Freezing curve

Figure 10. (b) Corresponding hydrogen-ion distribution curves. Freezing po-... 

Non-freezing water is observed for the sample with W = 0.21 gg". On the crystallization curves, freezing bound water is observed at a temperature lower than the melting temperature of free water (Nos 2 and 3). The melting peak of freezing bound water merges into that of of free water (Nos 6 and 7). 

A freezing-point curve (freezing point as a function of liquid composition) and a solubility curve (composition of a solution in equilibrium with a pure solid as a function of temperature) are different ways of describing the same physical situation. Thus, strange as it may sound, the composition xa of an aqueous solution at the freezing point is the mole fraction solubility of ice in the solution. 

Figure 12.7 Solid curve freezing-point curve of a liquid melt of Zn and Mg that solidifies to the solid compound ZnaMg. The curve maximum (open circle) is at the compound composition = 213 and the solid compound melting point 7" = 861 K. Dashed curve calculated using Eq. 12.5.23 with A(usH = 15.8 kJ mol . ...

Uquidus curve The freezing point of a molten mixture of substances varies with the composition of the mixture. If the freezing points are plotted as a function of the composition, the line joining the points is called a liquidus curve. Such mixtures usually freeze over a range of temperature. If the temperature at which the last traces of liquid just solidify (assuming that sufficient time has been allowed for equilibrium to be established) are plotted against composition the resulting line is called a solidus curve. 

At a given temperature and pressure, a pure compound can exist in one, two or three states. The compound exists at three different states at the triple point and at two different states along the curves of vaporization, freezing and sublimation. Refer to Figure 4.6. 

It should be noted that the modern view is that all partially miscible liquids should have both a lower and upper critical solution temperature so that all such systems really belong to one class. A closed solubility curve is not obtain in all cases because the physical conditions under normal pressure prevent this. Thus with liquids possessing a lower C.S.T., the critical temperature (the critical point for the liquid vapour system for each component, the maximum temperature at which liquefaction is possible) may be reached before the consolute temperature. Similarly for liquids with an upper C.S.T., one or both of the liquids may freeze before the lower C.S.T. is attained. 

It is a well-known fact that substances like water and acetic acid can be cooled below the freezing point in this condition they are said to be supercooled (compare supersaturated solution). Such supercooled substances have vapour pressures which change in a normal manner with temperature the vapour pressure curve is represented by the dotted line ML —a continuation of ML. The curve ML lies above the vapour pressure curve of the solid and it is apparent that the vapour pressure of the supersaturated liquid is greater than that of the solid. The supercooled liquid is in a condition of metastabUity. As soon as crystallisation sets in, the temperature rises to the true freezing or melting point. It will be observed that no dotted continuation of the vapour pressure curve of the solid is shown this would mean a suspended transformation in the change from the solid to the liquid state. Such a change has not been observed nor is it theoretically possible. 

System in which the solid phases consist of the pure components and the components are completely miscible in the liquid phase. We may now conveniently consider the general case of a system in which the two components A and B are completely miscible in the liquid state and the solid phases consist of the pure components. The equilibrium diagram is shown in Fig. 1,12, 1. Here the points A and B are the melting points of the pure components A and B respectively. If the freezing points of a series of liquid mixtures, varying in composition from pure A to pure B, are determined, the two curves represented by AC and BC will be obtained. The curve AC expresses the compositions of solutions which are in equilibrium, at different temperatures, with the solid component A, and, likewise, the curve BC denotes the compositions... 

The separation of the solid phase does not occur readily with some liquid mixtures and supercooling is observed. Instead of an arrest in the cooling curve at /, the cooling continues along a continuation of c/ and then rises suddenly to meet the line f g which it subsequently follows (Fig. 1,13, 1, iii). The correct freezing point may be obtained by extrapolation of the two parts of the curve (as shown by the dotted line). To avoid supercooling, a few small crystals of the substance which should separate may be added (the process is called seeding ) these act as nuclei for crystallisation. 

The general case of two compounds forming a continuous series of solid solutions may now be considered. The components are completely miscible in the sohd state and also in the hquid state. Three different types of curves are known. The most important is that in which the freezing points (or melting points) of all mixtures lie between the freezing points (or melting points) of the pure components. The equilibrium diagram is shown in Fig. 7, 76, 1. The hquidus curve portrays the composition of the hquid phase in equihbrium with sohd, the composition of... 

Two other types of equilibrium curves are occasionally encountered with the system of two components forming a continuous series of solid solutions. These are shown in Figs. 1,16, 3 and 1,16, 4. In the former the freezing or melting curve passes through a minimum (examples p-chloroiodobenzene, m.p. 57° - p-dichlorobenzene, m.p. 53° naphtha-... 

Fig. 8. Boiling and freezing temperatures of KOH solutions (33). The boiling point curve assumes a pressure of 101.3 kPa (760 mm Hg).

The coUigative properties of antifreeze chemicals may also result in boiling point elevation. As the chemical is added to water, the boiling point of the mixture increases. Unlike the freeze depression, the boiling elevation does not experience a maximum the boiling point versus concentration curve is a smooth curve that achieves its maximum at the 100% antifreeze level. The boiling point elevation can be another important characteristic for antifreeze fluids in certain heat-transfer appHcations. 

The increase in fuel viscosity with temperature decrease is shown for several fuels in Figure 9. The departure from linearity as temperatures approach the pour point illustrates the non-Newtonian behavior created by wax matrices. The freezing point appears before the curves depart from linearity. It is apparent that the low temperature properties of fuel are closely related to its distillation range as well as to hydrocarbon composition. Wide-cut fuels have lower viscosities and freezing points than kerosenes, whereas heavier fuels used in ground turbines exhibit much higher viscosities and freezing points. 

Salt Brines The typical curve of freezing point is shown in Fig. II-IIO. Brine of concentration x (water concentration is I-x) will not solidify at 0°C (freezing temperature for water, point A). When the temperature drops to B, the first ciystal of ice is formed. As the temperature decreases to C, ice ciystals continue to form and their mixture with the brine solution forms the slush. At the point C there will be part ice in the mixture /(/i+L), and liquid (brine) /i/(/i-t-L). At point D there is mixture of mi parts eutectic brine solution Di [concentration mi/(mi-t-mg)], and mo parts of ice [concentration mol m -t- mo)]. Coohng the mixture below D solidifies the entire solution at the eutectic temperature. Eutectic temperature is the lowest temperature that can be reached with no solidification. 

With liquids, the refractive index at a specified temperature and wavelength is a sensitive test of purity. Note however that this is sensitive to dissolved gases such as O2, N2 or CO2. Under favourable conditions, freezing curve studies are sensitive to impurity levels of as little as 0.(X)1 moles per cent. Analogous fusion curves or heat capacity measurements can be up to ten times as sensitive as this. With these exceptions, most of the above methods are rather insensitive, especially if the impurities and the substances in which they occur are chemically similar. In some cases, even an impurity comprising many parts per million of a sample may escape detection. 

Impurities in hydrocarbons can be characterised and evaluated by gas chromatography and mass spectrometry. The total amount of impurities present can be estimated from the thermometric freezing curve. 

Erstarnmgs-kurve, /. freezing-point curve, -punkt, m. freezing point setting point, solidification point coagulation point, -warme, /. heat evolved on solidification, heat of fusion. 

---