Pressure, osmotic vapour

The relation between osmotic pressure and vapour pressure was deduced by Gouy and Chaperon (1888), and independently by Arrhenius (1889). 

The depression of a melting point is one of the simplest manifestations of a colligative property. Other everyday examples include pressure, osmotic pressure, vapour pressure and elevation of boiling point. 

In these equations /q and are functions of pressure and temperature, but do not depend on x. Obviously /q is identical with the molecular potential g of the pure solvent (x = 0). Solutions in which go Si given by the simple expressions (43) and (44) are called ideal solutions. In these solutions the vapour pressure, osmotic pressure, etc. are determined solely by the entropy of mixing, i.e., by the tendency to attain the state of maximum probability. 

Van t Hoff proved by thermodynamics that Raoult s law of vapour pressure lowering and the formula for the molecular depression of freezing-point follow from the osmotic pressure equation. L. G. Gouy and G. Chaperon, Duhem, and Arrhenius, also showed by thermodynamics that the osmotic pressure and vapour pressure lowering are connected, and hence osmotic pressure and vapour pressure and freezing-point lowerings. 

With eq. (3) and (4) it is possible to determine the Xj parameters over a large range of concentration by measuring the osmotic vapour pressure difference of two solutions with slightly different concentrations. 

PEO 2000 for synthesis (Merck-Schuchardt) was chosen for osmotic vapour pressure measurements. Fructose p.a. (Fa. Merck) was used as calibrating substance. For the membrane osmosis PEO 35000 (Hoechst AG) was taken. This product was fractionated by slowly cooling a solution (10 wt.% PEO) of a mixture water/acetone (15/85 wt./wt.). This procedure was carried out to make sure, that the sample doesn t contain portions of low molecular polymers <20000 g/mol. The membranes (Sartorius, Gottingen, regenerated cellulose Cat.-Nr. 11539) have a lower limit for determination of molar masses of 20000 g/mol. 

V = dilute solution viscosity LS = light scattering OP = membrane osmotic pressure VPO = vapour pressure osmometry F = preparative fractionation... 

From (1.5.6) important thermodynamic properties of perfect solutions may be directly deduced e.g. Raoult s law for the vapour pressure, osmotic pressure, equilibrium between a liquid solution and a solid phase. 

The standard methods (vapour pressure, osmotic pressure. ..) for the experimental determination of the activity coefficients are described in all textbooks of chemical thermodynamics to which the interested reader is referred. 

The thermodynamic aspect of osmotic pressure is to be sought in the expenditure of work required to separate solvent from solute. The separation may be carried out in other ways than by osmotic processes thus, if we have a solution of ether in benzene, we can separate the ether through a membrane permeable to it, or we may separate it by fractional distillation, or by freezing out benzene, or lastly by extracting the mixture with water. These different processes will involve the expenditure of work in different ways, but, provided the initial and final states are the same in each case, and all the processes are carried out isothermally and reversibly, the quantities of work are equal. This gives a number of relations between the different properties, such as vapour pressure and freezing-point, to which we now turn our attention. 

Allow the added solvent, of volume V, to pass reversibly through a into A, against the osmotic pressure P of the solution (with the pure solvent under the pressure of its own vapour). 

Then if any two phases are separately in equilibrium with a third phase, they are also in equilibrium when placed in contact, so that if any one phase (e.y., the vapour) is taken as a test-phase, and the other phases are separately in equilibrium with this, the whole system will be in equilibrium. Under the conditions imposed, it is sufficient that the vapour pressure, or osmotic pressure, of each component has the same value at all the interfaces, for we may consider each component separately by intruding across the interface a diaphragm permeable to that compo- -nent alone. Then if the vapour, or osmotic pressures, are not equal at the third interface to their values at the first and second interfaces, i.e., at the interfaces on the test-phase, we could carry out a reversible isothermal cycle in which any quantity of a specified component is taken from the test-phase to the phase of higher pressure, then across the interface to the phase of lower pressure, and then back to the test-phase. In this cycle, work would be obtained, which however is impossible. Hence the two phases which are separately in equilibrium with the test-phase are also in equilibrium with each other. This may be called the Law of the Mutual Compatibility of Phases (cf. 106). 

If we take Dieterici s numbers for the vapour pressures, and Roloff s for the freezing-points, of solutions of potassium chloride, we can calculate the osmotic pressure (P0) from the two equations ... 

Let us suppose that we have a solution A in contact at one side with a surface of adsorption ab separating it from another phase -B which, for simplicity, we shall first take to be the vapour of the solvent. At the other side the solution is in contact wTith pure liquid solvent C through a semipermeable piston c, exposed to an osmotic pressure P. 

In physical chemistry, we apply the term colligative to those properties that depend upon number of molecules present. The principal colligative properties are boiling point elevation, freezing point depression, vapour pressure lowering, and osmotic pressure. All such methods require extrapolation of experimental data back to infinite dilution. This arises due to the fact that the physical properties of any solute at a reasonable concentration in a solvent are... 

Colligative1 properties of dilute polymer solutions depend only on the number of dissolved molecules and not on properties of the molecules themselves, such as mass or size. Osmotic pressure, freezing point depression, boiling point elevation, and vapour pressure lowering are the most prominent examples. These methods essentially allow one to count the number n of solute molecules. From n and the known total mass m of the solute the molar mass M is readily obtained as... 

This is the principle on which a DR works. The advantage of this process over the 3He evaporation is evident for example, at 0.28 K, the 3He vapour pressure is about 10-3 torr, whereas the osmotic pressure from the rich to the diluted phase is about 10 torr for T->0. Thus, it is always possible to force a 3 He flux from the concentrated phase to the diluted one. 

Methods for the determination of Molecular weight based on colligative property are vapour-pressure lowering, boiling point elevation (ebulliometry), freezing-point depression (cryoscopy), and the Osmotic pressure (osmometry). 

The successful development of asymmetric cellulose acetate membranes by Loeb and Sourirajan in the early sixties, at the University of California, Los Angeles, has been primarily responsible for the rapid development of Reverse Osmosis (RO) technology for brack sh/sea water desalination. Reverse Osmosis approaches a reversible process when the pressure barely exceeds the osmotic pressure and hence the energy costs are quite low. Theenergy requirement to purify one litre of water by RO is only O.OO3 KW as against 0,7 KV required just to supply the vaporisation energy to change the phase of one litre of water from liquid to vapour by evaporation. Thus RO has an inherent capability to convert brackish water to potable water at economic cost and thus contribute effectively to the health and prosperity of all humanity. 

Of the osmotic methods I would mention only two that we have examined and used at Aberystwyth. The indirect determination of vapour pressure lowerings can be made simply, quickly, and precisely using thermistors an accuracy equivalent to one-half per cent in AP is readily attained for M/20 solutions in benzene this is equivalent to a... 

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