.5 atm.). Above this temperature, the liquid and vapor phases become indistinguishable (the liquid/vapor interface disappears), therefore F = 1.

Line AC - this ice sublimation curve (sometimes called the sublimation line), reflecting the dependence water vapor pressure above the ice on temperature. This line corresponds to the monovariant equilibrium ice ↔ steam ( WITH= 1). Above the line AC is the ice area, below is the steam area.

Line AD - melting curve, expresses the dependence ice melting temperature versus pressure and corresponds to the monovariant equilibrium ice ↔ liquid water. For most substances, the AD line deviates from the vertical to the right, but the behavior of water is anomalous: liquid water occupies less volume than ice. An increase in pressure will cause a shift in equilibrium towards the formation of liquid, i.e. the freezing point will decrease.

Studies first carried out by Bridgman to determine the course of the melting curve of ice at high pressures showed that all existing crystalline modifications of ice, with the exception of the first, are denser than water. Thus, the upper limit of the AD line is point D, where ice I (ordinary ice), ice III and liquid water coexist in equilibrium. This point is located at –22ºС and 2450 atm.

Rice. 15. Phase diagram of water

Using the example of water, it is clear that the phase diagram is not always as simple as shown in Fig. 15. Water can exist in the form of several solid phases, which differ in their crystal structure (see Fig. 16).

Rice. 16. Expanded phase diagram of water over a wide range of pressure values.

The triple point of water (a point reflecting the equilibrium of three phases - liquid, ice and steam) in the absence of air is located at 0.01ºС ( T = 273,16K) and 4.58 mmHg. Number of degrees of freedom WITH= 3-3 = 0 and such an equilibrium is called invariant.

In the presence of air, the three phases are in equilibrium at 1 atm. and 0ºС ( T = 273,15K). The decrease in the triple point in air is caused by the following reasons:

1. Solubility of air in liquid water at 1 atm, which leads to a decrease in the triple point by 0.0024ºС;

2. Increase in pressure from 4.58 mmHg. up to 1 atm, which reduces the triple point by another 0.0075ºС.

Conditions of water.

Water can be in three aggregate states, or phases: solid (ice), liquid (water itself), gaseous (water vapor). It is very important that, given the ranges of atmospheric pressure and temperature that actually exist on Earth, water can simultaneously be in different states of aggregation. In this respect, water differs significantly from other physical substances, which are found under natural conditions predominantly either in a solid (minerals, metals) or in a gaseous (O 2, N 2, CO 2, etc.) state.

Changes in the aggregate state of a substance are called phase transitions. In these cases, the properties of the substance (for example, density) change abruptly. Phase transitions are accompanied by the release or absorption of energy, called the heat of phase transition (“latent heat”).

The dependence of the aggregate state of water on pressure and temperature is expressed by the state diagram of water, or phase diagram (Fig. 5.1.1.).

The BB"O curve in Fig. 5.1.1 is called the melting curve. When passing through this curve from left to right, melting occurs

Rice. 5.1.1. Water diagram

I – VIII - various modifications of ice

ice, and from right to left - ice formation (crystallization of water). The OK curve is called the vaporization curve. When passing through this curve, boiling of water is observed from left to right, and condensation of water vapor is observed from right to left. The AO curve is called the sublimation curve, or sublimation curve. When crossing it from left to right, ice evaporates (sublimation), and from right to left, condensation into the solid phase (or sublimation) occurs.

At point O (the so-called triple point, at a pressure of 610 Pa and a temperature of 0.01 ° C or 273.16 K), water is simultaneously in all three states of aggregation.

The temperature at which ice melts (or water crystallizes) is called the temperature or melting point T pl. This temperature can also be called the temperature or freezing point T sub.

From the surface of water, as well as ice and snow, a certain number of molecules are constantly being torn off and carried into the air, forming water vapor molecules. At the same time, some of the water vapor molecules return back to the surface of water, snow and ice. If the first process predominates, then water evaporation occurs, if the second process occurs, water vapor condenses. The regulator of the direction and intensity of these processes is the humidity deficit - the difference between the elasticity of water vapor saturating the space at a given air pressure and temperature of the water surface (snow, ice), and the elasticity of the water vapor actually contained in the air, i.e. absolute air humidity. The content of saturated water vapor in the air and its elasticity increase with increasing temperature (at normal pressure) as follows. At a temperature of O°C, the content and elasticity of saturated water vapor are respectively 4.856 g/m3 and 6.1078 hPa, at a temperature of 20°C - 30.380 g/m3 and 23.373 hPa, at 40°C - 51.127 g/m3 and 73.777 hPa.

Evaporation from the surface of water (ice, snow), as well as moist soil, occurs at any temperature and the more intense it is, the greater the moisture deficit. With increasing temperature, the elasticity of water vapor saturating the space increases, and evaporation accelerates. An increase in evaporation also leads to an increase in the speed of air movement over the evaporating surface (i.e., wind speed in natural conditions), increasing the intensity of vertical mass and heat transfer.

When intense evaporation covers not only the free surface of the water, but also its thickness, where evaporation occurs from the inner surface of the resulting bubbles, the boiling process begins. The temperature at which the pressure of saturated water vapor is equal to external pressure is called the temperature or boiling point T bp.

At normal atmospheric pressure (1.013 105 Pa = 1.013 bar = 1 atm = 760 mm Hg), the freezing points of water (melting ice) and boiling points (condensation) correspond to 0 and 100 ° on the Celsius scale.

The freezing point Tzam and the boiling point of water Tbip depend on pressure (see Fig. 3.9.2.). In the range of pressure changes from 610 to 1.013 105 Pa (or 1 atm), the freezing temperature decreases slightly (from 0.01 to 0 ° C), then when the pressure increases to approximately 6 107 Pa (600 atm) T freezing temperature drops to -5 ° C, with an increase in pressure to 2.2 108 Pa (2,200 atm), Tdz decreases to -22 ° C. With a further increase in pressure, Tdz begins to increase rapidly. At very high pressure, special “modifications” of ice (II-VIII) are formed, which differ in their properties from ordinary ice (ice I).

At real atmospheric pressure on Earth, fresh water freezes at a temperature of about 0 ° C. At maximum depths in the ocean (about 11 km), the pressure exceeds 108 Pa, or 1,000 atm (an increase in depth for every 10 m increases the pressure by approximately 105 Pa, or 1 atm). At this pressure, the freezing point of fresh water would be about -12° C.

To reduce the freezing point of water

its salinity influences.

1.4). An increase in salinity for every 10‰ reduces T by approximately 0.54° C:

T deputy = -0.054 S.

The boiling point decreases with decreasing pressure (see Fig. 3.9.2.). Therefore, at high altitudes in the mountains, water boils at a temperature lower than 100 ° C. With increasing pressure, T boil increases to the so-called “critical point”, when at p = 2.2 107 Pa and T boil = 374 ° C, water simultaneously has properties of both liquid and gas.

The diagram of the state of water illustrates two “anomalies” of water, which have a decisive influence not only on the “behavior” of water on Earth, but also on the natural conditions of the planet as a whole. Compared to substances that are compounds of hydrogen with elements that are in the same row as oxygen in the Periodic Table of Mendeleev - tellurium Te, selenium Se and sulfur S, the freezing and boiling points of water are unusually high. Considering the natural relationship between the freezing and boiling points and the mass number of the mentioned substances, one would expect water to have a freezing temperature of about -90° C, and a boiling point of about -70° C. Abnormally high values of freezing and boiling temperatures predetermine the possibility of the existence of water on the planet as in solid and liquid states and serve as the determining conditions for the main hydrological and other natural processes on Earth.

Density of water

Density is the most important physical characteristic of any substance. It represents the mass of a homogeneous substance per unit volume:

where m is mass, V is volume. Density p has the dimension kg/m3.

The density of water, like other substances, depends primarily on temperature and pressure (and for natural waters, also on the content of dissolved and finely dispersed suspended solids) and changes abruptly during phase transitions. With increasing temperature, the density of water, like any other substance , in most of the range of temperature changes decreases, which is associated with an increase in the distance between molecules with increasing temperature. This pattern is violated only when ice melts and when water is heated in the range from 0 to 4° (more precisely 3.98° C). Two more very important “anatomies” of water are noted here: 1) the density of water in the solid state (ice) is less than in the liquid state (water), which is not the case for the vast majority of other substances; 2) in the water temperature range from 0 to 4 ° C, the density of water does not decrease with increasing temperature, but increases. Features of changes in water density are associated with a restructuring of the molecular structure of water. These two “anomalies” of water are of great hydrological importance: ice is lighter than water and therefore “floats” on its surface; reservoirs usually do not freeze to the bottom, since fresh water cooled to a temperature below 4° becomes less dense and therefore remains in the surface layer.

The density of ice depends on its structure and temperature. Porous ice may have a density much lower than indicated in Table 1.1. The snow density is even less. Freshly fallen snow has a density of 80-140 kg/m3, the density of compacted snow gradually increases from 140-300 (before the start of melting) to 240-350 (at the beginning of melting) and 300-450 kg/m3 (at the end of melting). Dense wet snow can have a density of up to 600-700 kg/m3. Snowflakes during melting have a density of 400-600, avalanche snow 500-650 kg/m3. The layer of water formed when ice and snow melts depends on the thickness of the ice or snow layer and its density. The amount of water in ice or snow is equal to:

h in = ah l r l / r

where h l is the thickness of the layer of ice or snow, r l is their density, p is the density of water, and is a multiplier determined by the ratio of the dimensions h in and h l: if the water layer is expressed in mm, and the thickness of ice (snow) in cm, then a=10, with the same dimension a=1.

The density of water also changes depending on the content of dissolved substances in it and increases with increasing salinity (Fig. 1.5). The density of sea water at normal pressure can reach 1025-1033 kg/m3.

The combined effect of temperature and salinity on the density of water at atmospheric pressure is expressed using the so-called equation of state of sea water. Such an equation in its simplest linear form is written as follows:

p = p o (1 - α 1 T + α 2 S)

where T is the water temperature, °C, S is the salinity of water, ‰, p o is the density of water at T = 0 and S = 0, α 1 and α 2 are parameters.

An increase in salinity also leads to a decrease in the temperature of highest density (°C) according to the formula

T max.pl = 4 - 0.215 S.

Rice. 5.2.1. Dependence of the density of water at normal atmospheric pressure on the temperature and salinity of the water.

An increase in salinity for every 10‰ reduces Tmax by approximately 2° C. The dependence of the temperature of maximum density and freezing temperature on water salinity is illustrated by the so-called Helland-Hansen graph (see Fig. 3.10.1.).

The relationship between the temperatures of highest density and freezing influence the nature of the process of water cooling and vertical convection - mixing caused by differences in density. Cooling of water as a result of heat exchange with air leads to an increase in the density of water and, accordingly, to the lowering of denser water down. Warmer and less dense waters rise in its place. The process of vertical density convection occurs. However, for fresh and brackish waters with a salinity of less than 24.7‰, this process continues only until the water reaches its highest density temperature (see Fig. 1.4). Further cooling of the water leads to a decrease in its density, and vertical convection stops. Salt waters at S>24.7‰ are subject to vertical convection until they freeze.

Thus, in fresh or brackish waters in winter, in the near-bottom horizons, the water temperature is higher than on the surface, and, according to the Helland-Hansen graph, always above the freezing temperature. This circumstance is of great importance for the preservation of life in water bodies at depths. If water had the same temperature of greatest density and freezing, like all other liquids, then reservoirs could freeze to the bottom, causing the inevitable death of most organisms.

An “anomalous” change in the density of water with a change in temperature entails the same “anomalous” change in the volume of water: with an increase in temperature from 0 to 4 ° C, the volume of chemically pure water decreases, and only with a further increase in temperature does it increase; the volume of ice is always noticeably greater than the volume of the same mass of water (remember how pipes burst when water freezes).

The change in the volume of water when its temperature changes can be expressed by the formula

V T1 = V T2 (1 + β DT)

where V T1 is the volume of water at temperature T1, V T2 is the volume of water at T2, β is the coefficient of volumetric expansion, which takes negative values at temperatures from 0 to 4 ° C and positive values at water temperatures above 4 ° C and less than 0 ° C ( ice) (see table 1.1),

Pressure also has some effect on the density of water. The compressibility of water is very small, but at great depths in the ocean it still affects the density of water. For every 1000 m of depth, the density due to the influence of the pressure of the water column increases by 4.5-4.9 kg/m3. Therefore, at maximum ocean depths (about 11 km), the density of water will be approximately 48 kg/m 3 greater than on the surface, and at S = 35‰ it will be about 1076 kg/m 3. If water were completely incompressible, the level of the world's oceans would be 30 m higher than it actually is. The low compressibility of water makes it possible to significantly simplify the hydrodynamic analysis of the movement of natural waters.

The influence of fine suspended sediment on the physical characteristics of water and, in particular, on its density has not yet been sufficiently studied. It is believed that the density of water can only be influenced by very fine suspended matter at their exceptionally high concentration, when water and sediment can no longer be considered in isolation. Thus, some types of mudflows, containing only 20-30% water, are essentially a clay solution with increased density. Another example of the influence of small sediments on density is the waters of the Yellow River flowing into the Yellow Sea Bay. With a very high content of fine sediment (up to 220 kg/m3), river turbid waters have a density 2-2.5 kg/m3 greater than sea water (their density at actual salinity and temperature is about 1018 kg/m3). Therefore, they “dive” to depth and descend along the seabed, forming a “dense” or “turbidity” flow.

First, let’s agree that by the term “water” we mean H 2 O in any of its possible phase states.

In nature, water can be in three states: solid phase (ice, snow), liquid phase (water), gaseous phase (steam).

Let's consider water without energy interaction with the environment, i.e. in an equilibrium state.

There is always vapor near the surface of ice or liquid. The contacting phases are in thermodynamic equilibrium: fast molecules fly out of the liquid phase, overcoming surface forces, and slow molecules from the vapor phase pass into the liquid phase.

In a state of equilibrium, each temperature corresponds to a certain vapor pressure - total (if there is only vapor above the liquid) or partial (if there is a mixture of vapor with air or other gases). Steam that is in equilibrium with the liquid phase from which it was formed is called saturated steam, and the corresponding temperature is called the saturation temperature, and the pressure is called the saturation pressure.

Non-equilibrium state of water:

a) Mechanically non-equilibrium state. Let the vapor pressure above the liquid decrease below the saturation pressure. In this case, the equilibrium is disturbed, an uncompensated transition of the substance from the liquid phase to the gaseous phase occurs through the phase interface due to the fastest molecules.

The process of uncompensated transition of a substance from the liquid phase to the gaseous phase is called evaporation.

The process of uncompensated transition of a substance from the solid phase to the gas phase is called sublimation or sublimation.

The intensity of evaporation or sublimation increases with intensive removal of the resulting vapor. In this case, the temperature of the liquid phase decreases due to the departure of molecules with the highest energy from it. This can be achieved without lowering the pressure, simply by blowing the surface of the liquid with a stream of air.

b) Thermal disequilibrium. Let heat be supplied to the liquid in an open vessel. In this case, the temperature, and accordingly the pressure of the saturated vapor above the liquid, increases and can reach the full external pressure (P=P H). In the case when P = P H, at the heating surface the temperature of the liquid rises above the temperature of the saturated vapor at the prevailing pressure here, i.e. conditions are created for the formation of vapor in the thickness of the liquid.

The process of transition of a substance from the liquid phase to the vapor phase directly inside the liquid is called boiling.

The process of nucleation of vapor bubbles in the thickness of a liquid is complex. For water to boil, it is necessary to have centers of vaporization on the surface of the heat supply - depressions, protrusions, irregularities, etc. At the heating surface, during boiling, the temperature difference between water and saturated steam at the prevailing pressure here depends on the intensity of the heat supply and can reach tens of degrees.

The action of surface tension forces of a liquid causes overheating of the liquid at the phase interface when it boils by 0.3-1.5 degrees relative to the temperature of the saturated vapor above it.

Any process of transition of a substance from the liquid phase to the vapor phase is called vaporization.

The process opposite to vaporization, i.e. the uncompensated transition of a substance from the vapor phase to the liquid phase is called condensation.

At constant vapor pressure, condensation occurs (like boiling) at a constant temperature and is the result of heat removal from the system.

The process opposite to sublimation, i.e. The transition of a substance from the vapor phase directly to the solid phase is called desublimation.

Let us recall that the previously introduced concepts of saturated steam and saturation temperature, transferred to the boiling process, lead to equality of the temperatures of steam and liquid. In this case, both the pressure and temperature of the liquid and vapor phases are the same.

The liquid phase of water at boiling point is called saturated liquid.

Steam at boiling (saturation) temperature is called dry saturated steam.

A two-phase liquid + vapor mixture in a saturated state is called wet saturated vapor.

In thermodynamics, this term extends to two-phase systems in which saturated vapor can be above the liquid level or represent a mixture of vapor with liquid droplets suspended in it. To characterize wet saturated steam it is used concept of degree of dryness X, which is the ratio of the mass of dry saturated steam, m S.N.P. , to the total mass of the mixture, m SM = m S.N.P. + m J.S.N. , it with liquid in a state of saturation:

The supply of heat to moist saturated steam at constant pressure leads to the transition of the liquid phase of the mixture to the vapor phase. In this case, the temperature of the mixture (saturation) cannot be increased until all the liquid has been converted into vapor. Further supply of heat only to the vapor phase in a state of saturation leads to an increase in its temperature.

Steam with a temperature above the saturation temperature at a given pressure is called superheated steam. Temperature difference of superheated steam t and saturated steam of the same pressure t N called the degree of steam superheat D t P = t -t N.

As the degree of steam superheat increases, its volume increases, the concentration of molecules decreases, and its properties approach those of gases.

At k n= 1 the equation of the phase rule will take the form:

C = 3 - F,

If there is 1 phase in equilibrium, then C = 2, they say that the system bivariant;

2 phases C = 1, system monovariant;

3 phase C = 0, system invariant.

A diagram expressing the dependence of the state of a system on external conditions or on the composition of the system is called phase diagram. The relationship between pressure ( R), temperature ( T) and volume ( V) phases can be represented by a three-dimensional phase diagram. Each point (called figurative point) on such a diagram depicts some equilibrium state. It is usually more convenient to work with sections of this diagram using a plane p - T(at V = const) or plane p -V(at T = const). Let us examine in more detail the case of a section by a plane p - T(at V=const).

Let us consider, as an example, the phase diagram of a one-component system – water (Fig. 8).

Phase diagram of water

Phase diagram of water in coordinates p - T is presented in Fig. 8. It is made up of 3 phase fields- areas of various ( r, T)-values at which water exists in the form of a certain phase - ice, liquid water or steam (indicated in Fig. 8 by the letters L, F and P, respectively). For these single-phase regions, the number of degrees of freedom is two, the equilibrium is bivariant ( C = 3 - 1 = 2). This means that to describe the system it is necessary two independent variables - temperature and pressure. These variables can change in these areas independently, and there will be no change in the type or number of phases.

The phase fields are separated by 3 boundary curves.

AB curve - evaporation curve, expresses dependence vapor pressure of liquid water from temperature(or, conversely, represents the dependence of the boiling point of water on pressure). In other words, this line answers two-phase liquid water-steam equilibrium, and the number of degrees of freedom calculated by the phase rule is C = 3 - 2 = 1. Such a balance monovariant. This means that for a complete description of the system it is enough to determine only one variable- either temperature or pressure. The second variable is dependent, it is determined by the shape of the AB curve . Thus, for a given temperature there is only one equilibrium pressure or for a given vapor pressure there is only one equilibrium temperature.

At pressures and temperatures corresponding to points below line AB, the liquid will completely evaporate, and this region is the region of vapor.

At pressures and temperatures corresponding to points above line AB, the vapor is completely condensed into liquid ( C = 2). The upper limit of the evaporation curve AB is at point B, which is called critical point(for water 374 o C and 218 atm). Above this temperature, the liquid and vapor phases become indistinguishable (the clear liquid/vapor phase boundary disappears), therefore Ф=1.

AC line- thisice sublimation curve(sometimes called the sublimation line), reflecting the dependence water vapor pressure above the ice on temperature. This line corresponds monovariant ice-steam equilibrium ( С=1). Above the line AC is the ice area, below is the steam area.

Line AD - melting curve, expresses dependence ice melting temperature versus pressure and corresponds monovariant ice-liquid water equilibrium. For most substances, the AD line deviates from the vertical to the right, but the behavior of water is anomalous: liquid water takes up less volume than ice. Based on Le Chatelier's principle, it can be predicted that an increase in pressure will cause a shift in equilibrium towards the formation of liquid, i.e. the freezing point will decrease.

Fig.8. Phase diagram of water

Studies carried out by Bridgman to determine the melting curve of ice at high pressures showed that there is seven different crystalline modifications of ice, each of which, with the exception of the first, denser than water. Thus, the upper limit of the AD line is point D, where ice I (ordinary ice), ice III and liquid water are in equilibrium. This point is located at -22 0 C and 2450 atm.

Triple point of water(a point reflecting the equilibrium of three phases - liquid, ice and steam) in the absence of air is at 0.0100 o C and 4.58 mm Hg. Number of degrees of freedom WITH=3-3=0 and such an equilibrium is called invariant. When any parameter changes, the system ceases to be three-phase.

In the presence of air, the three phases are in equilibrium at 760 mmHg. and at 0 o C. A decrease in the temperature of the triple point in air is caused by the following reasons:

1. solubility of gaseous components of air in liquid water at 1 atm, which leads to a decrease in the triple point by 0.0024 o C;

2. increase in pressure from 4.58 mm Hg. up to 1 atm, which reduces the triple point by another 0.0075 o C.

Chapter 2.Phase rule for a one-component system

For a one-component system (K=1), the phase rule is written in the form

C = 3-F . (9)

If Ф = 1, then C =2, they say that the system bivariant;
Ф = 2, then C =1, system monovariant;
Ф = 3, then C =0, system nonvariant.

The relationship between pressure (p), temperature (T) and volume (V) of the phase can be represented in three dimensions phase diagram. Each point (called figurative point) on such a diagram depicts some equilibrium state. It is usually more convenient to work with sections of this diagram using the p - T plane (at V=const) or the p -V plane (at T=const). Let us examine in more detail the case of a section by plane p - T (at V=const).

2.1. Phase diagram of water

The phase diagram of water in p - T coordinates is shown in Fig. 1. It is made up of 3 phase fields- regions of different (p, T)-values in which water exists in the form of a certain phase - ice, liquid water or steam (indicated in Fig. 1 by the letters L, F and P, respectively). These phase fields are separated by 3 boundary curves.

Curve AB - evaporation curve, expresses the dependence vapor pressure of liquid water from temperature(or, conversely, represents the dependence of the boiling point of water on pressure). In other words, this line answers two-phase equilibrium (liquid water) D (steam), and the number of degrees of freedom calculated according to the phase rule is C = 3 - 2 = 1. This equilibrium is called monovariant. This means that for a complete description of the system it is enough to determine only one variable- either temperature or pressure, because for a given temperature there is only one equilibrium pressure and for a given pressure there is only one equilibrium temperature.

At pressures and temperatures corresponding to points below line AB, the liquid will completely evaporate, and this region is the region of vapor. To describe the system in this single-phase area necessary two independent variables(C = 3 - 1 = 2): temperature and pressure.

At pressures and temperatures corresponding to points above line AB, the vapor is completely condensed into liquid (C = 2). The upper limit of the evaporation curve AB is at point B, which is called critical point(for water 374 o C and 218 atm). Above this temperature, the liquid and vapor phases become indistinguishable (the clear liquid/vapor phase boundary disappears), therefore Ф=1.

AC line - this ice sublimation curve(sometimes called the sublimation line), reflecting the dependence water vapor pressure above the ice on temperature. This line corresponds monovariant equilibrium (ice) D (steam) (C=1). Above the line AC is the ice area, below is the steam area.

Line AD - melting curve, expresses dependence ice melting temperature versus pressure and corresponds monovariant equilibrium (ice) D (liquid water). For most substances, the AD line deviates from the vertical to the right, but the behavior of water

Fig.1. Phase diagram of water

abnormal: liquid water takes up less volume than ice. Based on Le Chatelier's principle, it can be predicted that an increase in pressure will cause a shift in equilibrium towards the formation of liquid, i.e. the freezing point will decrease.

The triple point of water (a point reflecting the equilibrium of three phases - liquid, ice and steam) in the absence of air is at 0.0100 o C and 4.58 mm Hg. The number of degrees of freedom is C=3-3=0 and such equilibrium is called nonvariant.

In the presence of air, the three phases are in equilibrium at 1 atm and at 0 o C. The decrease in the triple point in air is caused by the following reasons:
1. solubility of air in liquid water at 1 atm, which leads to a decrease in the triple point by 0.0024 o C;
2. increase in pressure from 4.58 mm Hg. up to 1 atm, which reduces the triple point by another 0.0075 o C.

2.2. Sulfur phase diagram

Crystalline sulfur exists in the form two modifications – rhombic(S p) and monoclinic(S m). Therefore, the existence of four phases is possible: orthorhombic, monoclinic, liquid and gaseous (Fig. 2). Solid lines delineate four regions: vapor, liquid, and two crystalline modifications. The lines themselves correspond to monovariant equilibria of the two corresponding phases. Note that the equilibrium line is monoclinic sulfur - melt deviated from vertical to the right(compare with the phase diagram of water). This means that when sulfur crystallizes from the melt, reduction in volume. At points A, B and C, 3 phases coexist in equilibrium (point A - orthorhombic, monoclinic and vapor, point B - orthorhombic, monoclinic and liquid, point C - monoclinic, liquid and vapor). It is easy to notice that there is another point O,

Fig.2. Sulfur phase diagram

in which there is an equilibrium of three phases - superheated orthorhombic sulfur, supercooled liquid sulfur and steam, supersaturated relative to steam, in equilibrium with monoclinic sulfur. These three phases form metastable system, i.e. a system that is in a state relative stability. The kinetics of the transformation of metastable phases into a thermodynamically stable modification is extremely slow, however, with prolonged exposure or the introduction of seed crystals of monoclinic sulfur, all three phases still transform into monoclinic sulfur, which is thermodynamically stable under conditions corresponding to point O. The equilibria to which the OA curves correspond are OM and OS (sublimation, melting and evaporation curves, respectively) are metastable.

In the case of the sulfur diagram, we are faced with the spontaneous mutual transformation of two crystalline modifications that can occur forward and reverse depending on conditions. This type of transformation is called enantiotropic(reversible).

Mutual transformations of crystalline phases, which can only occur in one direction, are called monotropic(irreversible). An example of a monotropic transformation is the transition of white phosphorus to violet.

2.3. Clausius-Clapeyron equation

Movement along the lines of two-phase equilibrium on the phase diagram (C=1) means a consistent change in pressure and temperature, i.e. p=f(T). The general form of such a function for one-component systems was established by Clapeyron.

Let's say we have a monovariant equilibrium (water) D (ice) (line AD in Fig. 1). The equilibrium condition will look like this: for any point with coordinates (p, T) belonging to the line AD, water (p, T) = ice (p, T). For a one-component system =G/n, where G is the Gibbs free energy, and n is the number of moles (=const). We need to express G=f(p,T). The formula G= H-T S is not suitable for this purpose, because derived for p,T=const. In general terms, Gє H-TS=U+pV-TS. Let's find the differential dG using the rules for the differential of a sum and a product: dG=dU+p. dV+V . dp-T. dS-S. dT. According to the 1st law of thermodynamics dU=dQ - dA, and dQ=T. dS,a dA= p . dV. Then dG=V . dp - S . dT. It is obvious that in equilibrium dG water /n=dG ice /n (n=n water =n ice =const). Then v water. dp-s of water. dT=v ice. dp-s ice. dT, where v water, v ice - molar (i.e. divided by the number of moles) volumes of water and ice, s water, s ice - molar entropies of water and ice. Let's transform the resulting expression into (v water - v ice). dp = (s water - s ice) . dT, (10)

or: dp/dT= s fp / v fp, (11)

where s fp, v fp are changes in molar entropy and volume at phase transition((ice) (water) in this case).

Since s fn = H fn /T fn, the following type of equation is more often used:

where H fp is the change in enthalpy during the phase transition,
v fp - change in molar volume during transition,
Tfp is the temperature at which the transition occurs.

The Clapeyron equation allows, in particular, to answer the following question: What is the dependence of the phase transition temperature on pressure? The pressure can be external or created due to the evaporation of a substance.

Example 6. It is known that ice has a larger molar volume than liquid water. Then, when water freezes, v fp = v ice - v water > 0, at the same time H fp = H crystal< 0, поскольку кристаллизация всегда сопровождается выделением теплоты. Следовательно, H фп /(T . v фп)< 0 и, согласно уравнению Клапейрона, производная dp/dT< 0. Это означает, что линия моновариантного равновесия (лед) D (вода) на фазовой диаграмме воды должна образовывать тупой угол с осью температур.

Example 7. A negative dp/dT value for the phase transition (ice) "(water) means that under pressure ice can melt at temperatures below 0 0 C. Based on this pattern, English physicists Tyndall and Reynolds suggested about 100 years ago that the known ease of gliding on ice on skates is associated with melting ice under the tip of the skate; The resulting liquid water acts as a lubricant. Let's check if this is true using the Clapeyron equation.

The density of water is b = 1 g/cm 3, the density of ice is l = 1.091 g/cm 3, the molecular weight of water is M = 18 g/mol. Then:

V fp = M/ in -M/ l = 18/1.091-18/1 = -1.501 cm 3 /mol = -1.501. 10 -6 m 3 /mol,

enthalpy of ice melting - H fp = 6.009 kJ/mol,

T fp = 0 0 C = 273 K.

According to Clapeyron's equation:

dp/dT= - (6.009.103 J/mol)/(273K. 1.501.10 -6 m3/mol)=

146.6. 10 5 Pa/K= -146 atm/K.

This means that to melt ice at a temperature of, say, -10 0 C, it is necessary to apply a pressure of 1460 atm. But the ice will not withstand such a load! Therefore, the idea stated above not true. The real reason for the melting of ice under the ridge is the heat generated by friction.

Clausius simplified the Clapeyron equation in the case evaporation and in ogonki, assuming that:

2.4. Entropy of evaporation

The molar entropy of evaporation S eva = H eva / T bale is equal to the difference S vapor - S liquid. Since S vapor >> S liquid, then we can assume S is used as S vapor. The next assumption is that steam is considered an ideal gas. This implies the approximate constancy of the molar entropy of evaporation of a liquid at the boiling point, called Trouton’s rule.

Truton's rule. Molar entropy of evaporation of any
liquid is about 88 J/(mol. K).

If during the evaporation of different liquids there is no association or dissociation of molecules, then the entropy of evaporation will be approximately the same. For compounds that form hydrogen bonds (water, alcohols), the entropy of evaporation is greater than 88 J/(mol. K).

Trouton's rule allows us to determine the enthalpy of evaporation of a liquid from a known boiling point, and then, using the Clausius-Clapeyron equation, determine the position of the monovariant liquid-vapor equilibrium line on the phase diagram.