Educational book on chemistry. Phase states and transformations of water 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 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.

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.

Studies pioneered by Bridgman to determine 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

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

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.

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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.

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 (see problem 11).

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 view, 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 evaporation different liquids If there is no association or dissociation of molecules, 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.