Vant Hoff

As already mentioned, there are two so called "dead volumes" that are important in both theoretical studies and practical chromatographic measurements, namely, the kinetic dead volume and the thermodynamic dead volume. The kinetic dead volume is used to calculate linear mobUe phase velocities and capacity ratios in studies of peak variance. The thermodynamic dead volume is relevant in the collection of retention data and, in particular, data for constructing vant Hoff curves. 

The second type of vant Hoff curve, also grossly exaggerated, is depicted in Figure 2. 

The first term on the right is the ideal, or vanT Hoff, term. At infinite dilution, tz/c must necessarily approach this limit, as may be shown (see Chap. VII) by compelling thermodynamic arguments. The higher terms represent the deviations from ideality predicted by the foregoing theory. It is these deviation terms which are subject to error as a result of the aforementioned limitations of this theory in dilute solutions. 

The analogy with the virial expansion of PF for a real gas in powers of 1/F, where the excluded volume occupies an equivalent role, is obvious. If the gas molecules can be regarded as point particles which exert no forces on one another, u = 0, the second and higher virial coefficients (42, Azy etc.) vanish, and the gas behaves ideally. Similarly in the dilute polymer solutions when w = 0, i.e., at 1 = , Eqs. (70), (71), and (72) reduce to vanT Hoff s law... 

The Hood s equation was based on the experimental results. Some theoretical significance to this equation was given by Vant Hoff (1884) on the basis of the effect of temperature on equilibrium constants. This idea was extended by Arrhenius in his attempt to obtain the relation between rate constant and temperature. The relation obtained was successfully applied by him to the effect of temperature data for a number of reactions and the equation is usually called the Arrhenius equation. 

The variation of equilibrium constant Kc with absolute temperature can be given by Vant Hoff s relation,... 

The concentration of complex in such a case must be calculated by making the use of steady-state-treatment. This type of complex is known as a Vant Hoff complex. 

However, if complex is of Vant Hoff type complex, [X] is determined by steady state treatment. On applying steady state conditions with respect to X, we get... 

In Vant Hoff intermediate, where concentration of the catalyst is negligible compared with substrate concentration, at higher substrate concentration the rate is given by... 

VANT HOFF S LAW OF FREEZING-POINT AND BOILING-OINT 351 From Equation (9.24),... 

OXYGEN, OXIDES 0X0 ANIONS Vancomycin-resistant enterococci, d-ALANYL-d-ALANINE LIGASE VAN DER WAALS FORCES VANT HOFF RELATIONSHIP COLLISION THEORY ARRHENIUS LAW TRANSITION-STATE THEORY TEMPERATURE DEPENDENCE VANT HOFF S LAWS VARIANCE... 

Vant Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018... 

It has already been stated that the retention of a solute depends on the magnitude of the distribution coefficient of the solute between the mobile and stationary phases. Furthermore, according to Vant Hoff s Law, the distribution coefficient will vary according to the exponent of the reciprocal of the absolute temperature. In addition, the dispersion of a solute band in a column will be shown to depend on the dlffusivity of the solute In both phases, the viscosity of the mobile phase and also on the distribution coefficient of the solute, all of which vary with temperature. It follows that, for consistent results, the column must be carefully thermostated. The column and its contents have a significant heat capacity and, consequently, it is of little use trytng to thermostat the column in an air bath for satisfactory temperature control, the thermostating medium... 

Conductivity measurements for solutions of living poly-pPL with DBCK+ counterion in CH2CI2/8PL mixture indicated that macroions and macroion-pairs are present in the system. In Fig.l, taken from Ref. 2 the Vant Hoff>s plots are given for dissociation constants of poly-ePL macroion-pairs with DBCK+ counterion (Kp) and similar plot for dissociation constants of Ph4B DBCK+ (Kpi). Dissociation of Ph4B"DBCK+ was investigated because this salt was further used in the kinetic measurements to shift the equilibrium between macroions and macroion-pairs towards the latter ones. 

El Shahawi concluded that polyurethanes were preferred over carbon because of, among other properties, ease of regeneration. To support this, they determined the H values of a number of pesticides by determining partition coefficient as a function of temperature. The partitioning of a solute is in part defined by the vant Hoff equation. The integrated form of the equation is ... 

The objections advanced by Becker [11] against the idea of ignition of an explosive mixture by a shock wave, where he cites Nernst [21] and Vant Hoff [22], are completely incorrect and are based on clear misunderstandings. Referring to the above authors, Becker states that adiabatic ignition requires much higher—up to 100 or 250 atm—pressures than the pressures available to us in a, detonation wave. 

In fact, Vant Hoff s 250 atm and Nernst s pressure significantly higher than 100 atm [21] are the pressures that explosive mixtures, adiabatically compressed to the temperature of auto-ignition, may develop in combustion. 

In contrast, the pressures of adiabatic (isentropic, according to Poisson) compression which are necessary to bring an explosive mixture to autoignition are 19.5-23.9 atm according to Vant Hoff s calculations, and 25-40 according to Falk s [23] data quoted by Nernst. 

Vant Hoff J. H. Vorlesungen iiber theoretische und physikalische Chemie. 2. Aufl. Berlin, 245 (1901). 

The temperature dependence of ki ) is given by two Arrhenius equations and one vant Hoff relation ... 

Figure 11. vant Hoff plots of the equilibrium constants Kcs and KDi88 of polystyrylsodium in three solvents and Arrhenius lines of the propagation constants of the three species... 

Vant Hoffs 1874 pamphlet, in Ramberg and Somsen, TheYoungJ. H. varit Hoff. tQuoted in translation in Alan J. Rocke, The Quiet Revolution Hermann Kolbe and the Science of Organic Chemistry (Berkeley and Los Angeles University of California Press, 1993), 329. 

That terminology can be confusing, because what we call chemical kinetics was called chemical dynamics by Vant Hoff not for the first time, the meaning of a technical term has changed with the years. 

In the late nineteenth century, Vant Hoff and Le Bel announced the tetrahedral bonding of carbon atoms. This provided an explanation of the existence of enantiomers. But whereas processes in living nature often produced either left- or right-handed molecules, chemists in the laboratory were at first able to... 

H. vant Hoff, according to H. Brunswig, Explosivstoffe, p. 17, Barth, Braunsehweig, 1909... 

Figure 3. Vant Hoff plot (desorption) for annealed MNih5Al0.5. AH = —6.7...

The magnitude of the equilibrium displacement depends on AT and AH for the equilibrium. The sign of AH1 determines the direction of the shift in accordance with the Vant Hoff equation. A typical equipment might discharge 10-25 kV in 1 cm3 of solution. Such a voltage discharge may produce about 45 J in 10-6 s corresponding to 4.5 x 107 W and temperature rise of 5-10°C. 

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