Van’t Hoff’s factor

Buliginski s and Quincke s linear equation was found to be only approximate by Heydweiller,io who showed that Zlor=100(or—(7o)/c(7o, where c=conc. in equiv. per lit., was not constant. E.g. for KCl c=0 031, Zlor=2 22 c=l. 43, Zlcr=2 44 and for CaCl2, c=0-658, Zlo =2 26 c=4-91, Zlor=2 82. For some salts, A a first increased and then decreased, with increase of c. A plot of Aa against /, van t Hoff s factor, went through a minimum for all the salts. The results could be represented by an equation of the type used by Griineisenii for viscosities ... 

NH4S0 4 S0"4+NH 4, and unless the first stage be completed, the calculation cannot easily be made. From the conductivity and f.p. measurements of a normal soln., S. Arrhenius calculated for the ternary ionization, (NH4)2S04 2NH 4+SO"4, the value 2 17 for J. H. van t Hoff s factor i but the result is not probable. H. Koppe calculated i=2 00 for the W-soln. from his osmotic measurements. The effect of additions of non-conductors to the soln. was studied by S. Arrhenius. The degree of ionization with a W-soln., at 25°, Is 0 0185 with methyl alcohol 0 0249 with ethyl alcohol 0 0267 with isopropyl alcohol 0 0212 with ether and 0 0171 with acetone. 

The above argument may be restated m the followmg way Suppose that one mole of KC1 is dissolved in V liters of solution Owmg to dissociation there are (1 - x) undissociated moles, x cations and anions, the total number of individuals being (x + x), where (1 + x) is identical -with van t Hoff s factor t Now suppose that the 10ns and the undissociated molecules obey the gas law If w, is the osmotic pressure of either of the 10ns and the osmotic pressure of the molecules it follows on the above assumption that—... 

This relation must hold if the mass law is obeyed By eliminating C, and C from this equation and from the thermodynamic equation (i), (viz 2dirJC, - dirujCu = o), it is seen that the necessary and sufficient condition that the law of mass action should hold is that at all concentrations dmUC = dirJdCu Now the computation of van t Hoff s factor i from freezing-point data, and the consequent calculation of the degree of ionisation on this basis assumes that the ions and the undissociated molecules are normal That is, it assumes dirJdC, = dirJdCu = RT... 

A theory close to modem concepts was developed by a Swede, Svante Arrhenins. The hrst version of the theory was outlined in his doctoral dissertation of 1883, the hnal version in a classical paper published at the end of 1887. This theory took up van t Hoff s suggeshons, published some years earlier, that ideal gas laws could be used for the osmotic pressure in soluhons. It had been fonnd that anomalously high values of osmotic pressure which cannot be ascribed to nonideality sometimes occur even in highly dilute solutions. To explain the anomaly, van t Hoff had introduced an empirical correchon factor i larger than nnity, called the isotonic coefficient or van t Hoff factor,... 

Hantzsch s work said his conclusions have lately been revised and criticized. In his extensive work published in 1941, Titov [35] drew attention to the fact that none of the existing view about the action of sulphuric acid on nitric acid explained Hantzsch s observation that the value of the van t Hoff i-factor for nitric acid dissolved in sulphuric acid may be close to 4. 

Let us apply the simplest form of van t Hoff s equation to the data from various distributions of E given in Table 5.4. Notice that if Eq. 5.72 is valid, then the ratio of the equilibrium constants equals that of the desorption energy factors calculated from 5.71. Then the Second Law value of the effective jet would come from ... 

Le Chatelier has extended van t Hoff s law and enunciated the important generalization any change in the factors of equilibrium from outside, is followed by a reversed ohange within the system . This rule, known as Le Chatelier s theorem, enables the chemist to foresee the influence of pressure and other agents on physical and chemical equilibria. 

Fischer and Walach i showed that if Knorr s pyrrole is dissolved in concentrated sulphuric acid at 40° and the solution then poured on ice, 2-ethoxycarbonyl-3,5-dimethylpyrrole-4-carboxylic acid results. Probably, dissolution of the diester in concentrated sulphuric acid generates the acylium ion (77) evidence for this is the van t Hoff cryoscopic factor of 3 5 observed for such solutions a xhe process cannot be complete at the freezing point, for complete acylization would give s factor of 5. Acyli-zation 184 AacI > will be facilitated by electron-releasing substituents and will not be subject to steric factors. In the pyrrole series, a balance has to be struck between the facilitation caused by increasing alkyl substitution in the nucleus and the retardation which would accompany salt formation by... 

The freezing point depression is proportional to the product of the solute s molality and the van t Hoff factor. For nonelectrolytes, such as C2H5OH (0.050 m), i = 1, and thus... 

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. 

In contrast to the formally analogous van t Hoff equation [10] for the temperature dependence of equilibrium constants, the Arrhenius equation 1.3 is empirical and not exact The pre-exponential factor A is not entirely independent of temperature. Slight deviations from straight-line behavior must therefore be expected. In terms of collision theory, the exponential factor stems from Boltzmann s law and reflects the fact that a collision will only be successful if the energy of the molecules exceeds a critical value. In addition, however, the frequency of collisions, reflected by the pre-exponential factor A, increases in proportion to the square root of temperature (at least in gases). This relatively small contribution to the temperature dependence is not correctly accounted for in eqns 2.2 and 2.3. [For more detail, see general references at end of chapter.]... 

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