Vapour pressure calculation

I thank Dr. G.G. Briggs for helpful discussions about vapour pressure calculations. 

The effect of pressure on conversion and selectivity has been tested first on HY, i.e. the more active catalyst for iso-butylbenzene formation under atmospheric pressure [5]. The sBB vapour pressure, calculated by [9] is 9.98 bar at 573 K. Therefore a pressure value of 10 bar could assure that the reaction occurs in liquid-phase. 

The vapour pressures obtained from dew point measurements will depend on the relationship used for the temperature dependence of the saturated vapour pressure. A number of relationships, = f (7), have been proposed for the equilibrium Se02(cr) Se02(g), see Section V.2.2.3. in Chapter V. In order to obtain consistency it is necessary to revise previous vapour pressures calculated from the dew point temperature, to conform with the accepted = f (7 ) function. The problem met in this revision has been the fact that in some instances only p values have been published, while the dew point temperatures and the relationship used to obtain are absent. 

Pd = Mean partial water vapour pressure, calculated by taking the dewpoints. 

YpD = Safety margin for partial vapour pressure, calculated using the meteorological Pd value vs. the Pd value calculated for the respective testing condition found in the previous column. 

To calculate the adequate relative humidity for long-term stability testing, the mean partial water vapour pressure calculated for Sanya (27.16 hPa) is used at the standard testing temperature 30°C to get 64.0% RH. Testing at 30°C would include a safety margin of 14% added to the MKT, and testing at 65% RH would include a safety margin of 2% for Pd. Sanya, however, presents an extreme climate compared to the other parts of the country. 

E was taken from the linear fit of the data obtained for cell IX. The vapour pressure calculations are compared with the corresponding measurements using the transportation method. The agreement betw n the two methods of measuring the iodine pressure is fairly good (see Fig. 5), the deviations being almost within the reported limits of error for the transportation method. 

The Knudsen and torsion-effusion methods have been combined in a single apparatus, for example by Lindscheid and Lange. In this work the torsion cell was suspended from a microbalance, thus enabling simultaneous observations of mass loss and cell rotation to be made. The values of vapour pressure calculated from the two sets of results can be combined through the Knudsen and torsion-effusion equations to obtain the molar mass of the vapour species. Lindscheid and Lange carried out such measurements for Fe, Co, and Ni, and for Ni + Co alloys. 

The composition of the vapour can easily be calculated as follows — Assuming that the gas laws are applicable, it follows that the number of molecules of each component in the vapour wdll be proportional to its partial pressure, i.e., to the vapour pressure of the pure liquid at that temperature. If and p are the vapour pressures of the two liquids A and B at the boiling point of the mixture, then the total pressure P is given by ... 

In most cases, systems deviate to a greater or lesser extent from Raoult s law, and vapour pressures may be greater or less than the values calculated. In extreme cases (e.g. azeotropes), vapour pressure-composition curves pass through maxima or minima, so that attempts at fractional distillation lead finally to the separation of a constantboiling (azeotropic) mixture and one (but not both) of the pure species if either of the latter is present in excess. 

Moisture precipitation Apart from wetting by sea-spray, moisture may either be deposited on a surface by rainfall or dew formation. For a known ambient humidity the dew point can be calculated, using the expression given previously, from standard tables giving the saturated vapour pressure of... 

Kirchhoffs investigation does not show that the sublimation and evaporation curves meet each other at the temperature at which solid and liquid are in equilibrium with vapour it proves that they are inclined at an angle, but the further fact that they intersect requires separate proof, which was inferred by James Thomson, and experimentally demonstrated by Ferche (1891) in the case of benzene the point of intersection, calculated from the vapour-pressure curves, was 5 405° C, whereas the melting-point was 5 42° C. 

The analogy between (17) and the Kirchhoff vapour-pressure equation ( 88) is evident. R. T. Hardman and the author have shown that (17) enables one to calculate the solubility when the solubility parameters A, B, C have been obtained, and this... 

Again, if we consider the initial substances in the state of liquids or solids, these will have a definite vapour pressure, and the free energy changes, i.e., the maximum work of an isothermal reaction between the condensed forms, may be calculated by supposing the requisite amounts drawn off in the form of saturated vapours, these expanded or compressed to the concentrations in the equilibrium box, passed into the latter, and the products then abstracted from the box, expanded to the concentrations of the saturated vapours, and finally condensed on the solids or liquids. Since the changes of volume of the condensed phases are negligibly small, the maximum work is again ... 

Measurements in this held have been made by Berthelot and Ogier with nitrogen tetroxide Ann. de Chim. et Phys., [v.], 30, 382 (1883)), and with acetic acid ibid., 400), and some calculations with reference to steam have been made by Nernst Verhandl. Deutsch. Phys. Ges., 15, 313) and Levy ibid., 330), who utilised the vapour-pressure measurements of Holborn and Henning Ann. der Physik, (1906), 21 (1907), 22, 23). Wiedemann had previously observed that the specific heats of ethylbromide, ethyl-acetate, and benzene increase with temperature at about the same rate as that of nitrogen tetroxide at 200°. In the case of steam it was assumed that (i.) the polymerisation is to double molecules... 

Equation (18) was applied by Margules (1895) to calculate the heats of admixture of water and alcohol from the vapour-pressure data of Regnault the results agreed with the direct determinations of Winkelmann (1873). 

The equations just obtained, and those relating to vapour pressures, are quite general and apply to solutions of any concentration. Unfortunately we are not yet in a position to calculate the magnitudes general case, although we have seen in 158 that the form of the chemical potential ft,... 

If we take Dieterici s numbers for the vapour pressures, and Roloff s for the freezing-points, of solutions of potassium chloride, we can calculate the osmotic pressure (P0) from the two equations ... 

Thus, if we find how the electromotive force changes when the temperature of the cell is altered on open circuit, i.e., when no current is passing, we can at once calculate A, the latent heat, just as we can calculate the latent heat of evaporation of a liquid when we know the variation of its vapour pressure with temperature. Since E changes only slightly with T, we can evaluate dE... 

The theory of concentration cells was first developed with great generality by Helmholtz (1878), who showed how the electromotive force could be calculated from the vapour pressures of the solutions, and his calculations were confirmed by the experiments of Moser (1878). 

The values of i calculated from (8) and (8) do not agree very closely, and it would appear, as Weinstein (loc. cit. 1068) remarks, that Although the calculations undoubtedly establish the legitimacy of the system of equations, the great uncertainty in the numerical determination of the decisive magnitudes forms a practical defect which will only be removed by observations over very wide intervals of the variables. Any discrepancy between the results of actual observations of equilibria, and those calculated by means of Nernst s chemical constants, need not, in the present state of uncertainty of the latter, cause any great alarm. Nernst himself apparently regards the constant < >, obtained from vapour-pressure measurements, as the most certain, and the others as more or less tentative. 

A simple rectifying column consists of a tube arranged vertically and supplied at the bottom with a mixture of benzene and toluene as vapour. At the top a condenser returns some of the product as a reflux which flows in a thin film down the inner wall of the tube. The tube is insulated and heat losses can be neglected. At one point in the column the vapour contains 70 mol% benzene and the adjacent liquid reflux contains 59 moi% benzene. The temperature at this point is 365 K. Assuming the diffusional resistance to vaponr transfer to be equivalent to the diffusional resistance of a stagnant vapour layer 0.2 mm thick, calculate the rate of interchange of benzene and toluene between vapour and liquid. The molar latent heats of the two materials can be taken as equal. The vapour pressure of toluene at 365 K is 54.0 kN/nt2 and the diffusivity of the vapours is 0.051 cm2/s... 

Wet materia], containing 70% moisture, is to be dried at the rate of 0.15 kg/s in a countercurrent dryer to give a product containing 5% moisture (both on a wet basis). The drying medium consists of air heated to 373 K and containing water vapour equivalent to a partial pressure of 1.0 kN/m2. The air leaves the dryer at 313 K and 70% saturated. Calculate how much air will be required to remove the moisture. The vapour pressure of water at 313 K may be taken as 7.4 kN/m-. 

There are two disadvantages to the existing vapour pressure tables. Rrst of all, like any experimental data, there is no agreement between sources. This is worsened by the decision to take only one value into account for each chemical substance. This fact may encourage the user to take on trust the figure proposed, which is sometimes unjustified. Secondly, these values are given for a temperature that does not always correspond to the thermal conditions in which the chemical substance will be handled. Some references, to overcome this difficulty, offer several values. For instance, Weka most often gives three values, 20, 30 and 50°C, and the coefficients A, B, C in Antoine s equation can thus be calculated ... 

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