Van’t Hoffs law

T V — nRT. Van t Hoff noted the parallel between this law and the ideal gas equation, and he proposed that solute molecules in solution act independently of one another. Van t Hoffs law worked for solutions of nonelectrolytes and weak electrolytes, but for strong electrolytes, van t Hoff had to multiply n by a coefficient, i. For HCl and NaCl the value of i was close to 2, and for CaCl2, i was close to 3. For this reason, strong electrolytes were considered to be exceptions to van t Hoffs law. 

The first theoretical basis for calculating the decrease of freezing point according to van t Hoff law as applied to nitric esters was given by Nauckhoff [5]. 

VAN T HOFF LAW. A dissolved substance has the same osmotic pressure as the gas pressure it would exert in the form of an ideal gas occupying the same volume as that of the solution. 

The Henry s law solubility of trace species such as HNO, HC1, HBr and HOC1 in sulfuric acid solutions is an important issue. Reactions (1) to (4) generate HNO, and its solubility determines whether the product dissolves or is released into the gas phase. As expected from Van t Hoff law, the solubilities of HNO, and HC1 have found to increase with decreasing temperature. In addition, the solubilities for both HC1 and HNO, increase as the concentration of sulfuric acid decreases [49,80]. Both of these factors will work together to predict that the highest solubilities for HC1 and HNO, in stratospheric sulfate aerosols will occur at low temperatures, where the sulfate particles will be most dilute. The measured solubility of HNO, in sulfuric acid is small enough that most of the stratospheric nitric acid will be in the gas phase. Thus the denitrification, which contributes to polar ozone depletion, will not occur on the global sulfate aerosol. 

The product k2 x K can now be comprised to a new rate constant keff, which is a rate constant for the overall reaction. In order to account for the temperature dependency of keff, the temperature dependencies for both, k2 and K, have to be considered. While k2 follows the temperature according to the Arrhenius equation, Equation (6), the temperature dependency of K is given by the van t Hoff Law, cf. Equation (16) ... 

In general, the heat of solution is a function of the hydrogen concentration. In the preceding section we derived an expression for infinite dilution. We will now consider the case of high concentration (region II of Figure 4.1). We have seen that the phase rule requires the pressure to be invariant at any temperature below the critical temperature. The equilibrium pressure Peq at the a (3 phase transformation is given by the van t Hoff law. 

The basis of any calorimetric purity method is the relationship between the melting depression of a substance and the level of impurities according to van t Hoffs law. The purity is readily calculated from the DSC curve of a single melting event of a few milligrams of the substance, without the need for reference standard of the drug substance and its impurities. 

Isotherms depend significantly on the coliunn temperatme. We have shown earlier (see Figmes 3.33a [38] and 3.33b [54]) isotherms determined at different temperatures for the same systems. From these results, it seems that the amotmt of low-molecular-weight components adsorbed at equilibrium with a constant mobile phase concentration increases by about 1% when the temperatme decreases by about 1°C. For more complex isotherms, Van t Hoff law may not apply. For example, with the bi- or tri-Langmuir isotherms, the equilibrium constant of the... 

The first term of this virial expansion [Eq. (4.67)] is linear in composition and is called the van t Hoff Law [Eq. (1-72)], which is valid for ver>--dilute solutions ------------------------------------------------------------... 

The concentration = (j)jb is the number density of A monomers and V = c /Aa is the number density of A molecules. The last relation of the above equation is a general statement of the van t Hoff Law, as each solute molecule contributes kT to the osmotic pressure in very dilute solutions. The membrane allows the B molecules to pass freely, but restricts all A molecules to stay on one side. This restriction leads to a pressure which is analogous to the ideal gas law (the osmotic pressure is kT per restricted molecule Y[ = kTv). This pressure is due to the translational entropy loss caused by the confinement of the A molecules. 

The Flory-Huggins mean-field theory recovers the van t Hoff Law 4Fq. (1-72)] in the dilute limit (as 0—>0). At higher concentrations, the mean-field theory predicts that two-body excluded volume interactions make osmotic pressure proportional to the mean-field probability of monomer-monomer contact (0 ) ... 

Up to the overlap concentration 0, the van t Hoff Law should approximately describe the osmotic pressure. Above the osmotic pressure should increase as a stronger function of concentration. This function must have the following form, to match the van t Hoff Law when 0 = 0 ... 

In dilute solutions, the van t Hoff Law should be valid and the function / approaches unity at low values of the argument ... 

The first term is proportional to the number density of chains [the van t Hoff law Eq. (1.72)] and is important in dilute solutions. The three-body term is larger than the linear term > 4>jN) at concentrations above... 

In dilute solutions 0 < 0, this scaling function approaches unity h (j>l4> ) 1 and the osmotic pressure obeys the van t Hoff law. In semidilute 0-solutions, h((f>j(f) ) is again assumed to be a power law ... 

The object of the present considerations is to develop and apply methods for determining the numerical relation which holds, in place of that given by van t Hoffs law, between the osmotic pressure of the 10ns and their concentration, and the similar relation for the undissociated molecules, with the further object of studying each effect separately as far as possible in the case of strong electrolytes, t e systems which do not obey the law of mass action The calculations will be based upon the assumption that the degree of ionisation may be determined from conductivity data, 1 e that y = A qjh. o... 

In general, the variation of the equilibrium constant, K, with temperature follows the Van t Hoff Law, i.e.,... 

The introduction by van t Hoff of the term solid solution resulted from the discovery of a number of deviations from the Raoult-van t Hoff law for the depression of the freezing-point by dissolved substances. In all cases, the depression was too small in some instances, indeed, the freezing-point was raised. To explain these irregularities, van t Hoff assumed that the dissolved substance crystallised out along with the solid solvent and he showed how this would account for the deviations from the law of the depression of the freezing-point, which had been developed on the assumption that only the pure solvent crystallises out from the solution. ... 

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 mass M can be determined by operating as follows. First, one determines the mass concentration p of the dissolved polymer and the corresponding chain concentration C. The latter quantity is obtained, for small chain concentrations, by measuring the osmotic pressure (Van t Hoff law, Chapter 5). 

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