§ 004 PURE SUBSTANCES Pure substances are materials that are characterized by a molecule when they are molecular materials like n-butane (molecule CH3CH2CH2CH3) and in all other cases by a chemical formula like NaCi for sodium chloride, common salt. Pure substances,, can take different forms, all having their own stability conditions in terms of\ temperature and pressure. phases and forms The three opening phrases, written by Gibbs under the heading "On Coexistent Phases of Matter" (p. 96 in the 1906 edition of The Scientific Papers of* J. Willard Gibbs, Vol I, Thermodynamics) read "In considering the different homogeneous bodies which can be formed out c any set of component substances, it will be convenient to have a term which shall' refer solely to the composition and thermodynamic state of any such body without, regard to its quantity or form. We may call such bodies as differ in composition or state different phases of the matter considered, regarding all bodies which differ; only in quantity and form as different examples of the same phase. Phases which can exist together, the dividing surfaces being plane, in an equilibrium which does not depend upon passive resistances to change, we shall call coexistent" And (p. 97), after the appearance of n + 2 - r (our c + 2-p; <-003) "Hence, if r = n + 2, no variation in the phases (remaining coexistent) is possible. It does not seem possible that r can ever exceed n + 2.An example ofn = 1 and r = 3 is seen in the coexistent solid, liquid, and gaseous forms of any substance of invariable composition". In the case of the first quotation the matter considered (any set of component substances) is (brought to equilibrium in an experimental set-up under certain conditions and subsequently) analyzed as for its homogeneous parts, which correspond to one or more phases (numbered I, II, III, or labelled a, p, y, ...). In the case of the second quotation the matter considered is a substance of invariable composition, and the phases are specified by their forms. Following Gibbs, we will use term 'phase' in the general context of equilibrium between phases of matter. The word phase is present in compound words, having a general nature. Compounds like phase diagram, Phase Rule, two-phase equilibrium curve, single-phase field, three-phase equilibrium. The term form' will be used primarily in the context of materials science. The determination of the form is the first step to the identification of a homogeneous material (phase). A form is characterized by a certain molar volume - which is a ^PeWams 29 nynU0(Js function of temperature and pressure - by a certain crystal structure tolien it is crystalline solid), and so on. And whenever, within a given form, two or more substances can form homogeneous mixtures of variable composition, the properties of the mixtures like molar volume will be continuous functions of the composition variables. Two phases in equilibrium can have the same form; and if so their compositions necessarily are different. {he PT phase diagram The basic structure element of the PT phase diagram for a pure substance is composed of three two-phase equilibrium curves emanating from the triple point. Figure 1. FIG. 1. Basic structure element of a pure substance's phase diagram A two-phase equilibrium curve has a double function: the (a + p) two-phase equilibrium curve i) represents the PT circumstances for which equilibrium can be realized between the 0. (1) 30 Levi In terms of temperature, p is the high-temperature form and a the / 0 In the case of Figure 1, p is the high-temperature form and at the same time low-pressure form: the slope of the two-phase equilibrium curve is positive. For substance water, on the other hand, liquid water is the high-temperature form & at the same time, the high-pressure form: the slope of the two-phase equilibnuj curve (the melting curve) is negative; see Figure 001:6. The change from ice? water at 0 °C, 1 atm is accompanied by a decrease in volume (-19.63 + 18.00 =) -1.63 cm3-moľ1 and a heat effect of 6008 J-moľ1. As a matter of fact, the thermal counterpart of AV is not the heat effect Q itself, a quantity related to it. The volume change av is a property which is expresse* m3, mol"1, and m3-moľ1 is equal to joule-per-mole-per-pascal; J moľ1 Pa'1. It meal that when AV is multiplied by the mechanical potential, the pressure P, a property obtained in J-moľ1 - like the heat effect Q. Analogously, the thermal counterpart AV is a property expressed in J-moľ1-K'1. This property is obtained when the hi effect (of the change a -»p) is divided by, the thermal potential, tl thermodynamic temperature at which the change takes place. It is the change | molar entropy AS (see below; ->106, in particular). Summarizing, in a PT phase diagram of a pure substance the single-phast fields are positioned such that i) on increasing pressure the changes are i) decreasing volume, and ii) on increasing temperature the changes are increasing entropy. Clapeyron's equation (->110) The volume change, ApaV, and the heat effect, Q""'0, not only (by thei| signs) determine the sign of the slope of the equilibrium curve, they also, by the magnitudes, determine the magnitude of the slope: dP dľ Q' T • a£v In this equation, T is the thermodynamic temperature, for which the slope ii taken. The relationship is referred to as Clapeyron's equation, after Emil| Clapeyron (1799-1864). Replacing the quotient of heat effect pnH tem«.«(..« ^ L ^dP/dr=as/a\/. dJnP dT ív0=-(-1/7fi)dr' (31 31 (3b) I neneral validity; its thermodynamic derivation is * i a special equation is obtained for the case that p J"3*0" i ,nd moreover, if p is taken as an ideal gas, and ^Jfi spedai case A^reduces to RTIP'and with (1/P) ^changes into Q a -* vap (4) (5) R titration sujgests a linear relationship between In P and 1/7". In Oflship is only roughly linear - owing to the fact that Q, along the JHppbrnes smaller with in creasing temperature. In any case, it J^oifimon practice to represent vapour pressure data - the pressure ..equilibrium .vith solid or liquid - in a InP vs 1/7" diagram. Such a ^ApfMsnfaKfe^bf-vapour pressure data is referred to as Clausius-Clapeyron plot; liquid vapour • increasing temp. •>.,Jhriple pt. 30 40 lisillifi 10 K/T - * FIG 2 Clausius-Clapeyron plot of the boiling curve for water; from below the triple point up to its end point, the critical point where the distinction between liquid and vapour comes to an end (->206) LevéR metastability One of the experiments described in § 001 was carried out - undedj atmospheric pressure - with an amount of water having a temperature of -5 "Cjf i.e. experimental circumstances under which liquid water may change! spontaneously into ice. Circumstances that correspond to a point in the phasef diagram lying in the single-phase field for ice. In itself, water having a temperature of -5 °C is not less stable than water havings a temperature of + 5°C. The only thing is that at -5 °C liquid water may change! spontaneously into ice, whereas at + 5"C it never will do. For these reasons liquid water at 1 atm and -5 °C is said to be metastable. It is (even) possible to experimentally study the equilibrium between supercooled water and gaseous water (—>Exc 3). It is customary to refer to this equilibrium between phases as an example of metastable equilibrium. Accordingly, the, extension (beyond the triple point) of the (liquid + vapour) equilibrium curve is"* referred to as metastable extension. Metastability is a fascinating and, at the same time, a complicating-phenomenon. Complicating, because spontaneity (irreversibility) does not go well with controllability (reversibility). Diamond and graphite are two forms of the substance carbon. One is inclined to think that diamond is the stable one of the two forms, but it is not (-»109). polymorphism In the realm of crystalline materials polymorphism is a common phenomenon - it is the fact that many substances give rise to more than one crystalline form. A speaking example is found in the substance carbon tetrachloride, especially so because of the occurrence of plastic crystalline forms. Substances, like carbon tetrachloride, having spherically shaped molecules, often manifest themselves in a plastic crystalline form. In plastic crystals the individual molecules occupy crystallographic positions whereas their directions in space are arbitrary: they have (a dynamical) orientational freedom. In contrast to 'normal' crystalline materials - where the molecules obtain orientational and translational freedom (no fixed positions) at the same time, i.e. at the melting point - for materials like carbon tetrachloride orientational freedom is obtained first and translational freedom in a second step. This is why the plastic crystalline state is referred to as a mesostate between 'normal' solid and liquid. In the case of carbon tetrachloride the normal solid is monoclinic, and at 225.4 K it changes into a rhombohedral plastic-crystalline form. The latter subsequently changes into liquid at 250.3 K. The curious thing about carbon tetrachloride is that it can take a second plastic crystalline form - face-centred cubic (fee) - which, invariably, is metastable. The form can be obtained by crystallization from the liquid, and, when it is heated, it melts at 244.8 K; see Figure 3. "The rhombohedral plastic crystalline form and the low-temperature monoclinic ■%rm stand to each other in, what is called, and enantiomorphic relationship: the twcKcrystalline forms can exist at the same time, in equilibrium with one another; a phenomenon referred to as enantiomorphism. The relationship between the two plastic crystalline forms, on the other hand, is a monotropic relationship: the two crystalline forms never coexist - the only thing is that the invariably metastable fee form can change spontaneously into the other; the phenomenon is referred to as monotropism. plast, cryst fee_z liquid ca4 ordered solid monoclinic plast, cryst rhombo liquid 200 K 250 K 300 K FIG. 3. Carbon tetrachloride's polymorphic relationships. Top: metastable sequence; bottom: stable sequence Occasionally, a form, which is stable in a certain span of temperature, reenters as the stable form in another span. Re-entrant behaviour is rather frequently observed for forms belonging to the mesostate of liquid crystals (van Hecke 1985). Re-entrant behaviour becomes a possibility when the heat effect of the transition is so small that it can change sign (before the form changes into liquid, or isotropic liquid in the case of liquid crystals). The scheme shown in Figure 4 pertains to iron, whose re-entrant form is the body-centred cubic one. At 1184 K an amount of heat of 900 J-mol"1 is needed to change bee iron into fee - at 1665 K, 837 J-mol"1 is needed to realize the opposite change! ferro ■ paramagnetic Cp 1042 1184 1665 1609 hoc heat effect (J-mol ) &.sir ! I I 900 0.0914 fee I occ I s I ! 837 13807 0.0605 0.918 3132 K - liquid vapour 349.6-10 13.4 RG 4 Sequence of Iron's forms. Heat effects of the transitions; increases in entropy divided by the gas constant 35 34 Level! In the scheme, Figure 4, the row labelled AS/R stands for the change i entropy {see above) divided by the gas constant. AS and R are expressed itjg J-K"1-mor1, their quotient being a dimensionless quantity. The advantage of usin (here) AS over using Q, the heat effect, is that, for certain classes of change, th former, unlike the latter, has a more or less constant value. As an example, for metallic sodium, melting at 370.98 K, the heat of melting is 2603 J-mol"1; as distinct from 1809 K and 13807 J-mol"1 for iron. Notwithstanding these large differences, the values of AS are quite comparable: 0.84 R for Na and 0.92 R for| Fe. This observation finds expression in Richards' rule, stating that the entropy of melting of (the outspoken) metals (excluding metals like Sb) is represented by AS « R. For the ionic alkali halides the entropy of melting is AS = 3 R. For the change from liquid to vapour at 1 atm pressure Trouton's rule states that AS »11 R; and it is known that the rule is reasonably well respected by non-polar liquids having boiling points in the range 0 to 300 °C, and consisting of small molecules. For Fe, far outside the 0 -» 300 °C temperature range (see Figure 4), the entropy of vaporization is about 13 R - still in the vicinity of the rule. *!fj|,s©d'a9ratins 2000 FIG. 5. Heat-capacities-divided-by-the-gas-constant of iron's forms (Barin 1989); see also Figure 4 a lambda type of transition In the scheme for iron, the cross on the temperature line represents the Curie temperature (1042 K): the temperature at which iron changes from a ferromagnetic to a paramagnetic material. The magnetic susceptibility of a ferromagnetic material decreases with temperature, and very rapidly so in the vicinity of the Curie point - where it falls down to a paramagnetic level (virtually zero). At the Curie temperature there is neither a change in crystal structure, which remains bcc, nor an (isothermal) heat effect. The heat effect involved in the change is spread out over a range in temperature. It manifests itself in the form of an extra heat capacity (~>1QZ), increasing with temperature, and falling down at the Curie point. The heat-capacity plot resembles the Greek letter lambda - it explains the use of the term lambda transition, see Figure 5. Unlike the transition from bcc to fee at 1184 K - where during the transition a bcc phase is in equilibrium with an fee phase and where AS has a finite, non-zero value - the transition at 1042 K has AS = 0, and it has nothing to do with an equilibrium between two phases. In the classification of transitions by Ehrenfest (1933), the transition at 1184 K is referred as a first-order transition, and the one at 1042 K as a second-order transition. • a glass transition The molecule which is pictured, Figure 6, has a rather planar structure: the carbon atoms 1,2,3,5 and 6 and the oxygen atom are about in the same plane (the plane of the paper); carbon atom 4 is below the plane, and the isopropylidene group originates from it in an upward direction. The molecule is a chiral molecule (cannot be superimposed on its mirror image) and, therefore, it is characteristic of a substance which is optically active (rotates the plane of polarization of polarized light); that substance is laevorotatory carvone. The mirror image of the molecule (C atom 4 above the plane and the isopropylidene group downward) is characteristic of the substance dextrorotatory carvone. f-carvone glass transition undercooled liquid --i--------- liquid , spontaneous crystallization monocl in ic solid liquid 250 K ISO 200 FIG. 6. Laevorotatory carvone - its forms and its behaviour Level Besides, ^-carvone and cf-carvone have the same thermo-physical properties, such as melting point and heat of melting (imagine that you can see the individual molecules in a beaker with boiling ^-carvone, the thermometei indicating t = 231 °C; then turn your back to the beaker and use a mirror to see what is going on in it; in the mirror you see molecules having the configuration ol d-carvone; the thermometer indicates f = 231 °C, the only difference being thai the numbers on the thermometer are written backwards). Nota bene, these observations certainty do not mean that a mixture of d- and l- carvone will manifest the same phase behaviour as d- or £- carvone individually (->005). Liquid carvone can be supercooled easily, i.e. prevented from crystallization at, • or below its melting point. Figure 7 is a thermogram which depicts the behaviour ] of a supercooled I- carvone sample, when heated in a Differential Scanning Calorimeter (DSC). In a DSC, the sample to be studied and a reference (e.g. an empty sample pan) are mounted on a metal block that can be heated at a certain rate. In simple terms, the thermogram represents the heat to be added or withdrawn from the sample, in order to keep it at the same temperature as the reference. The events, registered in t- can/one's thermogram in order of increasing temperature, are the so-called glass transition (-171 K); a crystallization process (-193 K to 208 K); followed by a recrystaliization phenomenon (-210 K to 218 K); and, finally, the melting of the sample (-248 K). ams 37 heat taken given off melting glass transition / crystallization 165 77K 215 265 FIG. 7. Thermogram of a supercooled liquid sample of laevorotatory carvone (Galiis et al. 1996) Like the magnetic transition in the bcc form of iron, the glass transition in a supercooled liquid can be regarded as a continuous, non-isothermal transition within a given form. Unlike the former, the latter has, for a given material, not a fixed position on the temperature scale: the glass transition temperature depends the cooling conditions to which the liquid is subjected. Below the glass on .tion temperature the positions of the molecules are fixed: any molecular ^vement is suppressed by the viscosity, which has become too high (Papon etal-2002). Each of the stable forms taken by a pure substance has its own stability field in the PTphase diagram. Forms can appear under conditions outside their stability fields, ,n which case they are said to be metastable. Frequently forms are seen that are metastable whatever the circumstances. EXERCISES 1. the position of phase symbols P The figure is part of the phase diagram of a pure substance, including the forms, a, (5 and y, of which the molar volumes increase in the order p, y, a. • Provide each of the single-phase fields with the correct (phase) symbol. • Arrange the (form) symbols in order of increasing molar entropy. 2. zero Celsius and zero Celsius The rounded difference in temperature between the triple point and normal freezing point of water is 0.01 K. This 10 mK (millikelvin) difference has been used to redefine the zero point of the Celsius temperature scale (<-002). • To appreciate this, apply Clayperon's equation to calculate, as an integer in mK, the difference in temperature between the two point's. The necessary data are given in the text. 38 3. water's triple point pressure Level 0 The table gives for the pure substance water the equilibrium vapour pressure over solid (ice) as well as over metastable liquid for six temperatures from - 5 °C to 0 °C. trc P(solid)/Torr Pfliquid) /Torr -5 3.013 3.163 -4 3.280 3.410 -3 3.568 3.673 -2 3.880 3.956 -1 4.217 4.258 0 4.579 4.579 In terms of Equation (5), think up a method in which linear least squares is used to calculate - from the given set of data - water's triple-point coordinates. • Next, carry out the calculation - temperature in two decimal places and pressure as an integer in Pa. 4. carbon dioxide's metastable normal boiling point Carbon dioxide is not an everyday substance as far as the positions of its triple point (216.8 K; 5.1 bar) and critical point (304.2 K; 73.9 bar) are concerned. • Use the data to make an estimate of i) its heat of vaporization, and ii) its (metastable) normal boiling point. 5. the substance water under high pressure The triple point data for the substance water shown here (see Tonkov 1992) involve, apart from the liquid, seven solid forms/phases - indicated by Roman numerals. • Use the information to construct the PT phase diagram; mark the single-phase fields with the appropriate symbol. • Estimate the pressure which is needed to solidify water at 100 °C. • Estimate the coordinates of the metastable triple point (II + V +1). triple point r/°C P/GPa l + lll + f -22 0.207 I + II + III -34.7 0.213 Ill + IV + i -17 0.346 II + III + V -24.3 0.344 V + VI + £ 0 0.625 V + VII + Í 81.6 2.15 VI + VII + VIII -3 2.12 ll + V + VI -60 0.6 NB. GPa = gigapascal = 109 Pa >hase diagrams 3Q 6 a rule to be respected by metastable extensions At t)ie {a + p + y) triple point, the metastable extension of a two-phase equilibrium ■ curve has to run into the field bounded by the stable parts of the other two equilibrium curves. wrong The negation of this statement can be reduced to an absurdity, i.e. is giving rise to contradictory conclusions. • Demonstrate this for the shaded field, remembering that at the a side of the (a + p) equilibrium curve p can change spontaneously into a. a phase diagram acts as a thermobarometer The PT phase diagram of aluminium silicate (AlsSi05) with its three solid forms sillimanite (I), andalusite (II) and kyanite (III) plays an important part in geology -thermobarometry in particular. The diagram is given in Tonkov's (1992) compilation, the equations for the (I + II) and (II + III) equilibrium lines being f /x = -415 P /GPa + 848, and t i°C = 920 P /GPa + 114, respectively. According to Althaus (1969), for the change from I to III at 600X, the heat effect is -9.08 kJ -mol"1 (heat given off) and the volume effect -5.51 cm3 -mol"1 (decrease). • Calculate the coordinates of the (I + II + III) triple point. • For 300 = 0.56 (Short and Roy 1964). hase diagrams 45 X 1 0 1 FIG.4. The (solid + liquid) loop and the solid-state region of demixing interfere with one another: the result is a phase diagram with a three-phase equilibrium line, which is the lower boundary of two (solid + liquid) two-phase regions, and the upper boundary of a (solid + solid) two-phase region For the combination of LiCI and KCI, with Li+ (0.76 A) and K+ (1.38 A), there is hardly any solid-state miscibiiity: the TX (solid + liquid) phase diagram is of the simple eutectic type (-> E*c 3)- The term eutectic is from the Greek eutektos, and it means readily melting: a eutectic mixture melts at a temperature lower than the melting points of the pure components. Besides, a three-phase equilibrium, such as in Figure 4 right-hand side, with a liquid phase and two solid phases in the succession solid-liquid-solid, is referred to as a eutectic three-phase equilibrium. Figure 5c is another example of a simple eutectic phase diagram; it is for the combination of dextrorotatory isopropylsuccinic acid (IPSA) and dextrorotatory methylsuccinic acid (MSA); succinic acid is butanedioic acid (HOOCCH2CH2 COOH). initial slopes (->208) The TX phase diagrams Figures 1,2b,3,4 all have (a + p) two-phase regions, limited by two equilibrium curves - one for the compositions of the a-phases, and the other for the B-phases. An equation for the initial slopes of the two equilibrium curves is the equation named after Jacobus Henricus Van't Hoff (1852-1911) - an equation similar to the one named after Clapeyron, Equation (004:4). The equation states that for small A7" = T-T%, where T° is the temperature at which pure A changes from the form a to the form B, the difference between the initial slopes of the equilibrium curves is given by the expression dX" /dT - <\X" IdT = -(Oa^ IRT?2 V (4a^ 46 Level 0 s phase diagrams 47 In this equation Q is the heat effect of the change, and R the gas constant. Otherwise formulated, with AX = X0 -X", the equation reads AX = -(Qa^/RT°2)AT. (4b): In terms of the entropy change, AS (*-004), the two equations change into dX*ldT-), decreases (<), oris equal to zero. The parts of the route are i) through the a field; ii) through the (L + a) field; iii) at the three-phase equilibrium; iv) through the (L + p) field; and v) through the L field. 3. phase diagram and cooling curve Lithium chloride (LiCI,; meltjng point 606 °C) and potassium chloride (KCI; m.p. 770 °C) are miscible in all proportions when liquid. Their solid state miscibility is negligible. A liquid mixture, having KCI mole fraction X= 0.1, will start to crystallize, when cooled, at t = 566 °C. The onset temperatures of crystallization for a number of other composition are (X = 0.2; t = 515 *C); (0.3; 452); (0.4; 370); (0.5; 443); (0.6; 541); (0.7; 618); (0.8; 685); and (0.9; 733). • Construct the (solid + liquid) 7X phase diagram. In an experiment, heat is withdrawn at a constant rate from a sample having X- 0.2. The initial and final temperatures are 600 "C and 200 X, respectively. • Make a graphical representation of the sample's temperature as a function of time (coolina curve: —>006) Level 0" a reciprocal system The four substances NaCI, KCI, NaBr, and KBr share four structural units which are the two anions and the two cations. A system composed of such four substances is referred to as a reciprocal (salt) system. • What is the number of independent variables necessary to define the composition of a like system? • What geometrical figure would you use to represent the compositions of a reciprocal system? increasing repulsive interaction and the phase diagram In the system {(1 - X) A + X B} the interaction in the liquid state between A and B is neutral, the (solid + liquid) TX phase diagram is eutectic. The melting points of A and B are 900 K and 450 K, respectively; the eutectic point has T= 400 K and X = 0.90. • Make a series of sketch drawings of phase diagrams to demonstrate what happens when the interaction between A and B in the liquid state is going to show an increasing, repulsive deviation from neutral mixing behaviour. NB. The properties of the pure components remain the same and so do the initial slopes (at X = 0, and X = 1) of the two liquidus curves (say over the first 10% of the Xaxis). overlapping two-phase regions The two (on their own correct) two-phase regions, (a + (3) and (6 + L), are partly overlapping. As a consequence, the true phase diagram must have an (a + L) two-phase region. • Guided by the rule for metastable extensions, make a sketch of the true phase diagram (first locate the two (L + 0 + a) three-phase equilibrium situations). phase diagrams 59 7 the construction of ternary phase diagrams The three optically active substances (-) IPSA (A), (+) IPSA (B), and (+) MSA (C), acting in Figure 5, are rather alike, and for that reason it can be assumed that the interaction between their molecules in the liquid state has a nearly neutral character. : As a result, their ternary phase behaviour can be predicted from the binary data with fair accuracy. The fact is that for neutral mixing behaviour, and for given, constant 7", the equilibrium solid C plus (liquid mixture containing C) simply satisfies the relations ship Xc = constant = Kc (likewise for A and B); and the equilibrium compound AB plus (liquid mixture containing A and B) satisfies the relationship XAXB = constant = KA6. • Use the binary phase diagrams, Figure 5, to construct isothermal sections of the ternary system; for i) f =100 "C; ii) the temperature of the upper eutectic in the system (+) MSA + (-) IPSA; and iii) ( = 80 °C. Clue. For each of the solids, stable at the temperature considered, determine the value of the equilibrium constant - like the above Kc or KAB - and use it to construct the complete ternary liquidus. Use the ensemble of liquidi to allocate the single- and two-phase fields, and the invariant triangles. NB. If an invariant triangle involves a liquid phase, then its "liquid vertex" is the intersection of two (of the constructed) liquidi. 8. the appearance of an incongruently melting compound In Figure 5a the left-hand liquidus (the A liquidus) intersects the liquidus pertaining to the 1:1 compound (the AB liquidus) at the left of the equimolar composition - the point of intersection being a eutectic point. When, in such a case, component A is given a higher melting point - all other things remaining the same - the situation may arise that the intersection is a peritectic point, at the right of the equimolar composition. When that is the case, AB's melting point becomes metastable: on heating, AB will, at the peritectic temperature, split up in solid A and liquid having the peritectic composition. The congruently-melting compound, Figure 5a, has changed into an incongruently-melting compound. • Construct the 7X solid-liquid phase diagram for a system involving an incongruently melting compound AB. 9. ternary compositions having a constant ratio of the mole fractions of two components In the ternary composition triangle ABC, the locus of the compositions that have the same ratio of the mole fractions of A and B is a straight line ending in vertex C. • Prove the validity of this statement - making use of the properties of similar triangles. Clue. On AB take a point P; on PC take a point Q; similar triangles ABC and RSQ, R and S being points on AB. 60 Level 0 1 10. cyciohexane with aniline - mixing and demixing {(1-X) mole of cyciohexane + X mole of aniline}, in spite of the fact that aniline (aminobenzene) is a nasty substance, is a superior system to demonstrate phenomena of mixing and demixing. The following description of actions and observations - representative of a classroom experiment - may make this clear. Eight test tubes provided with screw caps are filled - using a 10 ml measuring cylinder - with varying amounts of cyciohexane and ainiline; see table. After filling, the tubes 0, 6, and 7 show a single liquid; the tubes 2, 3, 4, and 5 show two, clearly separated liquids; and the content of the remaining tube, tube 1, looks milky. In a next step the tubes 2, 3, 4, and 5 are immersed in water with a temperature of 40 °C, contained in a plastic beaker. As a result of this action the two liquids, in all of the four tubes, change into a clear single liquid. Thereupon, the water and the tubes are allowed to cool to room temperature. Meanwhile the tubes are shaken every now and then; and for each sample the onset temperature of turbidity is registered, see table. A similar procedure is followed for the tubes 0,1, 6, and 7. The tubes are immersed in water having a temperature of 25 °C; and the whole is subsequently cooled by means of ice cubes. The samples undergo a change to a two-liquid situation; with the exception of tube 7, whose content is still homogeneous at 1 °C. § 006 DISTRIBUTION AND SEPARATION Tube cyciohexane aniline v at room onset of (ml) (ml) temperature turbidity 0 7.4 0.4 0.06 one liquid 6.0 1 7.9 0.9 0.12 milky 19.5 2 6.9 1.4 0.19 two liquids 26.0 3 5.8 2.8 0.36 two liquids 30.7 4 4.3 3.5 0.49 two liquids 30.5 5 3.0 5.0 0.66 two liquids 27.7 6 1.9 6.3 0.80 one liquid 14.4 7 1.0 7.1 0.89 one liquid <1.0 1 • What is the temperature of the room where the experiments are carried out? • For t > 0 °C, make a graphical representation - temperature versus mole fraction - of the binodal curve (the boundary of the region of demixing), and from the curve derive the coordinates of the critical point. • Sketch a plausible TX phase diagram for the system over the range from -50 °C to 200 °C. In more detail: use the region-of-demixing data; calculate the initial slopes of the two liquid! emanating from the melting points (mp) of the pure components; and consult Exc 212:12 for a rule of thumb, concerning the change from liquid to vapour. Cyciohexane: 84 gmol"1; 108 cm3mol"1 (25 °C); mp 6.6 °C; bp 81 °C; heat of j melting 2.66 kJmol"1. Aniline: 93 gmol"1; 91 crrfmof1 (25 °C); mp -6.3 °C; bp 185 °C; heat of melting 10.54 kJ-mol"1. elementary characteristic of equilibrium between phases in systems of two or ore components is the fact that the phases as a rule have different compositions. This property holds the possibility that substances can be separated from one another by means of phase changes. saturation When a drop of water is brought in an empty space, say a 200 m3 tank kept at 25°C, it will evaporate rapidly and completely. And free water molecules will be present'in every cubic micrometer of the space. Similarly a few sugar crystals will dissolve rapidly and completely in a cup of water. Water is a good solvent for sugar (molecules), and an empty space, or vacuum if you like, is a good 'solvent' for water (molecules). The amount of foreign molecules - solute molecules - a solvent can accommodate, however, is limited: at a certain 'moment' the solvent is saturated -and this moment differs from case to case. The moment of saturation, for water in a space, is reached when the chemical potential of gaseous water (mh7o) nas become equal to the chemical potential of liquid water (/4ro)- Water added after saturation has been reached will not evaporate anymore: there is equilibrium between a liquid and a gaseous phase, governed by the condition H,0 vap h,0' (1) xxxxxxxx xxxxxxxx FIG. 1. Two analogous cases: left, the saturation of an empty space by a volatile substance; right, the saturation of a liquid medium by a soluble substance And this condition is such that the amount of water in the gaseous phase will correspond to a vapour pressure of 23.756 Torr, for t = 25 °C.