Van *t Hoff s Law

The measurement techniques most frequently used are derived from Raoult s and Van t Hoff s laws applied to cryometry, ebulliometry, osmometry, etc. They are not very accurate with errors on the order of ten per cent. Consequently, the molecular weight is often replaced by correlated properties. The mean average temperature or viscosity can thus replace molecular weight in methods derived from ndM. 

Id. Treatment of Data.—Typical osmotic data are shown in Figs. 38 and 39. Here the ratio ( n/c) of the osmotic pressure to the concentration is plotted against the concentration. If the solutions behaved ideally, van t Hoff s law Eq. (11) would apply and m/c should be independent of c. Owing to the large effective size of the polymer molecules in solution (Fig. 34) and the interactions between them which consequently set in at low concentrations, /c increases with c with a... 

IdeaP temperature at which van t Hoff s law is obeyed for a given poor solvent-polymer system — KiT/ pi,... 

In this form, van t Hoff s law of osmotic pressure is also used to determine the molar masses of biological and synthetic macromolecules. When the osmotic pressure is measured for a solution of macromolecules that contains more than one species of macromolecule (for example, a synthetic pol5mer with a distribution of molar masses or a protein molecule that undergoes association or dissociation), the osmotic pressures of the various solute species II, are additive. That is, in sufficiently dilute solution... 

VAN T HOFF S LAW OF FREEZING-POINT DEPRESSION AND BOILING-POINT ELEVATION... 

Since van t Hoff s law is valid only for infinitely diluted solutions, one develops Iloj/c in power law series (break after the linear term in c)... 

How does the osmotic pressure depend on the temperature and the solute concentration State van t Hoff s law. 

Once having determined X, nion is calculated using an analogue of van t Hoff s law ... 

At the other occupation extreme, if the value of 6jt were unrealistically small in Equation 5.23, the final term could be replaced by -kT J2 J2 The resulting equation is van t Hoff s law ... 

This is known as the van t Hoff s law showing that, independent of the kinds of solvents, the osmotic pressure in dilute solutions is a function of the concentration of the solutes only. 

Let us assume that AP = 0, but there is a concentration difference and the solute can diffuse. If the solution is ideal, van t Hoff s law states that... 

K has been measured carefully as function of temperature over a considerable temperature interval for each temperature K may be determined from conductivity or from emf measurements, the latter technique being described in Section 4.13(d). The heat of ionization per unit advancement of the ionization reaction may be determined according to Eq. (3.7.4) in conjunction with van t Hoff s Law. This requires a knowledge of the manner in which y changes with T. Details, based on Section 3.10, are to be handled in Exercise 4.4.1, which the reader is advised to work out in detail. 

R = gas constant and T = absolute temperature). The so-called first virial coefficient, Bi, is simply equal to the reciprocal of the molecular weight, M. The evaluation of the second virial coefficient, Bi, has become one of the principal theoretical developments in recent years. In his theory of polymer solutions Flory (1953) has shown that Bi is proportional to a term (1 — 6/T), which vanishes T = 0. Accordingly 0 may be considered as the ideal temperature at which the above equation is reduced to the well-known van t Hoff s law, i.e.,... 

In equation 17, X represents the wave length of the monochromatic light used, A o is Avogadro s number, and B, which measures the deviation from van t Hoff s law, is the coefficient of the last term (c ) in the expres-... 

Thus van t Hoff s law leads to Eaoult s law that the relative lowering of the vapour pressure of a solution is independent of all chemical properties, and is determined only by the mol fraction of solute and solvent (p. 251). 

We can derive some further important results from van t Hoff s laws of osmotic pressure. 

As this line of reasoning only explains one of van t Hoff s laws, and is quite incapable of accounting for the identity of the osmotic pressure 3nd the gaseous pressure, and also for the proportionality between the osmotic pressure and the temperature, it is clear that the assumption of forces of attraction is not a sufficient explanation. Later on van t Hoff himself laid stress on the analogy between the dissolved and the gaseous states, and explained osmotic pressme, in the same way as gaseous pressure, by the collisions of the solute molecules with the semipermeable membrane.I This kinetic conception of... 

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... 

The measurements of Kahlenberg, Wilcox, and others Journ. Phys. Chem. 10,141 (1906) and 14,576 (1910)) have clearly been carried out with membranes which were not completely semipermeable. As ebullioscopic and kryoscopic determinations with the solutions used by these authors have shown that van t Hoff s laws hold at least approximately for these solutions, it is clear that their pressure measurements must be subject to a systematic error. It i.s natural to look for this error in the properties of the membrane. See v. Antropoff Zeitschr. f. physikal. Chemie, 76, 721 (1911). 

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