Colligative Properties of a Dilute Solution

Here Aso1,a is the molar differential enthalpy of solution of solid or gaseous A in the liquid mixture, and Asoi,a1 is the molar differential volume of solution. Equation 12.3.5 is a relation between changes in the variables T, p, and Xa, only two of which are independent in the equilibrium system. 

Suppose we set dp equal to zero in Eq. 12.3.5 and solve for dr/ dxA- This gives us the rate at which T changes with xa at constant p  

Freezing-point depression the decrease in the freezing point of the solution, compared to pure solvent at the same pressure. 

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CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS 12.4 COLLIGATIVE PROPERTIES OF A DILUTE SOLUTION... 

Although these expressions provide no information about the activity coefficient of a solute, they are useful for estimating the solute molar mass. For example, from a measurement of any of the colligative properties of a dilute solution and the appropriate theoretical relation, we can obtain an approximate value of the solute molality niB- (It is only approximate because, for a measurement of reasonable precision, the solution cannot be extremely dilute.) If we prepare the solution with a known amount a of solvent and a known mass of solute, we can calculate the amount of solute from b = nAMpjnB, then the solute molar mass is the solute mass divided by ns-... 

Calculate the following colligative properties of a dilute solution boiling-point elevation, freezing-point depression, and osmotic pressure. 

The depression of the freezing point of a solvent due to the presence of a dissolved solute is an example of a colligative property, that is, a property of a dilute solution that depends on the number of dissolved particles and not on the identity of the particles. Water has a freezing point depression constant, Kf, of 1.86 K kg mol-1. In other words, for every mole of nonvolatile solute dissolved in a kilogram of water, the freezing point of water is lowered by 1.86°C. The change in freezing point, A T, can be calculated from the equation... 

Sections 12.4.1-12.4.4 will derive theoretical relations between each of the four col-ligative properties and solute composition variables in the limit of infinite dilution. The expressions show that the colligative properties of a dilute binary solution depend on properties of the solvent, are proportional to the solute concentration and molality, but do not depend on the kind of solute. 

Explain each of the following statements (a) The boiling point of seawater is higher than that of pure water, (b) Carbon dioxide escapes from the solution when the cap is removed from a carbonated soft-drink bottle, (c) Molal and molar concentrations of dilute aqueous solutions are approximately equal, (d) In discussing the colligative properties of a solution (other than osmotic pressure), it is preferable to express the concentration in units of molality rather than in molarity, (e) Methanol (b.p. 65°C) is useful as an antifreeze, but it should be removed from the car radiator during the summa- season. 

Colligative A colligative property of a solute in a dilute solution is an effect whose magnitude depends only on the concentration of the solute particles (number of particles per unit volume of solution) and not on features such as size, shape or chemical composition. Examples are osmotic pressure, depression of freezing point, elevation of boiling point and the vapour pressure of the solution. If the value of any one of these is known for a particular solution, then the values of the others may readily be calculated. 

Vapor-Pressure Lowering n One of the colligative properties of a solution and the basis of a method for determination of the molecular mass of a solute. For a dilute solutions, the solvent vapor pressure lowering is determined by (po - p)/po = X2, where po and p are the vapor pressures of the pure solvent and the solution respectively and X2 is the mole fraction of the solute. 

In all other solutions the so called degree of dissociation, as determined from the measurement of some colligative property, merely indicates the magnitude of interionic forces, it cannot, however, be taken as a measure of the quantity of dissociated and undissociated molecules of the solute. A complete theory of strong electrolytes, at least of their diluted solutions, has been developed by Debye and Hiickel, this theory is the basis of modern electrochemistry. 

Since the density p appears in a dimensionless combination here, the concentration dependence of the chemical potential comes with a choice of concentration units. The first term on the right side of Eq. (3.1) expresses the colligative property of dilute solutions that the thermodynamic activity of the solute, is proportional to its concentration, p. The excess chemical potential accounts for intermolecular interactions between the solution molecules, and is given by the potential distribution theorem (Widom, 1963 1982) ... 

The theory of electrolytic dissociation, AVhereas the osmotic pressure and the other colligative properties of aqueous solutions of substances, such as cane sugar, obey van t Hoff s laws, marked deviations are met with in aqueous solutions of acids, bases, and salts, even at great dilutions. The osmotic pressure and lowering of the freezing point for these solutions are still found to be approximately proportional to the molecular concentration, but are considerably greater than the theoretical values. To allow for this van t Hoff introduced a new term into his osmotic pressure equation, writing for such solutions... 

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). 

Ionic solutes are dissociated in solution into cations and anions. Thus aim aqueous solution of NaCl contains 1 mol of Na ions and 1 mol of Cl ions per kilogram of solvent. There are 2 mol of particles per kilogram of solvent, and therefore the colligative properties of the solution are greater than those of a 1 m solution of nonionic solute. In very dilute solutions, the colligative properties of solutions of ionic solutes are a multiple of the analogous properties of nonionic solutes. For example,... 

The structure of LDA (15) is not the monomeric species suggested by structure 15, but rather an aggregate. Jackman,and later Seebach and co-workers studied the colligative properties of LDA as a solution in THF and concluded that dilute solutions exist as both dimers (20) and monomers (21).The structure of LDA is assumed to be the THF solvated dimer shown by Williard s X-ray structure, 22,which shows that the nitrogen may be more sterically encumbered than is suggested in the representation in Figure 9.1. 

Examine a system in which a dilute solution is separated from a concentrated solution by a semipermeable membrane, illustrated in Figure 14.23. During osmosis, water molecules move in both directions across the membrane, but the solute molecules cannot cross it. Water molecules diffuse across the membrane from the dilute solution to the concentrated solution. The amount of additional pressure caused by the water molecules that moved into the concentrated solution is called the osmotic pressure. Osmotic pressure depends on the number of solute particles in a given volume of solution and is a colligative property of solutions. 

Because chemical methods are rather limited, the most widely used techniques for measuring the molar mass of a polymer are physical. Methods that depend on the colligative properties of dilute solutions can be used to determine the molar mass of a substance. These include ... 

The colligative properties of solutions, e.g. osmotic pressure, boiling point elevations, freezing point depression and vapour pressure reduction, depend on the effect of solute concentration on the solvent aetivity. The ehemieal potential, yt, of a non-electrolyte in dilute solution may be expressed by... 

The next major step was the enunciation of Raoult s law (Raoult 1887, 1888). In 1887, Francois Raoult published his investigations on the vapor pressure of the solvent in dilute solutions. He studied five solutes in water and 14 solutes in each of 11 organic solvents and found that the diminution of the vapor pressure of the solvent upon addition of a given (small) amount of solute was proportionally the same for all cases. The proportionality factor is the mole fraction of the solute. This may be expressed in the currently accepted notation as p° -pi p°X2 this is known as Raoult s law. Raoult had previously discovered the laws of freezing point depression and boiling point elevation (Raoult 1878, 1882), three of the so-called colligative properties of dilute solutions. 

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