Diagram of the state of water and sulfur. Phase diagram of water
The state of a one-component system is determined by two independent parameters (for example, P and T), and the volume of the system is V = f(P,T). If, respectively, the pressure, temperature, volume of the system are plotted along the three coordinate axes, then a spatial diagram will be obtained that characterizes the dependence of the state of the system and phase equilibria in it on external conditions. Such a diagram is called a state diagram or a phase diagram.
For a one-component system two-dimensional the state diagram shows the conditions for the existence at various values of the parameters (T - temperature and P - pressure) of several phases, the simplest option is three phases: gas, liquid and solid.
Water Status Diagram
An example of such a diagram for water is shown in fig. 8.2.
The same water in a wider range of pressures and temperatures has several - phases - 9 in a solid state of aggregation (Fig. 8.3).
Sulfur state diagram.
Consider the phase diagram of the state of sulfur.
EA, AC and CN lines - temperature dependence saturated steam pressure over solid Srhombus., Smon. and Szh. respectively. Line AB is the temperature dependence of the phase transition Srhombus on the external pressure. Smon. The lines CB and OB are the dependence of the melting temperature Smon on the external pressure. and Srhombus. respectively. Stability region Srhombus. limited by lines EA, AB, BD. Stability region Smon. limited by lines BC, CA, AB. The region of existence of the liquid phase is located to the right of the lines BC and BD and above the line CN. The stability region of vaporous sulfur lies below the EA, AC, and CN lines.
In contrast to the state diagram of water with one triple point, there are three such points on the phase diagram of sulfur: A, B and C. In each of them, three phases can exist simultaneously. At point A - solid rhombic, solid monoclinic and vaporous sulfur; at point B - solid rhombic, solid monoclinic and liquid sulfur; at point C - solid monoclinic and vaporous sulfur and liquid sulfur.
Diagrams of the state of two-component systems. Thermal analysis
Two-component systems are called physico-chemical systems, which include two components. Components can be both simple substances and chemical compounds. The ratio between the components can significantly change the properties of the system. To determine the state of the system, it is unambiguously necessary to know the parameters: P, T and the concentrations of the components C1 and C2. The equation of state for a two-component system is: f(P,T,C1,C2)=0
The thermal analysis method is used to construct state diagrams.
Thermal analysis
The thermal analysis method is based on the analysis of cooling curves for mixtures of various compositions. The cooling curve is a temperature-time dependence of the cooling of the mixture, showing the points of phase transitions. On fig. 8.5. the shape of the cooling lines is shown (left part of the figure) on which, the plateau corresponds to the crystallization of a pure component (cr. A and B), the inflection point is the beginning of crystallization of one of the components of the solution.
Diagrams of the state of two-component systems at complete solubility of substances in the solid phase
An example of such a diagram is shown in fig. 8.5. - right part. Shows how this diagram is built from these cooling curves.
Crystalline sulfur can exist in two modifications - rhombic and monoclinic. Therefore, sulfur forms four phases - two crystalline, liquid and vapor. The state diagram of sulfur is shown schematically in Fig. 12.5.
The solid lines divide the diagram into four regions corresponding to the conditions for the equilibrium state of vapor, liquid, and two crystalline modifications. The lines themselves, corresponding to the conditions under which the equilibrium coexistence of the two corresponding phases is possible. Three phases are in thermodynamic equilibrium at points A, B and C. In addition, there is another triple point O, in which superheated rhombic sulfur, supercooled liquid sulfur, and supersaturated vapor with respect to vapor in equilibrium with monoclinic sulfur can coexist.
The chemical potentials of the three phases at the temperature and pressure corresponding to point O are the same. Due to this, three thermodynamically non-equilibrium phases can form a metastable system, that is, a system, that is, a system that is in relative stability. Metastability lies in the fact that none of the three phases tends to go into another, however, with long exposure or when crystals of monoclinic sulfur are introduced, all three phases turn into monoclinic sulfur, which is the only thermodynamically stable phase under conditions corresponding to point O.
Metastable triple points can give only those substances that form several crystalline modifications. In the same way, double equilibria are metastable, to which the curves OA, OB, and OS correspond.
If one crystalline modification should change into another with an increase in temperature, then some overheating above the stable equilibrium temperature is possible. This is because the transition from one crystal modification to another cannot be as easy as melting. the superheated modification must be kept for some time at the temperature reached in order for the crystals to reach the melting point, but overheating is impossible, since any further heat supply leads to the immediate destruction of the lattice.
We meet similar dependencies in the case of sulfur. If rhombic sulfur is heated fast enough, then it does not have time to turn into monoclinic sulfur. However, crystal cell orthorhombic sulfur cannot withstand unlimited overheating. At temperatures corresponding to the RH curve, the crystals decompose with the formation of a liquid phase, which under these conditions is also unstable with respect to monoclinic sulfur. In turn, the OA and OS curves represent, respectively, the sublimation curve of superheated rhombic sulfur and the boiling curve of supercooled liquid sulfur.
The crystal structure of a substance is determined not only by its chemical composition, but also by the conditions of formation. In nature, there are many examples when, depending on the conditions of formation, substances can have different crystal structures, i.e. grating type, and therefore different physical properties. This phenomenon is called polymorphism. The presence of one or another modification of a substance can thus characterize the conditions of its formation. Polymorphic modifications are denoted by Greek letters , , , .
Two types of polymorphism are possible: enantiotropic and monotropic.
Enantiotropy characterized by a reversible spontaneous transition at certain P and T of one form to another. This transition is accompanied by a decrease in the Gibbs energy as the thermodynamic conditions (P, T) change. On fig. 4.2 shows the enantiotropic transition from phase to phase at (P, T) ↔ . Up to the temperature and pressure of the phase transition (to the left of the point (P, T) ↔ ), the -modification of the substance is more stable, because it has less free energy G. At the point of intersection of the curves G =G , both phases are in equilibrium. Beyond this point, i.e. at high P and T, the -phase is more stable. Thus, the -phase is a low-temperature, α high-temperature modification of the substance.
Rice. 4.2. Change in the Gibbs function with enantiotropy
Enantiotropic transformations are characteristic of carbon, sulfur, silicon dioxide, and many other substances.
If only one phase is stable in the entire range of P and T, then the phase transition is not associated with certain values of P and T and is irreversible. This type of polymorphism is called monotropy (fig.4.3). The phase is more stable, the Gibbs energy of which is lower (in Fig. 4.3. phase ). Monotropic forms in natural conditions are less common; an example is the system
Fe 2 O 3 Fe 2 O 3
maghemite hematite
Rice. 4.3. Gibbs energy change under monotropy
On the phase diagram, the polymorphism of a substance is characterized by additional lines that limit the areas of existence of individual polymorphic modifications.
4.5.3. Sulfur phase diagram
As an example, consider the state diagram of sulfur, which can exist in the form of rhombic or monoclinic sulfur, i.e. she is dimorphic. On the phase diagram of sulfur ( rice. 4.4), in contrast to the water diagram, two fields of solid phases: an area of rhombic sulfur (to the left of the EABD line, field 1) and monoclinic (inside the ABC triangle, field 2). Field 3 - area of molten sulfur, field 4 - vaporous sulfur.
BC - monoclinic sulfur melting curve,
BD - melting curve of rhombic sulfur,
AB - polymorphic transformation curve: S rhombus ↔ S monocle
EA and AC are the sublimation curves of rhombic and monoclinic sulfur, respectively,
SC - liquid sulfur evaporation curve.
The dotted lines reflect the possibility of the existence of metastable phases, which can be observed with a sharp change in temperature:
A 
O: ↔ (S); CO: (S)↔ (S); VO: ↔ (S).
Rice. 4.4. Sulfur State Diagram
Triple points correspond to three-phase equilibria: A - orthorhombic, monoclinic and vaporous sulfur; C - monoclinic, liquid and vapor; Rhombic, monoclinic and liquid sulfur. At point O (the point of intersection of the dotted lines inside the triangle), there is a metastable equilibrium of three phases: rhombic, liquid and vapor.
Thus, using a phase diagram, one can determine the phase state of a substance under given conditions or, conversely, by detecting one or another polymorphic modification of a substance (for example, an alloy or a mineral), characterize the conditions for its formation.
Gibbs phase rule states that the number of degrees of freedom WITH equilibrium thermodynamic system is equal to the difference between the number of components TO and the number of phases Ф, plus the number of factors P, affecting the balance
The phase rule allows one to predict the behavior of the system with a change in one, two or more external conditions using the number of degrees of freedom and calculate the maximum number of phases that can be in equilibrium under given conditions. Using the phase rule, one can predict the thermodynamic possibility of the existence of a system.
Usually the value P = 2, since only two factors are taken into account: temperature and pressure. Other factors (electrical, magnetic, gravitational) are taken into account as needed. Then the number of degrees of freedom is
If the temperature (or pressure) in the system remains constant, then the number of state parameters is reduced by one more
If the temperature and pressure are kept constant in the system (P = 0), then the number of degrees is
The number of degrees of freedom for a one-component two-phase system (for example, crystal - liquid, crystal - vapor, liquid - vapor) is equal to
This means that each temperature corresponds to one single pressure value and, conversely, any pressure in a two-phase one-component system is realized only at a strictly defined temperature.
Therefore, the heating of any two coexisting phases must be accompanied simultaneously by a strictly defined change in pressure, i.e. the temperature and pressure of the two phases are related functional dependence P=f(T).
Example 5.1. Determine the largest number of phases that can be in equilibrium in a system consisting of water and sodium chloride.
Solution. In this system, the number of components (TO) equals two. Hence, C = = 4 - F. The largest number of phases corresponds to the smallest number of degrees of freedom. Since the number of degrees of freedom cannot be negative, the smallest value WITH equals zero. Therefore, the maximum number of phases is four. The given system satisfies this condition when a solution of sodium chloride in water is in equilibrium simultaneously with ice, solid salt and water vapor. In this state, the system is variant-free (invariant), i.e. this state is achieved only at strictly defined temperature, pressure and concentration of the solution.
One-component systems
At TO = 1 the phase rule equation will take the form
If there is one phase in equilibrium, then WITH = 2. In this case, we say that the system bivariant ;
two phase - C = 1, system monovariant;
three phases - WITH = 0, system is 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 (7), and volume (V) of the phase can be represented by a three-dimensional phase diagram. Each point (these are called figurative dot) on such a diagram depicts some equilibrium state. It is usually more convenient to work with sections of this diagram by a plane r - T (at V = const) or plane p - v (at T = const). Let us analyze in more detail the case of a section by a plane r - T (at V = const).
Consider, as an example, the phase diagram of a single-component system - water (Fig. 5.1).
Phase diagram of water in coordinates r - T shown in fig. 5.1. It is made up of three phase fields - areas of various (p, t) values at which water exists in the form of a certain phase - ice, liquid water or steam (indicated by the letters L, W 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 in order to describe the system, two independent variables - temperature and pressure. These variables can be changed in these areas independently, without changing the type and number of phases.
The phase fields are separated by three boundary curves.
Rice. 5.1.
Curve AB - evaporation curve , expresses dependence vapor pressure of liquid water on temperature (or represents the dependence of the boiling point of water on pressure). In other words, this line corresponds two-phase equilibrium liquid water - steam, and the number of degrees of freedom, calculated according to the phase rule, is C \u003d 3 - 2 \u003d 1. Such a balance monovariantly. This means that for full description system, it is enough to determine only one variable either temperature or pressure. The second variable is dependent, it is given by the shape of the curve lv. Thus, for a given temperature, there is only one equilibrium pressure, or for a given vapor pressure, only one equilibrium temperature.
At pressures and temperatures, corresponding points below the line AB, the liquid will evaporate completely and this area is the vapor area.
At pressures and temperatures corresponding to points above the line AB , the vapor is completely condensed into a liquid (C = 2). Upper limit of evaporation curve AB is at the point V, which is called critical point (for water 374°C and 218 atm). Above this temperature, the liquid and vapor phases become indistinguishable (the clear liquid/vapor interface disappears), so Ф = 1.
The AC line is the ice sublimation curve (sometimes called a line sublimation ), reflecting the dependence water vapor pressure over ice on temperature. This line corresponds monovariant ice-steam equilibrium (C = one). above the line AC lies the region of ice, below is the region of steam.
Line AD melting curve , expresses dependence melting temperature of ice on pressure and corresponds monovariant equilibrium ice - liquid water. For most substances, the line AD deviates from the vertical to the right, but the behavior of water is anomalous: liquid water occupies a smaller volume than ice. Based on the Le Chatelier principle, it can be predicted that an increase in pressure will cause a shift in the equilibrium towards the formation of a liquid, i.e. the freezing point will drop.
Research carried out by GT.-U. Bridgman to determine the course of the ice melting curve 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. So the upper limit of the line AD- point D where ice I (ordinary ice), ice III and liquid water are in equilibrium. This point is at -22°C and 2450 atm.
Triple point of water (a point reflecting the balance of three phases - liquid, ice and steam) in the absence of air is at 0.0100 ° C and 4.58 mm Hg. Art. Number of degrees of freedom C = 3 - 3 = 0, and such an equilibrium is called invariant. When any parameter is changed, the system ceases to be three-phase.
In the presence of air, the three phases are in equilibrium at 760 mm Hg. Art. and 0°C. The decrease in the temperature of the triple point in air is caused by the following at h and us and:
- 1) the solubility of the gaseous components of air in liquid water at 1 atm, which leads to a decrease in the triple point by 0.0024°C;
- 2) an increase in pressure from 4.58 mm Hg. Art. up to 1 atm, which reduces the triple point by another 0.0075°C.
Crystalline sulfur exists in the form two modifications - rhombic (S p) and monoclinic (S M). Therefore, the existence of four phases is possible: rhombic, monoclinic, liquid and gaseous (Fig. 5.2).
Solid lines limit four regions: vapor, liquid, and two crystalline modifications. The lines themselves correspond to monovariant equilibria of the two corresponding phases. Note that the balance line
monoclinic sulfur - melt deviated from the vertical to the right (compare with the phase diagram of water). This means that during the crystallization of sulfur from the melt, volume reduction. At points A, B and WITH three phases coexist in equilibrium (point A rhombic, monoclinic and steam, point V - rhombic, monoclinic and liquid, point WITH - monoclinic, liquid and vapor). It is easy to see that there is one more point O, in which there is an equilibrium of three phases - superheated rhombic sulfur, supercooled liquid sulfur and vapor supersaturated with respect to vapor in equilibrium with monoclinic sulfur. These three phases form metastable system , i.e. system in the state relative stability. The kinetics of the transformation of metastable phases into a thermodynamically stable modification is extremely slow, however, with long-term exposure or the introduction of monoclinic sulfur seed crystals, all three phases still transform into monoclinic sulfur, which is thermodynamically stable under conditions corresponding to the point O. The equilibria to which the curves correspond OA, OV and OS (curves of sublimation, melting and evaporation, respectively), are metastable.
Rice. 5.2.
Clausius-Clapeyron equation
Movement along the lines of two-phase equilibrium on the phase diagram (C = 1) means a coordinated change in pressure and temperature, i.e. R = f(T). General form such a function for one-component systems was established by Clapeyron.
Suppose we have a monovariant equilibrium water - ice (line AD in fig. 5.1). The equilibrium condition will look like this: for any point with coordinates (R, D) belonging to the line AD.
For a one-component system p = dG/dv, where G- Gibbs free energy, and v is the number of moles. Need to ExpressFormula Δ G=
= Δ H-T Δ S not suitable for this purpose, as it was bred for p, T = const. In accordance with equation (4.3)
According to the first law of tagshodynamics 
and according to the second law of thermodynamics _, and then
It is clear that in equilibrium
since the amount of ice formed in the equilibrium state is equal to the amount of water formed). Then
Molar (i.e. divided by the number of moles) volumes of water and ice; S of water, S of ice - molar entropies of water and ice. We transform the resulting expression into
(5.2)
where ΔSf, ΔVf p - change in molar entropy and volume at phase transition (ice -> water in this case).
Since it is more common to use the following form of equation:
where ΔHf p is the change in enthalpy during the phase transition; ΔV p - change in molar volume during the transition; ΔTf p 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 by the evaporation of a substance.
Example 5.2. It is known that ice has a larger molar volume than liquid water. Then, when water freezes, ΔVf „ = V | da - V water > 0, at the same time, DHf „ = = DH K < 0, since crystallization is always accompanied by heat release. Therefore, DHF „ /(T ΔVph p)< 0 и, согласно уравнению Клапейрона, производная dp/dT< 0. This means that the line of monovariant equilibrium ice - water on the phase diagram of water should form obtuse angle with temperature axis.
Clausius simplified the Clapeyron equation in the case evaporation and sublimations , assuming that:
Substitute (from the Mendeleev - Clapey equation
ron) into the Clapeyron equation:
Separating the variables, we get
(5.4)
This equation can be integrated if the dependence of ΔH IS11 on T. For a small temperature interval, we can take ΔH NSP constant, then
where WITH - integration constant.
Dependency In R from /T should give a straight line, from the slope of which it is possible to calculate the heat of evaporation D # isp.
Let us integrate the left side of equation (5.4) within the limits of R ( before p 2 , and the right one - from G to T 2> those. from one point (p, 7,) lying on the equilibrium line liquid - vapor, to another - (p 2, T 2):
We write the result of integration in the form
(5.6)
sometimes called the Clausius-Clapeyron equation. It can be used to calculate the heat of vaporization or sublimation if the vapor pressures at two different temperatures are known.
Entropy of evaporation
Molar entropy of evaporation 
equal to the difference
Because it can be assumed
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.
Trouton's rule: the molar entropy of evaporation of any liquid is about 88 JDmol 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 JDmol K). Trouton's rule allows you to determine the enthalpy of vaporization of a liquid from a known boiling point, and then, using the Clausius-Clapeyron equation, determine the position of the line of monovariant equilibrium liquid-vapor on the phase diagram.
Example 5.3. Estimate the vapor pressure over diethyl ether at 298 K, knowing its boiling point (308.6 K).
Solution. According to Trouton's rule AS.. rn = 88 JDmol K), on the other hand,
We apply the Clausius-Clapeyron equation (5.6), taking into account that at boiling (T = 308.6 K), the vapor pressure of ether p = 1 atm. Then we have: In /; - In 1 \u003d 27.16 x x 10 3 / 8.31 (1 / 308.6 - 1 /T), or In R \u003d -3268 / 7 "+ 10.59 (and this is the equation of the line of monovariant equilibrium liquid - vapor on the phase diagram of the ether). Hence, at T = 298 K (25°C), R = 0.25 atm.
Entropy of melting not so constant for different substances as the entropy of evaporation. This is due to the fact that disorder (which is measured by entropy) increases in the transition from solid to liquid state not as strong as during the transition to the gaseous state.
1.a)
Solid sulfur (see clause 7.1) has two modifications - rhombic
and monoclinic.
In nature, a rhombic shape is usually found, with
heating higher T per \u003d 95.4 ° C (at normal pressure) gradually turns into
turning into a monoclinic. On cooling, the reverse transition occurs.
Such reversible transformations of modifications are called enantiotropic.
b) So, at the indicated temperature, both forms are in equilibrium:
moreover, the transition in the forward direction is accompanied by an increase in volume. Naturally, according to Le Chatelier's principle, the transition temperature ( T per) depends on the pressure. Increasing pressure (Δ P> 0) will shift the equilibrium to the side with less volume (S rhombus), so to go to S mon higher temperature required T lane (Δ T ln > 0).
v) Thus, here the signs Δ P and Δ T lane match: curve slope T lane (P) - positive . On the state diagram (Fig. 7.3), this dependence is reflected by an almost straight line AB.
2.a) In total, sulfur has 4 phases: the two named solid, as well as liquid and gaseous. Therefore, there are 4 areas on the state diagram corresponding to these phases. And the phases are separated six lines, which correspond to six types of phase equilibria:
b) Without a detailed consideration of all these areas and lines, we briefly indicate the consequences for them from the phase rule (practically the same as for water):
I. in each of the 4 areas - the state bivariant:
Ф= 1 and WITH= 3 – 1 = 2 , (7.9,a-b)
II. and on each of the 6 lines - the state monovariant:
Ф = 2 and WITH= 3 - 2 = 1 . (7.10, a-b)
III. In addition, there are 3 triple points (A, B, C), for which
Ф = 3 and WITH\u003d 3 - 3 \u003d 0. (7.11, a-b)
In each of them, as in the triple point of the water diagram, three phases exist simultaneously, and similar states - invariant, i.e. it is impossible to change a single parameter (neither temperature nor pressure) so as not to “lose” at least one of the phases.
7.5. Clausius-Claiperon equation: general form
We obtain equations that determine the course of the phase equilibrium lines, i.e.
Addiction pressure saturated steam (above liquid or solid phase) on temperature and
Addiction melting point from external pressure.
1. a) Let us turn to the Gibbs molar energy, i.e., to the chemical potential:
(A bar above the values means that they refer to 1 I pray substances.)
b) Condition chemical equilibrium (6.4, b) between the phases of a one-component system has the form:
v) From this condition, in particular, it follows that upon transition 1 pray substance from one phase to another, its Gibbs energy does not change:
Here the indices "f.p." mean phase transition, and - heat (enthalpy) and entropy this transition(based on 1 mole substances).
2. a) On the other hand, the Gibbs energy of an equilibrium process depends on temperature and pressure:
For the above transition 1 mole substances from one phase to another
as follows:
where is the change in molar volume as a result of the phase transformation.
b) However, so that, despite a change in temperature or pressure, in our
the interfacial equilibrium was maintained in the system, all the conditions known to us must still be satisfied - thermal, dynamic and chemical equilibrium between the phases, i.e. equality (7.14,a) also remains valid.
