Pressure, osmotic

Osmotic pressure, another of the colligative properties, can be understood from Fig. 17.14. A solution and pure solvent are separated by a semipermeable membrane, which allows solvent but not solute molecules to pass through. As time passes, the volume of the solution increases while that of the solvent decreases. This flow of solvent into the solution through the semipermeable membrane is called osmosis. Eventually the liquid levels stop changing, indicating that the system has reached equilibrium. Because the liquid levels are different at this point, there is a greater hydrostatic pressure on the solution than on the pure solvent. This excess pressure is called the osmotic pressure. We can take another view of this phenomenon, as illustrated in Fig. 17.15. Osmosis can be prevented by applying a pressure to the solution. The pressure that just stops the osmosis is equal to the osmotic pressure of the solution. 

Osmotic pressure can be used to characterize solutions and determine molar masses just as the other colligative properties can however, osmotic pressure is particularly useful because a small concentration of solute produces a relatively large osmotic pressure. 

Experiments show that the dependence of the osmotic pressure on solution concentration is represented by the equation 

A molar mass determination using osmotic pressure is illustrated in Example 17.4. 

To determine the molar mass of a certain protein, 1.00 X 10 g of the protein was dissolved in enough water to make 1.00 mL of solution. The osmotic pressure of this solution was found to be 1.12 torr at 25.0°C. Calculate the molar mass of the protein. 

The normal flow of solvent into the solution (osmosis) can be prevented by applying an external pressure to the solution. The minimum pressure required to stop the osmosis is equal to the osmotic pressure of the solution. 

Osmotic pressure is also a colligative property. Before we talk about osmotic pressure let s turn our attention to the process of osmosis. Consider two solutions that are made out of the same solvent with different concentrations of solute separated by a semipermeable membrane. The solvent will flow through the semipermeable membrane from the solution of lower concentration to the solution of higher concentration. Thus, osmosis is defined as the flow of solvent through a semipermeable membrane resulting in the equilibrium of concentrations on both sides of the semipermeable membrane. 

Water will flow into the funnel through the semipermeable membrane, and the liquid level of the funnel will gradually increase. The osmotic pressure is the pressure required or applied to the solution to stop the flow of the solvent, or in other words, to stop the process of osmosis. The osmotic pressure and concentration are related by the following equation  

M is the molar concentration of the solute, R is the gas constant, and T is the absolute temperature. 

Unless Otherwise noted, all art on this page Is Cengage Learning 2014. 

Osmotic pressure is one of four well-known colligative properties of a nonelectrolyte solution the other three are lowering of vapor pressure, elevation of the boiling point, and depression of the freezing point. They are all expressed in terms of the change in the activity of the solvent a when a solute is present. The 

Physical Chemistry of Macromolecules Basic Principles and Issues, Second Edition. By S. F. Sun ISBN 0-471-28138-7 Copyright 2004 John Wiley Sons, Inc. 

By definition, the mole fraction is related to the concept of mole, which in turn is related to the molecular weight. We thus have the following correlation  

The value of oi can be determined with any of the four colligative properties. We have already discussed vapor pressure measurement. In this chapter, we discuss the measurement of osmotic pressure, neglecting boiling point elevation and freezing point depression because they are less important. 

The chemical potential, activity, and osmotic pressure are related by the following equation  

The osmotic pressure is one of the colligative properties, which depends on the molar concentration of the particles present in the solution. For the polyelectrolytes, however, only the counterions contribute to the osmotic pressure because their number is much larger than the number of macroions. For the polyelectrolyte, the real osmotic pressure is much lower than that calculated by the van t Hoff law because a large portion of the counterions is confined around the polyelectrolyte chains [84, 85, 87-89], The ratio between the real osmotic pressure and the theoretical calculated one, the osmotic coefficient, q , is a direct measure of the fraction of non-confined counterions. 

The osmotic pressure 77 is an intensive property of a solution and was defined in Sec. 12.2.2. In a dilute solution of low 77, the approximation used to derive Eq. 12.2.11 (that the partial molar volume Fa of the solvent is constant in the pressure range from p to p+ 11) becomes valid, and we can write 

In the limit of infinite dilution, — /jla approaches —TJT lnxA (Eq. 12.4.2) and Fa becomes the molar volume of the pure solvent. In this limit, Eq. 12.4.20 becomes 

Equations 12.4.23 and 12.4.24 show that the osmotic pressure becomes independent of the kind of solute as the solution approaches infinite dilution. The integrated forms of these equations are 

Equation 12.4.25 is van t Hoff s equation for osmotic pressure. If there is more than one solute species, vcb can be replaced by a v/ub by Y i a diese expressions. 

In Sec. 9.6.3, it was stated that 11/ms is equal to the product of and the limiting value of n/triB at infinite dilution, where pm = (pX Pa)/RTMa Yi A i the osmotic coefficient. This relation follows directly from Eqs. 12.2.11 and 12.4.26. 

The osmotic pressure of a solution is directly proportional to the concentration, expressed in molaritw of the solute in solution  

Like boiling-point elevation and freezing-point depression, osmotic pressure is directly proportional to the concentration of the solution. This is what we would expect, though, because all colligative properties depend only on the number of solute particles in solution, not on the identity of the solute particles. Two solutions of equal concentration have the same osmotic pressure and are said to be isotonic to each other. 

The osmotic pressure of the macromolecules is obtained by considering a change in the solution volume keeping the number of monomer units nm constant. 

FsiteVtot/a, and nm= t)Vtot/a. Inserting this relation in equation 2-28, and using the Flory-Huggins approach (eq.2-24), we get  

For very dilute solutions, equation (2-31) corresponds to the equation of state for an ideal gas. We can obtain a more general formulation, wi out the help of the lattice model by expanding the free energy (per cm ) as a function of the concentration. 

In three dimensions, two polymers which occupy the same volume of radius R have N v/R contact points. The free energy of the two interpenetrating polymers is proportional to the number of contacts. Setting as usual the Boltzmann constant equal to 1  

In good solvent the polymer dimension of the coil being dy = 5/3, equation 2-36 applies, while for a rod the dimensionality being equal to 1, tiie Onsager result can be used and the virial coefficient is proportional to the square of the rod length (8), i.e the square of the degree of polymerization. 

Also note that at low pressures the lines are almost linear and the data could be modeled by an equation involving just the first two or three terms of the virial equation. 

It was van t Hoff, winner of the very first Nobel prize in chemistry, who perceived an analogy between the properties of dilute solutions and the gas laws. We will see that many physical properties of dilute solutions, such as the amount of light scattered or the viscosity, can be written as a virial equation in the number of molecules (moles), N, or concentration of solute, c. We have written a general form of a virial equation in Equation 12-4, using the quantity P to represent some measured property of the solution and P0to represent the property of the pure solvent. 

FIGURE 12-2 Schematic plot of PV/nRT versus P for non-ideal gases. 

The first application of such equations to dilute solutions actually came from van t Hoff s measurements of the osmotic pressure of 1% solutions of cane sugar in water (relative to pure water), where the analogy to the virial equation of a gas expressed as a power series in the pressure is more direct. Accordingly, we will start our discussion of molecular weight measurements by considering osmotic pressure. 

FIGURE 12-4 Schematic diagram of the osmotic pressure experiment with the cap still on. 

In this chapter the effects of pressure balance and interfadal rheological properties on the stability of multiple emulsions are discussed. 

Sodium chloride and other electrolytes added initially in the inner or outer aqueous phase of W/O/W multiple emulsions can migrate across the oil layer and get into the other aqueous phase through molecular migration (CoUins, 1971 Chilamkurti and Rhodes, 1980). The migration of the electrolytes induces changes in osmotic pressure over time and consequently alters multiple emulsion stability. It has been observed that multiple emulsions stabilized by Span 83 and Tween 80 are more stable with sodium salicylate incorporated in the inner aqueous phase than with sodium chloride (Jiao et al., 2002). The difference in the stability of the multiple emulsions observed can be attributed to a faster migration of sodium chloride from the inner aqueous phase to the outer aqueous phase and a consequent more significant imbalance in the osmotic pressure compared to that with sodium salicylate. 

The transport mechanism of electrolytes through the oily liquid phase has been the subject of many investigations over the past decades. Nevertheless, there remains a lack of a clear understanding as to what and how various formulation parameters of multiple emulsions affect the kinetics and extent of the migration of electrolytes across the middle phase, and thereby influence the osmotic pressure. Partition coefficient, ionization, charge density, molecular weight, and molecular mobility of electrolytes can have some impact on electrolytes ability to cross the oil phase. The association of electrolytes with the surfactant, which may form inverted micelles in the oil phase, has also been considered (Chilamkurti and Rhodes, 1980). 

Sundelof claim osmotic pressure to offer one of the best methods available for thermodynamic measurements over a wide range of concentration. 

Measurements of osmotic pressure are frequently used to determine activity coefficients and solution molecular weights. The measurements are particularly useful in the determination of the properties of polymer solutions. 

The system under consideration consists of a liquid solution of r components (phase a) separated from pure liquid 1 (phase P) by a non-deformable, heat-conducting membrane permeable to component 1 

Comparison of Eq. (11-193) with Eq. (11-4) yields an explicit expression for the logarithm of the activity coefficient of the solvent in the form 

Equations (11-198) and (11-200) provide explicit expressions for /i in terms of the experimentally measured osmotic pressures. If equilibrium exists between the liquid and vapor phases, the osmotic pressure can be related to the vapor fugacities by the expression 

Equation (11-200) can be utilized to obtain an expression for the osmotic coefficient of component 1 in the form 

To calculate the osmotic pressure, we set the chemical potentials of the pure species on the left equal to the chemical potential of species a on the right  

The superscripts indicate the respective temperature and pressure. Applying the definition of fugacity, we can write the chemical potential at P + II as  

We can apply the thermodynamic web to determine the difference in Gibbs energy from P to P + n at constant T  

Equation (8.59) illustrates that the activity coefficient of the solvent can be found through measurement of the osmotic pressure. 

In the case that species h is dilute enough, the mixture forms an ideal solution. Applying ln(l — xj) —xj, we get  

The usefulness of osmotic pressure measurements is, nevertheless, limited to a relative molecular mass range of about 104-106. Below 104, permeability of the membrane to the molecules under consideration might prove to be troublesome and above 106, the osmotic pressure will be too small to permit sufficiently accurate measurements. 

Osmosis takes place when a solution and a solvent (or two solutions of different concentrations) are separated from each other by a semipermeable membrane - i.e. a membrane which is permeable to the solvent but not to the solute. The tendency to equalise chemical potentials (and, hence, concentrations) on either side of the membrane results in a net diffusion of solvent across the membrane. The counter-pressure necessary to balance this osmotic flow is termed the osmotic pressure. 

Osmosis can also take place in gels and constitutes an important swelling mechanism. 

The osmotic pressure II of a solution is described in general terms by the so-called viral equation 

The resulting relative molecular mass refers to the composition of 

The phenomenon of osmotic pressure is illustrated by the apparatus shown in Fig. 13.6. A collodion bag is tied to a rubber stopper through which a piece of glass capillary tubing is inserted. The bag is filled with a dilute solution of sugar in water and immersed in a beaker 

The equilibrium requirement is that the chemical potential of the water must have the same value on each side of the membrane at every depth in the beaker. This equality of the chemical potential is achieved by a pressure difference on the two sides of the membrane. Consider the situation at the depth h in Fig. 13.6. At this depth the solvent is under a pressure p, while the solution is under a pressure p + n. If p tt, x) is the chemical potential of the solvent in the solution under the pressure p + tt, and p°(T, p) that of the pure solvent under the pressure p, then the equilibrium condition is 

The problem is to express the p of the solvent under a pressure p + tc in terms of the p solvent under a pressure p. From the fundamental equation at constant T, we have dp° = V° dp. Integrating, we have 

F° is the molar volume of the pure solvent. If the solvent is incompressible, then V° is independent of pressure and can be removed from the integral. Then 

In terms of the solute concentration. In x = In (1 — X2). If the solution is dilute, then X2 1 the logarithm may be expanded in series. Keeping only the first term, we obtain 

In discussions of solution behavior, the osmotic pressure II becomes a property of primary interest. II depends on the temperature and the concentration of the solute. In this section we will discuss the form of this dependence and begin with considering dilute polymer solutions. 

As for low molar mass solutes, for polymers a virial expansion can also be used to give II in the limiting range of low concentrations 

This is a series expansion in powers of the solute concentration, and the Ai s are the i-th virial coefficients . For an ideal solution of low molar mass molecules all higher order virial coefficients beginning with the second virial coefficient A2 vanish, and we have furthermore 

The dependence i7(Cm) then agrees exactly with the pressure-concentration dependence of an ideal gas. Dissolved polymers do not constitute ideal solutions in this strict sense, even if all higher order virial coefficients vanish, because the first virial coefficient is not unity but given by 

The reason for the change is easily revealed. Regard that the osmotic pressure is exerted by the translational motion of the centers of mass of the polymers only and remains unaffected by the other internal degrees of freedom of the chains. This implies that, for polymer solutions, the polymer density 

If is also possible fo calculafe fhe change in fhe chemical pofenfial of fhe solvenf due fo fhe increase in pressure  

Although the partial volume of the solvent is formally a function of temperature, pressure, and composition, it is customary to ignore the small dependence of this quantity on these variables in a dilute solution and to treat the partial volume as equal to the pure component value, v. The integral is then easily carried out. When Equation 5.13 is invoked, the osmotic pressure can be expressed as  

The osmotic pressure is a direct measure of the change in chemical potential of the solvent due to the addition of solute. It can be measured by several experimental techniques. The osmotic pressure can then be compared with calculations of the change in chemical potential upon dilution. 

The osmotic pressure of an ideal solution can be calculated from the phenomenological expression for the chemical potential (Equation 5.12). The pressure dependence of the activity is ignored  

A typical definition of an ideal solution is one that obeys Raoult s Law. This definition is asymptotically correct in dilute solution. The osmotic pressure can then be expressed as  

When reading the Materials and Methods section of papers, it is frequently noted that calorimetric data were obtained for cells in simple, hypo-osmotic 

All the factors in this section will affect the metabolic activity and, consequently, the heat flux (see Reference [44,51]). 

We briefly review here thermodynamics of a nonideal binary solution. The osmotic pressure Ft is the extra pressure needed to equilibrate the solution with the pure solvent at pressure p across a semipermeable membrane that passes solvent only. The equilibration is attained when the chemical potential of t e pure solvent becomes equal to the chemical potential of the solvent molecule in solute volume fraction f at temperature T  

We separate the right-hand side into two parts  

The compressibihty of the solvent (9pi/9P)r is equal to the molar volume of the solvent in the solution, Vi, and can be assumed to be unchanged over a small range of pressures thus. 

Only under special conditions, i.e., when the polymer is dissolved in a theta solvent, will (jt/c) be independent of concentration. Experimentally, a series of concentrations is studied, and the results treated according to one or other of the following virial expansions  

The coeffidraits Aj, Fj and Aj, Fj are the second and third virial coefficients, which describe, respectively, intraactions between one polymer molecule and the solvent, and multiple polymer-solvent interactions. When solutions are suffidraitly dilute, a plot of (jt/c) against c is linear and the third virial coeffidents (A3, F3) can be neglected. The various forms of the second virial coeffident are interrelated by 

It has been found that g = 0.25 in good solvents, so Equation 9.13 becomes 

The corresponding values of the second viiial coefficient are obtained from the slopes of the plots and are equal to Aj = 2.08 x 10 and 1.63 X 10 m mol kg for toluene and acetone, respectively. 

To estimate molecular weights of several samples of poljretjrene from measurements of osmotic pressure of solutions in toluene. 

Measurements of osmotic pressure at 25 °C of solutions in toluene of a dozen different polj tjn enes were made by Bawn, Freeman, and Kamaliddin (Trans. Faraday Soc. 1950, 46, 862, supplemented by private communication from Bawn). The results obtained on four different samples are given, in sequence of increasing molecular weight, in table 1 where c denotes concentration, f volume fraction and II osmotic pressure. 

It will be assumed that the last sample S IB has a molecular weight not less than 1.5 x 10 . This assumption will be discussed later. 

The determination of molecular weight or of r depends on the classical law of van t Hoif which for our present purpose is conveniently written in the form 

The crux of the problem is how best to cany out the extrapolation to = 0 and this will depend on what we assume about the dependence of n on (p. We shall make the least restrictive assumption possible for the purpose, namely that 

Let us consider a solution (denoted by a single prime) separated from the pure solvent (denoted by a double prime) by a membrane which is permeable only to the solvent. A membrane of this kind is called a semi-permeable membrane. The chemical equilibrium eventually established between the phases is called osmotic equilibrium. 

The affinity corresponding to passage of solvent molecules (component 1) from the pure solvent to the solution is 

Let US suppose that the pressures applied to the two phases are p and p , then the chemical potential of solvent in the solution will be given, according to (20.8), by 

This cannot be equal to zero unless Hence osmotic equilibrium 

At osmotic equilibrium, therefore, the pressures applied to the phases must be different, and this difference 

Seawater varies from time to time and place to place, and contains at least trace amounts of all the elements of the periodic table. It is approximately 3 wt% dissolved solids, mostly NaCl, Na2S04, MgCla, and KCl, which, if they are totally ionized, lead to a water mol fraction 0.98 [4]. To estimate the two fugacities in Eq. 14.11, we return to Example 7.3, which shows the effect of pressure on fugacity of liquids, and combine that with Eq. 7.27 to find 

This is very similar to the boiling-point elevation and freezing-point depression cases we considered in Section 8.10. In both of those cases the solute was inactive, either because its vapor pressure was 0.00 in those cases or because its permeability through the membrane is 0.00 in this case. The behavior of the solvent, which is close to pure, can be estimated by Raoult s law in all three cases. For the pure water, v, and y, are unity, and for the water in the solution, with mol fraction 0.98, Raoult s law is certain to be practically obeyed, so that y, is certain to be practically unity. The partial molar volume of water in pure water is practically the same as that in dilute solutions, so we may take the In of both sides and combine the two integrals, noting that the pressure of the salt water is greater than that of the freshwater, Ending 

As a simple example of the importance of osmotic equilibria, consider the various ways humans have developed to 

A nonvolatile solute added to a solvent affects not only the magnitude of the vapour pressure above the solvent hut also the freezing point and the boiling point to an extent that is proportional to the relative number of solute molecules present, rather than to the weight concentration of the solute. Properties that are dependent on the number of molecules in solution in this way are referred to as colligative properties, and the most important of such properties from a pharmaceutical viewpoint is the osmotic pressure. 

Whenever a solution is separated from a solvent by a membrane that is permeable only to solvent molecules (referred to as a semi-permeable membrane), there is a passage of solvent across the membrane into the solution. This is the phenomenon of osmosis. If the solution is totally confined by a semipermeable membrane and immersed in the solvent, then a pressure differential develops across the membrane, which is referred to as the osmotic pressure. Solvent passes through the membrane because of the inequality of the chemical potentials on either side of the membrane. Since the chemical potential of a solvent molecule in solution is less than that in pure solvent, solvent will spontaneously enter the solution until this inequality is removed. The equation which relates the osmotic pressure of the solution. If, to the solution concentration 

On application of the van t Hoff equation to the dmg molecules in solution, consideration must be made of any ionisation of the molecules, since osmotic pressure, being a colligative property, will be dependent on the total number of particles in solution (including the free counterions). To allow for what was at the time considered to be anomalous behaviour of electrolyte solutions, van t Hoff introduced a correction factor, i. The value of this factor approaches a number equal to that of the number of ions, v, into which each molecule dissociates as the solution is progressively diluted. The ratio ijv is termed the practical osmotic coefficient, p. 

When Equation (10.105) is substituted in Equation (10.103) and Equation (10.106) in the similar equation for the second component, with appropriate values of the mole fraction, the two equations can be solved to give the values of a and b. We must emphasize that the values so obtained are valid only for the saturated phases, and the use of such values to obtain values of the excess chemical potentials in the homogenous regions of composition depend upon the validity of Equation (10.104). 

The measurement of osmotic pressure and the determination of the excess chemical potential of a component by means of such measurements is representative of a system in which certain restrictions are applied. In this case the system is separated into two parts by means of a diathermic, rigid membrane that is permeable to only one of the components. For the purpose of discussion we consider the case in which the pure solvent is one phase and a binary solution is the other phase. The membrane is permeable only to the solvent. When a solute is added to a solvent at constant temperature and pressure, the chemical potential of the solvent is decreased. The pure solvent would then diffuse into such a solution when the two phases are separated by the semipermeable membrane but are at the same temperature and pressure. The chemical potential of the solvent in the solution can be 

A binary system consisting of two parts separated by a diathermic, rigid membrane has three degrees of freedom. The particular system under discussion can be made univariant by fixing the temperature and pressure of the pure solvent the equilibrium pressure on the solution is then a function of the composition of the solution. The condition of equilibrium is 

The difference between the chemical potential for the two standard states is 

A measurement of P for a given mole fraction, xu permits the calculation of the value of A/i at P and xt. Such values are not at a constant pressure. When values of A/i are desired at the pressure of the solvent, P, the correction 

Consider two solutions separated by a membrane that will allow solvent particles through, but not solute particles. (This is called a semi-permeable membrane, and they are very important in biology - and in you Think about why your kidneys are there, for a start.) All particles are moving, so solvent particles can hit the membrane and pass through it. Pretty obviously, the solution that has the greater concentration of solvent particles - i.e. the less concentrated solution (the dilute one with fewer solute particles in it) will have more solvent particles going through the membrane. 

The osmotic pressure of a solution is the pressure that has to be exerted on the more concentrated solution side of a semi-permeable membrane to just stop overall passage of solvent into it from pure solvent on the other side of the membrane. 

The solution with the higher concentration of solute is said to be hypertonic , while the solution with the lower concentration is hypotonic . You have probably come across these terms, hyper- and hypo-, in other areas, such as the slang term for being over-excitable - a person is described as being hyper They actually originate from old Greek words now used in medical terms hyper- means excessive and hypo- means under. So hypertension is high blood pressure and hypotension is low 

One type of semi-permeable membrane is usually made of cellophane these days, but originally it was made of pig s intestines It allows solvent to pass through it and small particles of solute such as salt, but not large molecules (so salt, glucose, amino acids or water would pass through the intestine wall, but not molecules of protein or starch). Similarly, water, urea and ionic materials can be removed from blood by the kidneys. 

There are other types of semi-permeable membrane that will not allow charged particles such as Na or to pass through, but will allow through uncharged particles of almost any size. A lot of biology involves selective membranes of one kind or another. 

The equation for freezing-point depression is analogous to that for boiling-point elevation  

What mass of ethylene glycol (C2H6O2), the main component of antifreeze, must be added to 10.0 L of water to produce a solution for use in a car s radiator that freezes at — 10.0°F (—23.3°C) Assume that the density of water is exactly 1 g/mL. 

Solution The freezing point must be lowered from 0°C to -23.3°C. To determine the molality of ethylene glycol needed to accomplish this, we can use the equation 

This means that 12.5 mol of ethylene glycol must be added per kilogram of water. We have 10.0 L, or 10.0 kg, of water. Therefore, the total number of moles of ethylene glycol needed is 

Like the boiling-point elevation, the observed freezing-point depression can be used to determine molar masses and to characterize solutions. 

The free energy A of the system is obtained from the integration of eqn (5.9). It is convenient to take the system of non-interacting polymers (v = 0) as a reference state. The difference in the free energy A-Ao between the two states is 

In the Gaussian approximation, the integrals on the right-hand side can be performed rigorously (see Appendix 5.II). Given the free energy, the osmotic pressure is calculated by 

The first two terms are easUy understood the first term represents van t Hoff s law (clN)kBT (c/N being the number of polymers in unit volume), and the second term is the excluded volume interaction between the segments. The last term represents the correction to the second term due to the chain connectivity i.e., the effect that the intramolecular excluded volume interaction does not contribute to the osmotic pressure. 

From eqn (5.45) it will be seen that as c- 0, the osmotic compressibility (dlT/dc) becomes negative, which is of course incorrect. It follows that the theory presented above is only valid if 

This gives eqn (5.5). The situation c c is described by the theory of semidilute solutions. 

As this depends on the fractional power 9/4 of the concentration, it is impossible to reach this result no matter how higher-order terms in the perturbational calculation are obtained. It has an exponent higher by 1 /4 than the exponent of the second virial term. Around the overlap concentration where the volume fraction is numerically 0 10 , this discrepancy cannot be neglected. 

Use an ideal value for the van t Hoff factor unless the question clearly indicates to do otherwise, as in the previous example and in some of the end-of-chapter exercises. For a strong electrolyte dissolved in water, the ideal value for its van t Hoff factor is listed in Table 14-3. For nonelectrolytes dissolved in water or any solute dissolved in common nonaqueous solvents, the van t Hoff factor is considered to be 1. For weak electrolytes dissolved in water, the van t Hoff factor is a little greater than 1. 

Osmotic pressure depends on the number, and not the kind, of solute particles in solution  

Like molecules of an ideal gas, solute particles are widely separated in very dilute solutions and do not interact significantly with one another. For very dilute solutions, osmotic pressure, 77, is found to follow the equation 

In this equation n is the number of moles of solute in volume, V (in liters), of the solution. The other quantities have the same meaning as in the ideal gas law. The term n/Vis a concentration term. In terms of molarity, M, 

Osmotic pressure increases with increasing temperature because T affects the number of solvent-membrane collisions per unit time. It also increases with increasing molarity because M affects the difference in the numbers of solvent molecules hitting the membrane from the two sides, and because a higher M leads to a stronger drive to equalize the concentration difference by dilution and to increase disorder in the solution. 

The wood frog can survive at body temperatures as low as —8.0 °C. Calculate the molality of a glucose solution (CgHi206) required to lower the freezing point of water to —8.0 °C. 

A The wood frog survives winter by partially freezing. It protects its cells by flooding them with glucose, which acts as an antifreeze. 

The process by which seawater causes dehydration (discussed in the opening section of this chapter) is osmosis. Osmosis is the flow of solvent from a solution of lower solute concentration to one of higher solute concentration. Concentrated solutions draw solvent from more dilute solutions because of nature s tendency to mix. 

Pressure of excess fluid = osmotic pressure of solution 

A FIGURE 12.16 An Osmosis Cell In an osmosis cell, water flows from the pure-water side of the cell through the semipermeable membrane to the salt water side. 

SO that y = j Substituting this value in equation (111), we obtain 

A solution of propanol in water having 71.69% CH3CH2CH2OH by mass—an azeotrope—has a lower boiling point than any other solution of these two components. In fractional distillation, solutions having less than 71.69% of the alcohol yield the azeotrope and water as ultimate products. Solutions with more than 71.69% of the alcohol yield the azeotrope and propanol. 

In each case, the azeotrope is drawn off through the condenser (Fig. 14-18), and the other component remains in the pot. 

One of the most familiar azeotropes consists of 96.0% ethanol (C2H5OH) and 4.0% water, by mass, and has a boiling point of 78.174 °C. Pure ethanol has a boiling point of 78.3 °C. Dilute ethanol-water solutions can be distilled to produce the azeotrope, but the remaining water cannot be removed by ordinary distillation. As a result, most ethanol used in the laboratory or in industry is oriy 96.0% C2H5OH. To obtain absolute, or 100%, C2H5OH requires special measures. 

In the previous section our primary emphasis was on solutions containing a volatile solvent and volatile solute. Another common type of solution is one with a volatile solvent, such as water, but one or more nonvolatile solutes, such as glucose, sucrose, or urea. Raoult s law still applies to the solvent in such solutions—the vapor pressure of the solvent is lowered. 

A FIGURE 14-20 Observing the direction of flow of water vapor 

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It must be kept in mind that both pictures are modelistic and invoke extrather-modynamic concepts. Except mathematically, there is no such thing as a two-dimensional gas, and the solution whose osmotic pressure is calculated is not uniform in composition, and its average concentration depends on the depth assumed for the surface layer. 

It was pointed out at the beginning of this section that ir could be viewed as arising from an osmotic pressure difference between a surface region comprising an adsorbed film and that of the pure solvent. It is instructive to develop... 

To review briefly, the osmotic pressure in a three-dimensional situation is that pressure required to raise the vapor pressure of solvent in a solution to that of pure solvent. Thus, remembering Eq. Ill-16,... 

A film at low densities and pressures obeys the equations of state described in Section III-7. The available area per molecule is laige compared to the cross-sectional area. The film pressure can be described as the difference in osmotic pressure acting over a depth, r, between the interface containing the film and the pure solvent interface [188-190]. 

This subject has a long history and important early papers include those by Deijaguin and Landau [29] (see Ref. 30) and Langmuir [31]. As noted by Langmuir in 1938, the total force acting on the planes can be regarded as the sum of a contribution from osmotic pressure, since the ion concentrations differ from those in the bulk, and a force due to the electric field. The total force must be constant across the gap and since the field, d /jdx is zero at the midpoint, the total force is given the net osmotic pressure at this point. If the solution is dilute, then... 

In the preceding derivation, the repulsion between overlapping double layers has been described by an increase in the osmotic pressure between the two planes. A closely related but more general concept of the disjoining pressure was introduced by Deijaguin [30]. This is defined as the difference between the thermodynamic equilibrium state pressure applied to surfaces separated by a film and the pressure in the bulk phase with which the film is equilibrated (see section VI-5). 

Theta conditions in dilute polymer solutions are similar to tire state of van der Waals gases near tire Boyle temperature. At this temperature, excluded-volume effects and van der Waals attraction compensate each other, so tliat tire second virial coefficient of tire expansion of tire pressure as a function of tire concentration vanishes. On dealing witli solutions, tire quantity of interest becomes tire osmotic pressure IT ratlier tlian tire pressure. Its virial expansion may be written as... 

Figure C2.1.5. Reduced osmotic pressure FT / (RTc as a function of the weight concentration c of polystyrene (M = 130 000 g mor ) in cyclohexane at different temperatures. At 7"= 35 °C and ambient pressure, tire solution is at tire 0 conditions. (Figure from 1741, reprinted by pennission of EDP Sciences.)...

Figure C2.1.8. Reduced osmotic pressure V l(RTc as a function of the polymer weight concentration for solutions of poly(a-metliylstyrene) in toluene at 25 °C. The molecular weight of poly(a-metliylstyrene) varies...

Alexander S, Chaikin P M, Grant P, Morales G J, Pincus P and Hone D 1984 Charge renormalisation, osmotic pressure, and bulk modulus of colloidal crystals theory J. Chem. Phys. 80 5776-81... 

Van t Hoff was the recipient of the first Nobel Prize in chemistry in 1901 for his work in chemical dynam ICS and osmotic pressure—two topics far removed from stereochemistry... 

In Chap. 8 we discuss the thermodynamics of polymer solutions, specifically with respect to phase separation and osmotic pressure. We shall devote considerable attention to statistical models to describe both the entropy and the enthalpy of mixtures. Of particular interest is the idea that the thermodynamic... 

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

The criterion for phase equilibrium is given by Eq. (8.14) to be the equality of chemical potential in the phases in question for each of the components in the mixture. In Sec. 8.8 we shall use this idea to discuss the osmotic pressure of a... 

Osmotic pressure is one of four closely related properties of solutions that are collectively known as colligative properties. In all four, a difference in the behavior of the solution and the pure solvent is related to the thermodynamic activity of the solvent in the solution. In ideal solutions the activity equals the mole fraction, and the mole fractions of the solvent (subscript 1) and the solute (subscript 2) add up to unity in two-component systems. Therefore the colligative properties can easily be related to the mole fraction of the solute in an ideal solution. The following review of the other three colligative properties indicates the similarity which underlies the analysis of all the colligative properties ... 

As noted above, all of the colligative properties are very similar in their thermodynamics if not their experimental behavior. This similarity also extends to an application like molecular weight determination and the kind of average obtained for nonhomogeneous samples. All of these statements are also true of osmotic pressure. In the remainder of this section we describe osmotic pressure experiments in general and examine the thermodynamic origin of this behavior. 

Figure 8.7 Schematic representation of an osmotic pressure experiment.

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