Knudsen method

In the Langmuir free-evaporation method, the sample is suspended freely in a vacuum system with no container sunounding it. As very low levels of vapour pressure can be measured it has advantages over the Knudsen method where the lower limit is about 10" atm. (Kubaschewski et al. 1993). It is therefore more usefril in materials with high sublimation energies and therefore inherently low vapour pressiues. It has a further advantages in that there is no container with which to react, but there are more significant problems associated with temperature measurement. 

The heats of sublimation were determined for 6-azauridine (14), 6-azathymine (15) and 6-azacytosine (16) in order to elucidate the effect of substituents on the intermolecular energies. For 6-azauridine (14) a value of 130.9 kJ mol-1 was determined by the Knudsen method (74MI21900, 75M121900). 

Knudsen method, calculated-Antoine eq., Hoyer Peperle 1958)... 

Data were also obtained by this method for the solid states for the methyl ester of 2,4-D, the n-propyl ester of 2,4,5-T, and the butyl ester (liquid) of 2,4-D. The results are shown in Table III. These data were fitted by the least squares method to the Clausius-Clapeyron equations given in footnotes to Table III. These equations were used to estimate the vapor pressures at several temperatures, including the melting point. In Table IV, these are compared with estimates from other sources. Jensen s unpublished data with the Knudsen method compare favorably with those reported in this work, but the published values obtained by other methods are larger. 

The heat of vaporization depends on the measurement of vapour pressure. The low volatility of the metals and their salts and oxides restricts us to two methods of measurement, the Knudsen method and the rate of evaporation method. The principle of the Knudsen method, which depends on the rate of effusion of the vapour from a small orifice in a heated cell containing the material, has been discussed in Section 3.3. The rate of evaporation method, due to Langmuir 293 depends upon the assumption that there is no activation energy opposing condensation on this view the rate of... 

Beryllium— The most recent measurement of the vapour pressure of beryllium is due to Holden, Speiser, and Johnston 228 who used both the Langmuir rate of evaporation method and the Knudsen method. A third law calculation of AHq for vaporization showed no drift over a temperature range from 1,172° to 1,552° K, with a mean value of 76-57 iO-37. Previous measurements in this temperature range 2 gave a bad trend in third law... 

A 2nd and 3rd law analysis of six reported vapor pressure studies is tabulated below. Five studies (1.-5) used the Langmuir free evaporation method while one study (6) used the Integral variation of the Knudsen method. 

The vapor pressure over vanadium was measured by Edwards et al. (j ) using the Knudsen method and by Farber and Snvastava (6) using effusion-mass spectrometric techniques. Our 2nd and 3rd law analysis is tabulated below, where reaction (A) refers to the sublimation V(cr) = V(g) and reaction (B), the vaporization V(t) = V(g). 

Zaitsau et al. [44] measured the vapor pressure of a series of [C mim NTf2] ionic liquids using the integral effusion Knudsen method and correlated the A H with the molar volumes and the surface tensions of the compounds. What is clear from this study is that the values for A H are approximately half that used in Rebelo s initial estimate and further indicated that the Eotvos-Guggenheim correlations which are suitable for molecular solvents do not apply for ionic liquids. 

One method which is known under the name of permeametry [131] or Poiseuille-Knudsen method [124] is based on the law of gas permeability in a porous media in the two flow regimes molecular flow (Knudsen) and laminar or viscous flow (Poiseuille). According to Darcy s law, the gas flux through a membrane with a thickness / can be written as / = KAP/l, where K is the permeability coefficient and AP (AP = Pi - P2) the pressure difference across the membrane. If the membrane pore diameter is comparable to the mean free path of the permeating gas, K can be expressed as a stun of a viscous and a non-vis-cous term... 

For very low vapor pressures (below about 10 Pa), the vapor pressure can be measured by the Knudsen method, in which the rate of escape of vapor through a small hole is measured. The kinetic theory of gases (with correction factors for hole geometry, etc.) is used to relate the rate of effusion to the vapor pressure. The attainable accuracy of such methods is around 1% to 10% at best, but it is often the only experimental option for substances of very low volatility. 

Gas Saturation Method. For vapor pressures less than 1 torr, a gas saturation method is most often employed. The effusion method or Knudsen method also has been used in this pressure range, but it has proved quite imprecise (15). 

Kana an [72-kan] reported experimental data obtained by both Knudsen and torsion methods. The data obtained by the torsion method was selected. The data obtained by Knudsen method is about 17% lower. 

The dissociative evaporation scheme can also be determined by measurii the total vapor pressure by the Knudsen method and deducing the amount of evaporated matter from the... 

These methods were developed based on the moleeular kinetie theory of gases. The Langmuir method is based on the evaporation of substanee from a free surfaee into a vacuum. The Knudsen method is based on the evaluation of the outflow rate of a vapor jet from... 

The Knudsen method is based on a measurement of the mass rate of the vapor outflow through a hole. Knudsen proposed the following expression ... 

Cater, E.D. (1970) Measurement of the gross equilibrium vaporization rate (Knudsen methods). In Physicochemical Measurements in Metals Research, edited by Rapp, R.A. New York Interscience, pp. 21-94. 

The torsion-effusion modification of the Knudsen method, originally introduced by Volmer, helps to reduce some of the problems described above. In this method, vapour from the specimen effuses from two (or possibly more) holes in opposite vertical faces of a cell suspended from a fine wire. The cell is thereby caused to rotate and the torque imparted by the effusing vapour is opposed by the torque in the suspension. The vapour pressure is calculated by use of the equation ... 

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