G1 Molecular phenomena when fluids meet. Gases and solids

If you shake oil with water strongly and then stop, gravity will separate the mixture into two layers, the water below, the oil above; the same happens if you repeat the experiment with sand and water. These are mechanical mixtures: Fluid with fluid, fluid with solid, and you can distinguish the components by eye.

In contrast, if you mix acetic acid with water, or tar with turpentine, or sugar with water, you obtain a physical mixture, a solution, the parts of which you cannot separate mechanically; the components have mixed molecularly. However, such mixtures can not be achieved with two arbitrarily selected fluids or with any fluid and every solid, because a fluid's property to dilute with other fluids or dissolve solids is limited. (However, two gases in contact always mix molecularly.) We call the dissolving fluid solvent, the diluted fluid and the dissolved solid soluble. A fluid's ability to dissolve increases with the temperature, but it is limited at each temperature. In the process, the fluid accepts a certain maximum amount from a certain substance. Once the solution has reached that state, it is said to be saturated, otherwise diluted.

The difference between a mechanical mixture and a a physical solution is displayed by the means, which are required to separate the components of a mixture. The dissolved solid substance separates from the solvent on heating of the mixture; the fluid evaporates and the solid remains; or when the solution is cooled below the temperature, at which it is saturated with the available quantity of dissolved substance - at the lower temperature it is then oversaturated, that is, it retains only as much dissolved substance as it needs to be saturated at that temperature, the remainder is precipitated as crystals.

Occasionally, precipitation does not occur immediately, that is, the solution does not precipitate, although it is oversaturated, but this hehaviour only can occur, if it is totally at rest. If it is disturbed, say, only a little dust or such like drops into it, the precipitation occurs suddenly and the fluid temperature rises. Evaporation demands comparatively much energy. Solutions demand for decomposition more energy than for mixing.

The behaviour of diluted solutions is treated in Physical Chemistry. We will only discuss here two of the most important phenomena: Diffusion and Osmosis. We will then always be concerned with watery solutions and pure water, but the processes are essentially the same for all fluids which can be physically mixed.

Diffusion

If you put water on top of a watery solution of potassium bichromate, so that there lies in the container below a layer of salt solution and on top of it, in touch with it, water, then the salt overcomes gradually gravity and rises into the water; you can see that clearly, because the salt solution is yellow red and the water assumes from day to day more its colour. The original solution dilutes then as long as the salt in all the fluid is distributed uniformly (you say: Until the solution has everywhere the same concentration.) The two fluids (solution and water) have penetrated one another molecularly and diffused one into another. Diffusion is a transport of molecules. It it takes place between two fluids at rest, it is very slow; in contrat, it is very fast if the fluid is stirred. Sugar sweetens from the bottom of a glass of water the entire content - but only slowly; it does so fast, if it is stirred, because this action increases and enlarges the areas, along which diffusion occurs.

Our body really takes in by diffusion nourishment, which we bring to it by consuming food. For this inception serves a system of very thin-walled capillaries, which perpetrate the entire animal organism. The capillaries lead on the one side to the arteries, on the other side to the veins. During blood circulation, the heart pushes the blood in bursts into the arteries and out of these into the capillaries; the blood returns from the capillaries through the veins to the heart. The fluid with the nourishment from the digestive process enters through the wall of tissue which covers the digestion channel into the capillaries, which are there in enormous numbers, diffuses through the capillary walls into the blood and reaches through the blood circulation the heart, from where it passes on to the organs of the body. The capillary system extracts from the organs the used up substances which sooner or later become carbonic acid and urea.

The working muscle consumes oxygen. Oxygen is delivered to the muscle fibres by blood, which travels through the capillaries perpetrating the tissue, whence the capillaries mediate the gas- and substance-exchange between the blood and the tissue.

The capillaries exist in enormous numbers, distributed very regularly between the muscle fibres. "If we assume that a human being has a muscle weight of 50 kg and the number of his capillaries is 1000 per mm², all these tiny tubes, placed end to end have a total length of 100,000 km or 2½ times Earth's circumference, and a total surface of 6,300 m². You see how a large exchange of substances can take place through such huge surfaces in a short time" (August Krohg1874-1949).

Diffusion rate. Crystalloids, colloids

Let a certain quantity of hydrochloric acid demand for diffusion in water (at 10ºC) the time interval 1, then the interval for the diffusion of equal quantities of cooking salt is 2.33, of sugar 7 and of magnesium sulphate 7 (Thomas Graham 1805-1869).

The substances in solutions form two groups. They differ in that the one diffuses very slowly like protein and caramel with diffusion times of 49 and 98, the other very fast like the readily crystallizing crystalloids. The second group also contains not so fast crystallizing substances, which Graham named after their main representative, glue (Latin cola = glue) - colloids - which include starch, dextrin, rubber, tannin, also silicic acid, ferrous oxide, and many other metal oxides. There does not exist an essential difference between the solutions of colloids and crystalloids. (In former times, colloidal solutions were not considered to be solutions.) But the slowness of the diffusion of colloids suggests small osmotic pressure - justifiably, as Wilhelm Pfeffer 1845-1920 has shown by measurements - and a large resistance, which the molecules experience during their motion in water. Both phenomena can be explained on the basis of the assumption that colloids have unusually large molecular weight.

Osmosis. Osmotic pressure

During diffusion of a salt solution in water, the salt leaves the solution for the water until it is distributed uniformly everywhere. It overcomes in the process the resistance, which the fluid activates against its motion, that is, it has energy. Wherever it cannot react by motion, it does by pressure, which can be demonstrated by completely stopping the motion of the salt, for example, as follows: Close a container, filled to its brim with concentrated salt solution, air tight with a pig's bladder, so that the membrane touches the solution, and submerge it vertically in pure water. The membrane will gradually vault like a dome (Fig. 266), because the pure solvent enters the pores from one side, the solution from the other side. In the pores occurs interaction, which you can envisage to be attraction, resulting from the endeavour of the solid particles to link up with the solvent. But the membrane is semi-permeable, that is, it allows solvent to pass through its pores, but not the dissolved substance. The mutual attraction of the solid and fluid particles expresses itself from the side of the solids as pressure against the membrane. The pressure vaults it outward, because it is elastic, and enlarges the space with the solution. New solvent enters the enlarged space through the pores. Diffusion has also occurred through the separating membrane. It is called osmosis and the pressure exercised by the dissolved substance osmotic pressure.

Osmosis was discovered by Nollet 1748 with a container, filled to the brimwith alcohol and closed by a pig's bladder, which had stood for several hours in water (to protect the alcohol against entry of air). The bladder had admitted the water into the container, but only very little alcohol. As water and alcohol were being exchanged, that is, the container closed with the pig's bladder contained water and was below alcohol, the pig's bladder vaulted concavely into the water container. It had let water escape and allowed only a little alcohol to enter. - Especially Physical Chemistry is concerned with osmotic processes in diluted solutions, that is, in the osmosis through a wall separating a diluted solution and solvent.

However, while the processes described above (salt solution and water, alcohol and water) explain what is understood by osmosis and osmotic pressure, they do not assess the magnitude of the pressure. For that purpose one requires a membrane, which admits the solvent through its pores, but stops completely the passage of the solved substance. A skin from an animal like the pig's bladder is not totally semi-permeable. Indeed, there passes during the process a little bit of salt through the pores. However, there are natural and artificial semi-permeable membranes; in the first place is that of V. Traube (1867) made out of ferro-cyanide-copper, which develops at the interface between a solution of yellow potassium ferro-cyanide and a solution of copper-sulphate. It lets water pass, but not ,amy water soluble substances, for example, cane sugar. It was used by by Wilhelm Pfeffer 1877 for measurement of osmotic pressure (Fig. 267).

Pfeffer employed a cell Z made out of unburned clay, created the ferro-cyanide-copper precipitate in the pores of the wall by filling the cell with copper-vitriol solution, filled the cell completely with cane sugar solution and submerged the whole system, tightly closed, in water. The mercury of the manometer dropped gradually in the one leg and rose in the other, because water intruded through the membrane into the container. After several weeks, the mercury attained its maximum height. The manometric difference in heights yielded a measure of the osmotic pressure in atmospheres.

Van't Hoff presented the action of osmotic pressure in the following manner (Fig. 268): AB is a tube, M a completely semi-permeable membrane, which joins tightly the wall and can move inside it without friction, L a sugar solution, W pure water. If the pressure of the water column W were larger than the upwards directed osmotic pressure of L, M would sink, that is, the solution become more concentrated (since water would move out of the solution and move through the pores to the upper side of M. If the pressure on W were smaller than that from L, M would rise, that is water would move from above to the lower side of M and L would become diluted. In both cases M would move until the osmotic pressure and that of the water column reach equilibrium.

Osmosis displays the difference in the diffusion rates of the crystalloids and colloids. Parchment allows crystalloids tpass for asufficiently long time, but almost stops colloids. Colloids and crystalloids can be separated by dialysis (Thomas Graham). If you place a mixture of both on a frame, tightly covered by parchment (dyalisator), and allows it to swim on water, the crystalloids diffuse over a sufficiently long period through the parchment into the water, the colloids stay behind.

Osmosis through semi-permeable walls controls many physiological processes - plant- as well as animal ones; the penetration of sap through the walls of cells and blood vessels takes place through osmosis.

The laws of osmosis form a main chapter of Physical Chemistry. They are concerned with questions such as the dependence of osmotic pressure on:

1. the concentration of solutions,
2. the temperature,
3. the nature of the dissolved substance,
4. the nature of the solvent - questions which can only be answered by experiment.

A large number of measurements under very different conditions has demonstrated (Van't Hoff): Osmotic pressure does not depend on the nature of the solvent and otherwise obeys the gas laws, whence the osmotic pressure of a solution is the same as the pressure, which the molecules would exercise, if the solvent were absent, but the space, which it occupies, were at the disposal of those molecules in the gaseous state.

Osmotic Pressure of diluted solutions and the gas equation

However, the analogy between the osmotic pressure and the pressure of a gas is more than something external. The dissolved substance is split into molecules (van't Hoff). In order to demonstrate the foundation of this point of view, we recall once again the Law of Boyle and Gay-Lussac for the relationship between the volume, pressure and temperature of a gas in the more convenient form: pV = 0.0820T litre atmospheres. Van't Hoff gives the same equation also for solutions, when p is the osmotic pressure (in atmospheres, T the absolute temperature of the solution and v that volume of the solution (in litres), which contains at the present concentration one gram-molecule of the dissolved substance. If this equation really yields the relationship between concentration, temperature and osmotic pressure, then the osmotic pressure can be computed, if the concentration and temperature of a solution are known.

But it can also be measured. The agreement between the measurement and calculation is almost perfect. Van't Hoff draws from each relationship between the osmotic pressure and the concentration of a solution the conclusion: The osmotic pressure is equal to the pressure (for example, against a membrane), which the molecules would generate as gas molecules, if at the present concentration the solvent were removed from the space, which the solution occupies, and the molecules of the dissolved solid would fill the space as gas molecules.

This theory rests on Avogadro's Law for gases - the equation pV = 0.0820 T is based on it! - whence this law turns out to be valid for solutions as well. There correspond to the different gases the different soluble substances, to the volume of the gases the volume of the solution. Let there be given different solutions - all with the same solvent - , then van't Hoff's approach yields the result: Equally large volumes of these different solutions contain at equal osmotic pressure and at equal temperature equally many molecules. In particular, we see that the magnitude of the osmotic pressure does not depend on the chemical nature of the dissolved substance, but only on the number of dissolved molecules (provided always that the solvent is the same). This law is usually given the form: Equi-molecular solutions, which have been produced with equal volumes of the same solvent, have at the same temperature the same osmotic pressure. (Note: The masses, the total number of grams are specified by the molecular weight number, contain equally many molecules, that is, they are equi-molecular.

Solubility of gases (Henry's Law)

The fact, that a substance dissolved in a solution presses equally strongly on a semi-permeable wall (M in Fig. 268) as it would press at equal temperature and equal concentration as gas on an ordinary wall, is confirmed by the actual relationship between the solubility of a gas in a fluid and its pressure. If a gas is bounded by a fluid, always a part of it is dissolved. The amount depends on the nature of both, but specially on the pressure acting on the gas. If the fluid has taken in as much gas as it can accept at the pressure, by which the gas presses on its surface - in other words, if there exists equilibrium between the solution and the gas above it - then the Law of William Henry 1775-1836 1803 applies. The amount of gas, dissolved in 1 cm³ of fluid, is proportional to the gas pressure. Let carbonic acid press on water (at a certain temperature) in a state of equilibrium at 2, 3, ··· n atmospheres, then Henry's Law says: The water contains 2, 3, ··· n times as many grams of carbonic acid as at the pressure of 1 atm. The volume of carbonic acid (in cm³), which the water contains in solution, is therefore, if both are in equilibrium, always the same, because, by Boyle's Law, the quantity of carbonic acid at a pressure of one atmosphere has the same volume as the n times as large quantity (dissolved at n atmospheres) has the pressure of n atmospheres. From the fact that a gas, which is soluble in a fluid, dissolves to an amount proportional to its pressure on the fluid, follows the proportionality between the pressure of the dissolved gas and the concentration of the solution and, correspondingly, the osmotic pressure of the solution. Moreover, thermodynamic considerations (which we cannot discuss here) yield then that the pressure of the dissolved gas is equal to the osmotic pressure of the solution. This is true for all gases and vapours, which dissolve proportionally to their pressure in an arbitrary solvent, that is, which obey Henry's Law of Absorption (van't Hoff 1885). From the strictness, with which the Absorption Law applies, follows that also the osmotic pressure obeys the gas laws.

Due to Bunsen, the volume (in cm³) of a gas , which is soluble in 1 cm³ of fluid, is called the absorption coefficient. It is for

The amount of dissolved gas at a certain pressure only remains in the solution as long as the pressure is maintained. If it is reduced, gas escapes from the solution until equilibrium is restored., that is, until the remaining amount of gas corresponds to the new (smaller ) pressure. If you open a bottle of soda water, the atmospheric pressure operates on its surface. However, the carbonic acid has been dissolved under a much higher pressure and been kept in solution in the closed bottle. That is why it escapes with much effervescence when the bottle is opened.

1 cm³ dissolves always at a given temperature and given pressure the same of a given gas, irrespectively of whether yet another gas is in the solution or not. If a mixture of gases touches the fluid, the fluid takes of each individual gas just as much as if the other gas were not present. (Dalton 1807). But it also does not take in more, only as much as corresponds to its coefficient of absorption. For example, if water has dissolved at a given pressure as much carbonic acid as it can and you increase the pressure by pressing another gas, say, air into the space above the solution, the water does not dissolve any more carbonic acid, but only the gases in the air corresponding to their absorption coefficients. The pressure of the carbonic acid has not changed, the increase in pressure was due to the air.

Water dissolves twice as much oxygen as nitrogen. Air, dissolved in water, is therefore relatively richer in oxygen than normal air. (This is important for animals which breathe through gills.)

The solution of a gas in a fluid has somewhat the character of a chemical process. This explains partly that the same gas under otherwise equal conditions is differently strongly soluble in different fluids; for example, carbonic acid is three times as soluble in alcohol as in water.

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