Van t Hoff s equation

For example, in the case of dilute solutions, the van t Hoff s equation may be used to piedict the osmotic pressure (jr = CRT) where n is the osmotic pressure of the solution, C is the molar concentration of the solute, ft is the universal gas constant and T is the absolute temperature, Fm dissociating solutes, the concentration is that of the total ions. For example, NaCI dissociates in water into two ions Na" " and Cl . Therefore, the total molar concentration of ions is hvice the molar concentration of NaCI. A useful rule of thumb for predicting osmotic pressure of aqueous solutions is 0,01 psi/ppm of solute (Weber, 1972). 

Eykman has verified van t Hoff s equation with a large number of substances used as solvents. The values of L, calculated from (18), and those observed directly, are given below in a few cases ... 

It can now be used for the extremely important purpose of calculating calcium sulphate and 4,000 dyne/cm. for barium sulphate. These figures entirely confirm the conclusion to which we have come on general grounds, that the surface tensions of solids must have high values. The applicability of the Ostwald-Hulett formula is limited, since it is based on Van t Hoff s equation for osmotic pressure, which only holds for small concentrations and, therefore, in the present case, for low solubilities. 

From the assumptions made in deducing it, it appears that this formula is inapplicable to any but dilute solutions. At higher concentrations the discrepancies become considerable between the osmotic pressures actually measured and those calculated from Van t Hoff s equation. The following figures for cane sugar may serve as an example —... 

Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, using software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Rtf. To facilitate these calculations, the following data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sh, is defined as Sh = 0.04 Re0 75 Sc0-33, where Sc is the Schmidt number (2) osmotic pressure follows van t Hoff s equation, ie, 7r = iCRgTy where i is the number of ions (3)... 

The values of these three parameters are all negative, as expected for a spontaneous transformation. It is also logical that entropy is decreased when the analyte moves from the mobile phase into the stationary phase where it is essentially fixed. Because of this, Van t Hoff s equation can be used in a fairly rigorous way to predict the effect of the temperature on the retention times of the analytes. 

Equal ion (2.8) is called Van t Hoff s equation and is a very important one in physical chemistry. It can be shown at once that the same equation holds for K(P, T). 

Equation (2.9.14) is one formulation of van t Hoff s equation (1886). The cautionary discussion concerning AGd and AGd also applies to AH This represents the differential enthalpy... 

The temperature dependence of the. equilibrium constant is given by van t Hoff s equation ... 

Substituting this value of S in (2), we obtain the law of mass action and at the same time the integrated form of van t Hoff s equation for the heat of reaction Reaktionsisochore). To illustrate the method, let us carry out the calculation for the formation of sulphur trioxide from sulphur dioxide and oxygen according to the equation 2SO2 + 02 = 2S0 ... 

Equations (4a) and (8) have only quite recently been subjected to the test of experiment, chiefly by Haber and Nernst. For historical reasons both Nernst and Haber make van t Hoff s equation their starting point. 

The first column contains the temperature in degrees centigrade, the second the experimental values of /i, and the third the heat of dissociation calculated by van t Hoff s equation. The fourth column contains the values of the heat of neutralisation of strong acids and bases determined calorimetrically by Wormanmt... 

Comparing equation (16a) with equations (10) and (11a) on p. 307, we find that the thermodynamically undetermined integration constant of van t Hoff s equation (reckoning with partial pressures instead of concentrations) is given by... 

In the first place the latter equation is satisfied for any gaseous phase which behaves as a mixture of perfect gases, whereas the van t Hoff equation is obeyed if the solution is not only ideal but also at the same time very dilute. The existence of deviations from van t Hoff s equation does not in any way prove that the solution is non-ideal. 

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 ... 

If a meaningful equilibrium constant, K, could be written for this process, the number of junctions should change with temperature in a way that is determined by Van t Hoff s equation ... 

K, and using the van t Hoff s equation, the enthalpy of complex formation was calculated to be -AH = 16.7 4.3 kJ/mol. It was found, moreover, that the absorption intensity in ultraviolet at wavenumber of v = 35 000 cm is the greatest at equimolar concentration of the substances tested. Therefore in the complex one n-butyro-nitrile molecule corresponds to one n-dodecene-1 molecule (Fig. 13). 

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