Osmotic Pressure

W. C. McC. Lewis
1917 Scientific American  
ALTHOUGH the concept of osmotic pressure has played an outstanding part during the last thirty years in the development of physical chemistry, it is a remarkable fact that even at the present time no very general agreement has been reached as to the actual mechanism of the phenomenon itself. The view that osmotic pressure is a simple bombardment pressure identical in nature with the pressure exerted by a gas, the dis solved substance functioning as a gas and bombarding the semipermeable
more » ... , has long been held, though not without considerable scepticism on the part of those who rightly maintained that a solution was after all a liquid in the ordinary sense of the term and that in a system of this nature we have to deal ' with forces the magnitude of which is extremely large. Un doubtedly the simple bombardment view owes its pop ularity to the very simple and obvious explanation which it offers of the fact that the gas law holds good for the dissolved substance in dilute solution, a fact first discovered by the eminent Dutch physical chemist van 't Hoff. On the other hand attempts have not been wanting to show that van 't Hoff's law is the limiting expression of a more complicated law which can be derived by regarding the phenomenon of osmotic pres sure as primarily connected with the solvent and only in a secondary sense with the dissolved substance. One of the most recent attempts in this direction, and one which is at the same time eminently successful, is that of Tinker, briefly outlined in the Phil. Mag. vol. xxxii. p.295, 1916, and the British Assoc. Rep., 1916. Tinker bases his considerations on the Dieterici equation of fluids. Aceording to Dieterici a pure liquid possesses what may be called a liquid pre5sure-when the liquid is acting as a solvent we may call this pressure the solvent pressure-denoted by the symbol 7r, which is connected with the free or uno(�cupied space in the liquid and with the temperature by the ordinary gas law. Thus if we denote the volume of the liquid by V and the occupied space by b, then the free space is V-b and the pressure 7r is related to this free space by the eq'lation OT (V -b) = R T. This solvent or liquid pressure is itself a bombard ment pressure due to the kinetic energy of the moelcules of the liquid, the pressure being exerted on any imaginary unit area in the interior of the liquid. It is a quantity which cannot be measured directly, for any direct measurement in\'olvps a contact surface at which the observed bombardment pressure is very much less than 7r As a matter of fact 7r may be several hundreds or thousands of atmospheres, whill' the bombardment pressure actually observed is exceedingly smalL The vapor pressure of the liquid, in fact, gives us a measure of this latter quantity. The reason why the ob�(�rved bombardment pressure is so small is, that when a mole cule approaches the surface it is drawn back by strong unbalanced forces of attraction which tend to prevent it passing across the surface. In the interior of the liquid, on the other hand, these forces, though still as strong as before, mutually destroy one another and the molecule is free to exert an enormous bombardment pressure at an imaginary plane. Exactly the same thing may be said of the molecules of the dissolved sub stance, though on account of their smaller concentration in the interior they exert there a correspondingly smaller pressure. At the free surface of the solution the mole cules of a solute such as sugar are so effectually drawn back that even their vapor pressure is immeasurably smalL It is very reasonable to assume that a similar state of things holds at the surface of a membrane en closing the solution, and if this be so, it is evident that the bombardment pressure of the solute upon the mem brane must be quite negligible, and cannot therefore account for the observed osmotic pressure. We now come to the problem of how to acco unt for the phenomenon of osmotic pressure at all. For the sake of simplicity we shall restrict ourselves to the ideal solution; the ideal solution being one in which the volume of the mixture is exactly equal to the sum of the volumes of the two constituents separately. In such a case the fundamental idea advanced by Tinker is that the solvent pressure in the solution is less than the solvent pressure in the pure solvent itself "hich lies on the other *Science Prooress. side of t�e membrane. To sec how this might occur, let us thmk of equal volumes of two separate gases, A and B. If these are mixed, and the resulting volume is just double the original volume of either, it follows that partial pressure of each constituent-say the substance A-in the resulting mixture is exactly half of its value in the original state. It is to be observed that this diminution in the pressure exerted by A is brought about, although the effective space occupied by any smgle molecule is just the same before and after mixing, i.e., the space per molecule = total numb �:r of mole � ules, total volume and in the case considered we have doubled the number of gas molecules and doubled the volume at the same time. To return to the case, of the solution, the par tial liquid pressure of the constituent, which we call the solvent, is diminished by the presence of the solute, for exactly the same reason that the partial pressure of the gas A was diminished. If therefore the solvent and solution are separated by a membrane, permeable to the solvent, impermeable to the solute, the solvent pressure on the pure solvent side is greater than the solvent pressure on the solution and therefore some solvent is forced into the solution. ' That is, the phenomenon of osmosis occurs. Further, we can apply an external pressure to the surface of the solution by means of a piston or an inert gas, and so prevent osmosis taking place. This applied pressure is nu merically equal to the osmotic pressure of the solution and, in fact, the method is employed experimentally t� determine osmotic pressure. By compressing the solu tion in this way we obviously diminish the free space in the solution, and, therefore, cause the solvent pressure in the solution to rise, until it is equal to the solvent pressure in the pure solvent itself, and no further osmosis can take place, i.e., the solvent is now passing in and out of the membrane at the same rate. N ow we know that liquids are very imconpressible. It follows therefore that there must be very little free space in liquids. If this were not the case, it would be quite inconceivable that the application of an external pressure of a few atmospheres by the piston could sens ibly affect the free space, and, consequently, the value of the solvent pressure. As a matter of fact, the free or unoccupied space in a liquid is about one-fifth to one tenth of the total volume occupied by the liquid. It is thus seen that the osmotic pressure may be ex plained as due to a difference between the value of the solvent pressure 7r in the pure solvent and the value of the solvent pressure 7r ' in the solution. This is the new con cept of osmotic pressure, especially for solutions which approximate to the ideal case. In the case of non-ideal solutions the osmotic pressure is a more complex phenom enon, but the underlying idea is the same. It is not proposed to enter into the case of non-idpal solutions in this place. One point only remains to be considered in connection with the ideal solution. It has been stated, that the osmotic pressure depends upon the difIerence of the rr values. This must not be taken as meaning that the osmotic pressure P is simply "-"'. The actual relation between them is easily shown to be, in the case of a dilute solution: where V is the volume of one grammolecule of the sol vent and R is the gas constant. Tinker has shown fur ther that this expression leads at once to the van 't Hoff law for the osmotic pressure. The new concept of osmotic pressure is therefore quite in agreement with the striking experimental facts demonstrated by van 't Hoff and is capable of accounting for them in a satisfactory manner. We are therefore no longer tied to the bom bardment view which attributes the osmotic effects to a simple gas pressure exerted by the solute. Several other relationships, which cannot be discussed here may likewise be deduced, with the help of the concept of solvent pressure. The position is therefore a hopeful one and it may not be long before we possess a really comprehensive and satisfactory theory of dilute solu tions not simply from the thermodynamic standpoint but from the molecular standpoint as well.
doi:10.1038/scientificamerican12011917-343asupp fatcat:mt23p44jlfgw7iwch6i5hd3i4y