J10 Heat

Change of aggregate state of substances through change of heat content

Change of aggregate state of substances and the equation of Clapeyron-Clausius






Temperature increases by heat intake are accompanied by increases of the volumes of substances. The molecules increase their mutual distances, the density becomes smaller. The further the temperature rises, the more the coherence of the molecules is relaxed. In the end, the loosening reaches a stage, at which it manifests itself characteristically: Solids become fluids (melts) or gases (sublimates), fluids become gaseous (boil) and multi-atomic gaseous substances decompose into their chemical components (dissociate). A substance, when it arrives at its melting temperature, does not at first become hotter while heat is supplied (but you must ensure that the heat is spread uniformly, in order to avoid temperature differences inside it!), but becomes first if all totally fluid - only then will the temperature rise again. What happened to the heat, which the body took in between the instants, at which it had reached the melting point and when the temperature of the molten substance begins to rise again? Answer: The heat has performed work; it has overcome the cohesion of the molecules to the point, that it has converted the solid state into the fluid state. That is similar to the work which is required to pulverize a solid. But also in the finest powder are the smallest particles very large compared with fluid particles and infinitely far away from each other compared with their former mutual distances. Conversion of a solid substance into a liquid substance demands comparatively more work.

Evaporation is quite similar: When the temperature of a fluid arrives at its boiling point, it does not rise in spite of further heat input, but the fluid converts itself completely into steam. Also here arises the question: What has happened to the heat, which entered the fluid between the instant, at which it reached the boiling point, and when it converted completely into steam? And again, the answer is: It has performed work while is was overcoming completely the cohesion of the molecules.

Whether during melting or evaporation or sublimation of a substance or the conversion of two allo-tropic forms of the same substance into each other - as that of white tin into grey tin or conversely, of mono-clinic sulphur into rhombic sulphur or conversely - heat converts itself always into work. The substance is at the pressure p and the temperature T partly in the one, partly in the other aggregate state, whence its total volume is composed of two, distinctly different parts. Let the part in the aggregate state (2) have per mass unit the specific volume v2, that in the state (1) correspondingly v1. From this state onwards, let the substance pass through a Carnot process - similar to that described before - back to its inital state. With the aid of the two main theorems of Thermodynamics, we arrive then at the equation of Clapeyron* and Clausius l = T(v2 - v1)dp/dT, where l is the quantity of heat, required to take 1 gram of the substance from the aggregate state (1) into the aggregate state (2), p and T are the pressure and temperature at which this occurs, v1 and v2 are the specific volumes (of 1 gram) of the substance in the aggregate states (1) and (2). This equation applies to heats of melting, evaporation and sublimation (as well as of convection), depending on whether (2) and (1) refer to the fluid and the solid aggregate state, of the vapour and fluid state, or the vapour and the solid state. (dT and dp refer to infinitely small changes of the temperature and pressure. From the fraction dp/dT, for the geometrical meaning of which you should refer to Fig. 11, you can compute T in its dependence on p - that is, how the melting or boiling temperature T changes with the pressure p, acting on the melting or boiling substance.

* Formulated in the wake of Carnot's work in 1834 by Clapeyron and strictly justified by Clausius.

Melting temperature and melting heat

The molecular changes of solid and liquid substances due to heat input are frequently noticed before they have accepted the new aggregate state: At high temperature, iron is malleable and readily welded, viscous fluids become thin liquid, etc. The temperature at which a solid becomes liquid is called the melting point (more strictly speaking: At which the solid and liquid phases at atmpsheric pressure are present simultaneously and lastingly). It depends essentially only on the chemical kind of substance, only a little on the acting pressure. Unless stated otherwise, the melting point is the temperature, at which a substance melts under the pressure of 1 atm. Since the heat which performs the melting work vanishes as heat, it is called latent - latent melting heat. You understand by this term effectively the number of calories, which are required to liquify 1 g at the temperature of the melting point and the pressure of 1 atm:

substance   C   DT/100 atm   cal/g   substance   C   DT/100 atm   cal/g
mercury   38.87       2.8   antimony   630.5       39
ice   0   - 0.76   79.7   silver   960.5       26
benzol   5.5   2.90   30.4   gold   1063       15.9
glacial acetic acid   6.6       45   copper   1083       41
sulphur (mono-clinic)   119           cast steel   ~1400        
tin   231.85   0.328   13.8   iron   1530       49
bismuth   271   -0.356   10.2   platinum   1770       27
cadmium   320.95   0.629   10.8   iridium   2340        
lead   327.4   0.803   5.5   tantal   2850        
zinc   419.45       23.0   wolfram   3380        

Of all substances ice has the largest latent melting heat (water the largest specific heat). In order to determine it, you pour (for example, in a lecture theatre) over 1 kg of ice 1 kg of water at temperature 80C, mix all of it well and protect it against external heat exchange. In the end, the ice has vanished and you have 2 kg of water at 0C. The 80 kcal, which the kilogram of water has given away during its cooling from 80C to 0C, have converted the kilogram of ice at 0C into water; since the water has the temperature 0C, the 80 kcal have only been used to melt the ice. In the sense of its definition, the latent melting heat of the water is about 80 cal.

Pressure dependence of the melting temperature

A substance changes its volume as it melts,- that is why pressure affects melting. If the volume inceases in the process, the increase in pressure aggravates the melting and increases thus the required temperature (as well as the required amount of heat); however, if the volume becomes smaller, as happens with certain substances(cf.later), the pressure increase makes melting easier and thereby reduces the temperature, required for melting (and the associated amount of heat), both the more the larger is the increase in pressure. The connection between the pressure increase and the melting temperature is given by the equation of Clausius-Clapeyron. We will write it here in a somewhat changed form: p = (v2 - v1)T/l, where p is the change of the melting temperature, linked to the pressure change, in degree/atm (dT/dp), v2 is the specific volume of the melted substance, v1 that of the solid in cm/g, l the melting heat in cal/g and T the melting temperature (absolute).

Thus, if the specific volume of the melt is {larger/smaller} than that of the solid, then the melting temperature {rises(p>0)/drops(p<0)} at rising pressure. Thus, the melting point of wax at 800 atm is higher by 15.5C (Hopkins), that of paraffin under 100 atm by 3.5C (Bunsen) than at 1 atm. The melting point of mercury can be raised from -39C to 10C by a rise in pressure by 15 000 atm. From the enormous pressure, which the layers of Earth's interior receive from the upper layers, Kelvin concludes that, in spite of the high temperatures rocks can be solid, which at the same temperature melt in a melting oven at atmospheric pressure.

The melting curve, which displays the dependence of the melting temperature on the pressure, can bepresented within a certain range by an interpolation formula; according to Tammann, it has always a maximum of the melting temperature and melting temperature. However, this is contradicted by the melting curve of helium (Simon), which has been determined up to 42 absolute and 5 600 kg/cm as well as those of hydrogen, neon, nitrogen and argon.

In contrast to almost all substances, water has in its fluid state a smaller specific volume that in its solid state. This explains why ice swims on top of water. In contrast, substances which expand during melting, that is, have in their liquid state a smaller specific weight than in their solid state, sink in their melt. Depending on whether a substance sinks or rises in its melt, this shows that it expands or contracts on melting, and then again whether a rise in pressure raises or lowers its melting point. Also cast iron, type metal, bismuth contract on melting. Ice at 0C has the specific weight 0.9999. For ice, the specific volume is v2 = 1.0908, for water v1 = 1.001 cm. From T = 273.2 and l = 79.7 follows p = -.0075, that is, at an increase in pressure by 1 atm the ice melting point drops by 0.0075 C below 0C. There exists an observations that at 8.1 atm a temperature decrease was 0.059C, at 18.8 atm 0.129C, while calculations yield 0.059C and 0.123C (James and William Thomson 1849). Using a pressure estimated at 13 000 atm, Mousson has caused ice to melt while it was being kept at temperatures between -18C and 20C. (Statement by Clausius.)

Lowering of melting point (regelation) of ice

Thus, at a raised pressure, ice melts at a temperature lower than 0C. A lowering by 0.0075 atm is, of course, much too small, in order to be detected. But in the regelation of ice (Faraday), which is due to a lowering of the ice melting point by an increase in pressure, it manifests itself already at very small pressures. If you press two pieces of ice at 0C together, provided their surfaces are already wet, the excess pressure causes melting at the contact surface. The cooled water at a temperature below 0C escapes from the excess pressure, comes thus under the normal atmospheric pressure, becomes solid again (regelation) and joins the two pieces of ice. If the area of contact between them is very small, a smaller pressure is sufficient to join the pieces of ice. In the case of all the phenomena related to the regelation of ice, you should take into consideration that it depends on the pressure, that is, the force per cm, that is, the action is more noticeable, the smaller at a given load is the area, over which it works. It is like this when you skate on ice! The weight of the skater rests on the edge of the skate, where the ice melts. The water skin between this edge and the ice reduces as lubricant the friction between them to a minimum - hence you can slide along.

Regelation explains that you can use the pressure of your hand at 0C to form hard snow balls, which is impossible at lower temperatures. With snow at -1C, you would have to apply already 1/0.0075 = 134 atm, in order to start the melting process. Regelation also explains that the snow under the feet of pedestrians and under cart wheels gradually becomes coherent ice, that beyond the border of eternal snow the snow in the lower layers is converted into ice by the weight of the snow above (development of glaciers), that moreover the low layers of ice are melted by the pressure of those above and that water escapes from the pressure, the upper layers displace the lower ones and cause the glaciers to move, that you can give ice under sufficently high pressure any form (recrystallization).

Temperature dependence of the melting heat

Starting from the expression dQ = dU + dA, you can compute the melting heat; dQ is here the quantity of heat, taken in by the body for melting (total melting heat), dU is the change of its internal energy during melting (internal melting heat) and dA the work done during melting. This work equals the product of the pressure and the change of volume p x (vfluid - vsolid). In general, compared with the total heat of melting, it is of no consequence, because the change of volume is small. For example, during the melting of 1 g ice, it is 0.0022 cal compared with 80 cal of the total melting heat. Also the quantity of heat, required for melting, changes, if the melting temperature changes due to a rise of pressure. We denote the ratio of the very small increase in heat dw to the very small increase in temperature dT by the fraction dw/dT. According to Clausius, you have dw/dT = cfluid - csolid + w/T. However, the specific heats c of the fluid and solid substance are those under the changed pressure - they must be determined specially. Clausius found for melting ice at 0C and atmospheric pressure dw/dT = 0.603, that is, when the melting point of the ice is lowered by 1 by the corresponding increase in pressure, the melting heat decreases by 0.603 cal.


The liquefaction of solids by heat intake (melting) is the opposite to the solidification of melted substances by heat loss or pressure increase (according to the equation of Clapeyron-Clausius). Not all melts rigidify immediately as their temperature drops below their melting temperature or their pressure is raised above the melting pressure: In this state, they are said to be undercooled. But the melts of different substances bear undercooling very differently and when they eventually rigidify, they also differ by the mode of their rigidification - already according to their rate of cooling. One has not succeeded in transforming a metal melt into the glass like aggregate state ; they have been given the amorphous state of metalloid melts only for those of selen and those of sulphur. All other elements regidify crystalline (X-ray spectroscopic), even boron, carbon amd silicon. But certain melted compounds can be transformed into the glasslike aggregate state; above all, boric acid, silicic acid, phosphoric acid (B2O3, SiO2, P2O5) and certain of their salts (borate, silicate, phosphate). Also, as they are slowly cooled, they do not crystalize, remain complely clear and transparent, and just for that reason they are the basic substances of glass production - all along silicate glasses, borate and phosphate glasses since Friedrich Otto Schott 1851-1935 1886.

Crystallization of undercooled melts starts at single points (nucleus) and propagates from there in the directions of the different crystallographical axes at different velocities, the ratio of which determines the form of the growing crystal, because individual crystall faces grow at different rates. As the temperature drops, the directions of faster growth move more and more into the foreground, whence the crystal loses faces. The linear crystallization velocity lies between a few and several hundert mm/min. Experience with the production of single crystalls has shown that the velocities for zinc, tin and lead are between 90 and 140 mm/min. Whether a melt crystallizes during undercooling or becomes an amorphous glass depends essentially on the development of the number of nuclei per second and per cm and the crystallization rate. If the nuclei only develop at lower temperatures, they grow extremely slowly and the melt can be undercooled into glas by suffiently fast cooling. If the melt undercools beyond the temperature of noticeable formation of nuclei into glass, it persists for a long time. If afterwards nuclei form,they cannot be detected, because they grow too slowly. However, their growth can be accelerated by heating and made visible. This phenomenon appears in the devitrification of glasses, which have been stored for a long period: The growing nuclei generate tension and can burst the glass.

Isotropically and anisotropically solidified melts differ fundamentally in those properties (elasticity, strength), which decide their suitability as industrial materials. You should recall here the hardness and brittleness of different kinds of glass and compare it with the elasticity and pliability of the metals, the capacity of some of which for change of shape (plasticity) is so large, that at a sufficiently high pressure they can be forced even at room temperature through a narrow nozzle. If you deform a metal at room temperature - the technical term is cold stretching - by pulling, pressure, rolling, stamping, etc., its physical and and chemical properties change very little, but its technological ones very noticeably ( limit of elasticity, tensile strength, hardness, malleability). The metal becomes stronger, but its plasticity drops. Deformation takes place by internal, crystalline gliding: The crystals displace with respect to each other (Fig. 399) along certain crystallographic sliding planes and in these in certain derections by finite distances, but without disrupting their coherence. You speak in this sense about flowing of a crystalline material. Accordingly, the flowing of an amorphous substance differs fundamentally from that of a crystalline substance. The paths of the molecules of an amorphous substance are curved, those of a crystalline substance broken lines, formed by the almost straight segments of the sliding process. In a crystal, displacements only occur along individual sliding faces, while the mass between them moves as a whole without a change of shape. Crystallites become stretched. Also after the strongest deformation, X-ray pictures display in a cold stretched metal exactly the same space lattice. (Debye, Scherer). Since plastic deformation of metals involves sliding and consolidation means aggravation of plastic deformation, it must be traced back to an inhibition of the sliding process, the cause of which had not been discovered in 1935.












If stretched metals are heated, a general change occurs in their crystal structure - recrystallization - and the changes of their technical properties induced by stretching recede. In the place of the stretched structure of a cold stretched metal (Fig. 400a) appears step by step a new, at first finely grained crystal structure (Fig. 400b, c), which on heating to higher temperatures becomes coarser. A coarse structure is often technically unfavourable. The size of the nuclei depends on the temperature of heating and on the entire pretreatment.

Pressed bodies, electrolytically precipitated metals and those, which in a solid state undergo structural conversions, also recrystallize. Hence it is not certain that recrystallization rests generaly on the removal of a forced state. The technical processing of most metals (whether they are incadescent fibres, container iron sheets or machine parts or for whatever purpose) demands alternating stretching and heating, so that the components repeatedly recrystallize, which may damage them severely during an abnormal course of recrystallization. The nature of stretching and recrystallization was not completely understood and represented in 1935 a main topic of metallurgy. Recrystallization also occurs in keramics, but also in quite different areas such as the generation of glacier muclei, the migration of glaciers and the general deformation of ice; the phenomena are explained, according to Tamman, by processes other than regelation; they also occur in geology during marblization of limestone and during the formation of crystalline slate (crystalline rock, mica slate), which according to their structure are located between those rocks generated by melting (plutonic like granite, porphyry, basalt) and the sedimentary rocks (neptunic like clay, lime, gipsum).

Conversion of fluid state into gaseous state

The basic difference between the transition of the fluid state into a gaseous state and that of a solid state into the fluid state is that the first (at a given pressure) does not only occur at a definite temperature, but at every temperature - it is true, only on the surface and is not necessarily appreciable: The fluid evaporates. But when evaporation has lasted long enough, the entire present fluid disappears. (Cf. below regarding evaporation of solids and sublimation). The temperature, at which a fluid does not only become gaseous at the surface, but also inside it in such a manner that the vapour pressure of the fluid overcomes the external pressure, is called the boiling point. When the temperature has arrived at the boiling point, it does not rise more in spite of further heat input, but the heat is employed totally as latent evaporation heat in the conversion of the fluid into vapour. Like the melting temperature, also the boiling temperature does not only depend on the chemical nature of a fluid, but also on the pressure acting on the fluid. (When we speak of boiling, of the vapour pressure of a fluid, etc., we always have in mind a pure fluid, without any content of substances, which are soluble in it.) The pressure on the fluid impedes evaporation; the higher is the pressure, the more heat must be supplied to the fluid and the more its temperature raised, in order to initiate boiling. Thus, for all fluids, raising the pressure leads to a rise in the boiling temperature. We understand by the boiling temperature and the latent evaporation heat just their numerical values at the pressure of one atmmosphere: The latent evaporation heat is then stated for 1 gram of the substance in calories.


In what follows, we will talk mainly about water and water steam, because their behaviour altogether characterizes that of fluids and vapours and they are most important for us.

The supply of heat to water from the bottom (during normal cooking) at first causes the lower layers to heat up, thereby expand and reduce their specific weight. Consequently, continuously the lowest layers rise and cause a lasting motion in the water, which contributes to the uniformity of the temperature increase throughout the entire mass of water. At the bottom of the pot form gradually bubbles ; they are filled by water vapour, which means: The heat has overcome partly the cohesion of the water particles. As soon as a bubble has been formed, it grows quickly and eventually rises; this means: It has overcome the pressure of the water column above it and that of the atmosphere.

However, the temperature in the upper layers is lower than in the bubble of steam; as a result, the steam condenses again into water (however, the condensed content of a bubble fills less space as before; water particles, which were separated by the bubble, rush into the freed space, collide and cause the singing, which you hear before the water really boils.) During its condensation, the bubble passes its latent heat on to the water. It causes thereby further heating of the upper layers. In the end, all layers are hot enough and let the rising steam bubbles pass through to the surface. The formation of steam bubbles occurs then throughout the mass with bubbling motion: The water boils. The steam bubbles burst and empty their content into the air, but the steam is invisible. Only at a certain distance above the boiling water forms mist. It arises through condensation of the steam (into fine water drops), because the temperature there is no longer high enough. The visible fog is also water; it mixes with the air gradually and becomes invisible.

In order to be able to rise, the steam bubbles must overcome the entire pressure acting on them. That is why the boiling temperature of a fluid does not only depend on the pressure on the surface of the fluid, but also on the height of the water column, the pressure of which the rising bubbles must also overcome. However, it also depends on somthing else, namely on the presence or absence of air bubbles* and on the nature of the walls of the vessel. However, the temperature of the steam, which rises out of the boiling fluid, is according to experience - at equal air pressure on the surface - always the same and depends much less on circumstances other than the temperature of the boiling fluid and does not, in general, coincide with it. Hence you define: The boiling point of a fluid is the temperature of the steam of the boiling fluid, as it is displayed by a thermometer in the flow of the steam. You fix the boiling point of water on the thermometer scales while the thermometer body [not dipped into the boiling water, but ] is completely surrounded by the steam, which rises from the water. However, the statement of a boiling temperature has no value without the statement of the simultaneous level of the barometer, because the atmospheric pressure influences it decisively. If you boil water at sea level at 100C, it will boil, for example, on the St. Gotthard (about 3000 m) at 92.9C. The lower boiling temperature corresponds to the lower atmospheric pressure**.

* Delay in boiling

If a fluid does not contain any gas and is heated in a vessel, to the walls of which it adheres strongly, the generation of steam bubbles is delayed for a very long time. Its temperature can then rise far above the normal boling point without it starting to boil (Delay in boiling). If at last it starts, it occurs suddenly and violently withr strong pulses by the fluid. Improvements of the equipment for removal of gas from fluids have made it possible, to raise them to higher temperatures, water drops swimming on a mixture of clove oil and linseed oil, at atmospheric pressure, to 180C (Maxwell).

** Thermometric-barometric measurement of height (thermo-hypsometry)

The saturation pressure of water steam has been measured exactly over a large temperature range; tables yield the pressure which belongs to an oberved boiling temperature. It is equal to the pressure on the water surface, whence it indicates immediately the reading of the barometer. Thus, if water boild in an open container and you measure the boiling temperature, you can by means of these tables employ a thermometer as a barometer. For example, if you boil water at the foot of a mountain at 98C and a simultaneous observation on top of the mountain yields 95C, you find in the tables the corresponding information, which you require for the barometric measurement of the hieght of the mountain. Hypsothermometers have the form shown in Fig. 401. They are in most cases only subdivided between 90C and 102C in tenths or even hundredths of degrees; the tables contain the steam stress for every tenth of a degree. A drop of the boiling temperature by 1C corresponds to a pressure decrease of about 27 mm and on Earth's suface to a vertical elevation of about 297m.

Pressure dependence of the boiling point

The boiling point of a fluid is merely the temperature of the steam which rises from the boiling fluid at the pressure of 760 mm mercury. A boiling temperature, which has been determined under other conditions, must be accordingly corrected: For this purpose, you must know the dependence of this temperature on the pressure. - If we reduce the air pressure on the water under the bell of an air pump, we can cause water to boil at each temperature without input of heat - merely by diluting sufficiently the air pressing on the water's surface. If the water has 10C, it boils when the pressure has dropped to 9.21 mm mercury. If you now close the connection from the bell to the air pump, the wate continues to boil for a while. Thereby rises again the pressure under the bell, because the pressure of the remaining air is augmented by that of the steam of the water; eventually, as the pressure rises to a certain value, boiling will stop. (On this possibility of evaporating water by reduction of the pressure acting on it rests the effectiveness of steam storages.) The air under the bell does not influence the amount of developing steam, which eventually , when the boiling stops, remains under the bell. Also the presence of a gas other than air does not change anything, unless chemical interaction occurs, which we exclude (Dalton).

The magnitude of the pressure which the steam eventually exerts, when the boiling has stopped, depends only on its temperature; neither reduction nor increase of the volume of steam have an effect. If you reduce it, the steam pressure (as this would happen with a gas) does not rise, but the amount of steam becomes less by a part of it condensing into water; if you increase it, the pressure does not drop, but but one part of the fluid yet evaporates, and increases the amount of steam, while the pressure does not change. You only must keep the temperature constant: Remove the (originally latent) heat, which was freed by condensation, or supply heat from outside required for the evaporation (during an increase in volume). Otherwise, in the first case, heat is passed on to the fluid, that is, the temperature is increased, and in the second case it is removed from the fluid, that is its temperature is reduced.

Saturation pressure

In other words: The space into which the fluid can evaporate accepts a certain amount of steam - not more nor less at the prevailing temperature - as long as the steam is still in contact with the fluid. It saturates itself with it as long as fluid still exists. If you reduce the pressure acting on the fluid, by relinking the bell for an instant with the air pump, boiling restarts and continues until the former steam pressure is reached, that is, the space is again saturated with steam. Hence, steam and fluid are in equilibrium, as long the space outside the fluid is saturated with steam: The steam has the saturation pressure. Already the smallest perturbation converts fluid into steam or steam into fluid. The steam itself, which fills in the equilibrium state the space, is said to be saturated. According to the molecular theory of evaporation, in spite of saturation the formation of steam continues, but simultaneously with its condensation, so that the amount of fluid does not change, just about like on a lake, into which rain falls, while simultaneously an equal amount of water evaporates.

boiling point 1 atm   C   boiling point 1 atm   C     saturation pressure   of water steam
helium   -268.9   alcohol   78     0C   0.006
hydrogen   -252.8   benzol   80     10C   0.012
nitrogen   -195.8   water   100.00     20C   0.023
oxygen   -183.00   oil of turpentine   159     30C   0.042
nitric oxide   -90   anilin   184     40C   0.073
carbonic acid   -78.51   naphtalene   217.96     50C   0.122
ammonia   -33.36   banzophenon   320.95     60C   0.197
sulphurous acid   -10   mercury   357     70C   0.307
ether   34.5   sulphur   445.6     80C   0.467
carbon disulfide   46   zinc   906     90C   0.692
chloroform   62   copper   2300     100C   1.000

The saturation pressure has for every temperature a certain value. In order that the steam can emerge from a fluid in bubbles - in which, of course, it is saturated - in other words: The fluid can boil, obviously the pressure on the fluid must not be larger than the pressure of the saturated steam at the given temperature and the space outside must not have been previously saturated with steam. For example, at the temperature of 10C, the saturation pressure is 0.012 atm or 9.21 mercury; as long as the pressure on the fluid was larger, the steam could not form bubbles and emerge through the surface; only at the pressure of 9.21 mm it became possible. Hence we conceive a sharply pronounced relationship, on the one hand, between the boiling temperature (at a given pressure) and, on the other hand, the pressure of the saturated steam. Hence we define the boiling temperature as follows: The boiling point of a fluid at a given pressure is the temperature, at which its saturated steam has the same pressure as that acting on the fluid.

Reduction of steam pressure. Raising of boiling point. Reduction of freezing point of diluted solutions

The vapour pressure, boiling temperature and freezing temperature of a fluid change as the fluid dissolves any substance. 1. The saturated vapour above the solution has a smaller pressure than the saturated vapour at equal temperature above the pure solvent; 2. The solution boils only at a higher temperature. 3. It rigidifies only at a lower temperature than the pure solvent. These changes depend quantitatively on the amount of the substances dissolved - in brief, the concentration of the solution. According to the law of Franois Marie Raoult 1838-1901 1888, the relative reduction of the vapour pressure of the solution of a not noticeably volatile substance is independent of its chemical nature as well of that of the solvent and equals at all temperatures the ratio of the dissolved molecules to the all together present ones. (Relative reduction of the vapour pressure means: Lowering of vapour pressure divided by the initial vapour pressure.) In general, raising of the boiling point as well as lowering of the freezing point (at least not with very strong solutions) is proportional to the concentration, for example, it is twice as large for a 2 % sugar solution twice as large as for a 1& one under otherwise teh same conditions.

In general, during boiling of a solution, evaporates only the solvent, during freezing only the solvent freezes. As a consequence, the solution becomes more concentrated in the measure in which the solvent disappears by evaporation or freezing; the molecules of the dissolved sunstance become therefore compressed into a smaller space, which they oppose and the overcoming of which demands work - in this case: heat. The resistance, by which they oppose their restriction, can be compared to the pressure of a gas, which is confined to a smaller space and the overcoming of which demands work - here heat, a demand which did not arise during boiling and freezing of the pure solvent.

The physical properties of diluted solutions - that is, of solutions, in which the concentration of the solvent by far exceeds those of the other components - differ only a little from those of the pure solvent; the thermal properties are connected simply to the lowering of the vapour pressure of the solution by simple thermodynamic relations. A thourough treatment of the topic belongs to Physical Chemistry. The following examples demonstrate one of the pratically most important results.

Raoult's determination of molecular weight

The molecular weight of a substance, which decomposes during evaporation, cannot be determined by means of the ordinary methods, but, according to Raoult, from the lowering of the freezing point, which the substance causes during solution in a solvent. Only diluted solutions can be employed and only such solvents, which do not change the substance chemically, that is, only dissolve it, like water does with sugar. (The method cannot be applied to electrolytes [salts. alkalis and acids], the molecules of which split in the solvent.) Between the amount of dissolved substance, of the solvent, of the lowering of the freezing point and the molecular weight of the substance holds a relationship (which has been discovered by Raoult experimentally). It is based on what follows:

The lowering of the freezing point of a solution is proportional to the amount of dissolved substance; for example, in 100 g solvent, 1 g causes twice as large a reduction as 0.5 g. Moreover: The reduction is inversely proportional to the amount of the solvent used; for example, 1 g of a substance in 100 g of a solvent causes twice as large lowering as in 200 g. These relations allow not to consider at all the magnitude of the quantities used - provided only they are known quantities - and allow conversion of the observed reduction of the freezing point to that, which would have been observed, if, for example, one had worked with 0.5 g of the substance in 100 g solvent. The lowering, converted to 1 g substance and 100 g solvent, Raoult calls reduced lowering of the freezing point; his method is now based on the relationship between the reduced lowering of the freezing point and the molecular weight of the dissolved substance. The core of the method is the law, found empirically by Raoult and Coppet: When equally large quantities of the same solvent are used, for example, every time (we limit ourselves to two cases) 100 g, and when in one of the two quantities of fluid another substance is dissolved and the dissolved weights of the two substances are in the ratio of their molecular weights, then each of the two solutions experience the same lowering of the freezing point. For example, if the two substances have the molecular weights M and m, and you dissolve M g and m g of them, respectively, each of the two solutions have the same lowering of the freezing point, say t. Since M g causes the lowering t, 1 g would cause the lowering tM = t/M and 1 g of the other substance tm= t/m, whence the reductions of the freezing points, which two substances cause in the same solvent under otherwise the same conditions are in the inverse ratio of their molecular weights: tM /tm = m/M. Hence, if you know the reduced freezing point lowering tm, caused by a substance of known molecular weight in a certain solvent, you can compute the hithereto unknown molecular weights M1, M2 , of other substances by measuring the lowerings of the freezing points t1, t2, , which these substances cause in the same solvent. You have then for the computation of the molecular weights M1, M2 , the equations:

M1, = mtm/t1, M2 = mtm/t2, etc.

The quantity mtm, the reduced freezing point lowering times the molecular weight of the same substance in the same solvent is for the solvent concerned a constant. It must be found for each solvent with substances of known molecular weight. For 100 g solvent for water 18.5, benzol 51, glacial acetic acid 39, formic acid 28. If you denote it by C, the relation between the molecular weight of the substance and the reduced freezing point lowering it causes is Mtm = C.

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