Osmotic pressure colligative property

In this example two factors are affecting the chemical potential of the solvent on the right-hand side, /Tsolventl (RHS)  

We already know how the presence of solute lowers the chemical potential of the solvent (by RT nx in dilute solution) from the previous Frames 51 and 52 (e.g. equation (51.7))  

Regarding the effect of pressure on a pure phase since (Frame 18, section 18.3 where in a detailed note the applicability of equation (53.3) is discussed at length (see Note 18.1))  

The change in molar Gibbs energy, dGm (and hence in chemical potential, d/x) when the temperature, T is held constant (so that dT = 0) and the pressure is changed from P = P to P( = P + IT can be found by integration of equation (53.3) 

We can assume that the molar volume of the solvent will be essentially unaffected by the osmotic pressure difference since liquids are virtually incompressible then equation (53.4) leads to  

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Molar masses can also be determined using other colligative properties. Osmotic pressure measurements are often used, particularly for solutes of high molar mass, where the concentration is likely to be quite low. The advantage of using osmotic pressure is that the effect is relatively large. Consider, for example, a 0.0010 M aqueous solution, for which... 

The final colligative property, osmotic pressure,24-29 is different from the others and is illustrated in Figure 2.2. In the case of vapor-pressure lowering and boiling-point elevation, a natural boundary separates the liquid and gas phases that are in equilibrium. A similar boundary exists between the solid and liquid phases in equilibrium with each other in melting-point-depression measurements. However, to establish a similar equilibrium between a solution and the pure solvent requires their separation by a semi-permeable membrane, as illustrated in the figure. Such membranes, typically cellulosic, permit transport of solvent but not solute. Furthermore, the flow of solvent is from the solvent compartment into the solution compartment. The simplest explanation of this is the increased entropy or disorder that accompanies the mixing of the transported solvent molecules with the polymer on the solution side of the membrane. Flow of liquid up the capillary on the left causes the solution to be at a hydrostatic pressure... 

Of all of the colligative properties, osmotic pressure shows the most dramatic effect. For example, a 1.0 M solution of glucose exerts an osmotic pressure of 24.5 atm at 25°C. A pressure of 24.5 atm is equivalent to 360 psi ... 

Physical properties of a solution generally differ from the same properties of the pure solvent. Under certain conditions, the changes in the values of several properties—such as vapor pressure, boiling point, and freezing point—depend only on the concentration of solute in the solution, and not on what the solute and solvent are. Such properties are referred to as colliga-tive solution properties. (A fourth colligative property—osmotic pressure—will not concern us in this text.)... 

Like other colligative properties, osmotic pressure measurements can be used to determine molecular masses. 

There are many measurement techniques for activity coefficients. These include measuring the colligative property (osmotic coefficients) relationship, the junction potentials, the freezing point depression, or deviations from ideal solution theory of only one electrolyte. The osmotic coefficient method presented here can be used to determine activity coefficients of a 1 1 electrolyte in water. A vapor pressure osmometer (i.e., dew point osmometer) measures vapor pressure depression. 

The presence of a solute affects some of the physical properties of a solution, but the identity of the solute makes little difference in the colligative properties. Vapor-pressure lowering, freezing-point depression, boiling-point elevation, and osmotic pressure are four such properties. 

Calculate the molar mass of a nonvolatile solute from the changes it causes in the colligative properties (vapor-pressure lowering, boiling-point elevation, freezing-point lowering, or osmotic pressure) of its dilute solution (Section 11.5, Problems 41-56). 

Colligative Properties Vapor Pressure Lowering, Freezing Point Depression, Boiling Point Elevation, and Osmotic Pressure 567... 

Historically, chemists have used the group of colligative properties— vapor pressure lowering, freezing-point depression, boiling-point elevation, and osmotic pressure—for molecular mass determinations. In Example 14-9, we showed how this could be accomplished with osmotic pressure. Example 14-10 shows how freezing-point depression can be used to determine a molar mass and, with other information, a molecular formula. To help you understand how this is done, we present a three-step procedure in the form of answers to three separate questions. In other cases, you should be prepared to work out your own procedure. 

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. 

As Morawetz puts the matter, an acceptance of the validity of the laws governing colligative properties (i.e., properties such as osmotic pressure) for polymer solutions had no bearing on the question whether the osmotically active particle is a molecule or a molecular aggregate . The colloid chemists, as we have seen, in regard to polymer solutions came to favour the second alternative, and hence created the standoff with the proponents of macromolecular status outlined above. 

The properties of a solution differ considerably from those of the pure solvent Those solution properties that depend primarily on the concentration of solute particles rather than their nature are called colligative properties. Such properties include vapor pressure lowering, osmotic pressure, boiling point elevation, and freezing point depression. This section considers the relations between colligative properties and solute concentration, with nonelectrolytes that exist in solution as molecules. 

Osmotic pressure, like vapor pressure lowering, is a colligative property. For any nonelectrolyte, ir is directly proportional to molarity, M. The equation relating these two quantities is very similar to the ideal gas law ... 

The lowering of freezing point and the generation of osmotic pressure both depend on the total concentration of solute particles. Therefore, by using the colligative property to determine the amount of solute present, and knowing its mass, we can infer its molar mass. 

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... 

For practical purposes, the colligative property that is most useful for measuring relative molar masses of polymers is osmotic pressure. As Table 6.2 shows, all other properties take such small values that their measurement is impractical. 

Colligative properties measure average relative molar masses, M, and in the case of osmotic pressure, II, the important relationship is ... 

While Arrhenius was studying conductivity, others were characterizing colligative properties of solutions. The Dutch chemist J. T. van t Hoff studied osmotic pressure and derived the law of osmotic pressure,... 

The number average molecular weight is required. This is obtained directly from measurements of a colligative property, such as the osmotic pressure, of dilute polymer solutions (see Chap. VII). It is often more convenient to establish an empirical correlation between the osmotic molecular weight and the dilute solution viscosity, i.e., the so-called intrinsic viscosity, and then to estimate molecular weights from measurements of the latter quantity on the products of polymerization. 

The dissolution of a solute into a solvent perturbs the colligative properties of the solvent, affecting the freezing point, boiling point, vapor pressure, and osmotic pressure. The dissolution of solutes into a volatile solvent system will affect the vapor pressure of that solvent, and an ideal solution is one for which the degree of vapor pressure change is proportional to the concentration of solute. It was established by Raoult in 1888 that the effect on vapor pressure would be proportional to the mole fraction of solute, and independent of temperature. This behavior is illustrated in Fig. 10A, where individual vapor pressure curves are... 

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. 

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