The Dead-space Volume

The Dead-space Volume.—This is the volume of gas that occupies the flow line from the point of injection to the point of detection. It is determined, at mean column pressure poJ% from 

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Note that the dead space volume is treated as having a uniform well-mixed composition. 

Steps 3 and 4 are not required if the dead space volume is determined in another way. 

When thermal equilibrium reached (i.e. after c. 3-5 hours), the dead space volume is determined as in Steps 3 and 4 of the discontinuous manometric procedure in Section 3.3.1. In the case of low-temperature calorimetry this must be done between Steps 2 and 3, by simply connecting the adsorption bulb to the manometric equipment. 

The determination of the dead space volume of the adsorbent bulb is not quite as straightforward as one might think. It is necessary to consider the following three questions (1) How do we define the remaining gas volume in relation to the volume occupied by the adsorbent (2) What is the most suitable procedure (3) If gas expansion is to be used, then which gas (e.g. He or Nj) should be adopted, and at what temperature ... 

The indirect route for determining the dead space volume makes use of an estimated volume of the adsorbent sample. This volume can be obtained in two ways ... 

Helium is often used in adsorption manometry for the determination of the dead space volume (see Chapter 3), but this procedure is based on the presupposition that the gas is not adsorbed at ambient temperature and that it does not penetrate into regions of the adsorbent structure which are inaccessible to the adsorptive molecules. In fact, with some microporous adsorbents, significant amounts of helium adsorption can be detected at temperatures well above the normal boiling point (4.2 K). For this reason, the apparent density (or so-called true density ) determined by helium pycnometry (Rouquerol et al., 1994) is sometimes dependent on the operational temperature and pressure (Fulconis, 1996). 

The cryogenic adsorption system was specially developed to measure adsorption isotherms of H2 and D2. This system is equipped with a closed helium cycle two-stage Gifford McMahon refrigerator to operate under cryogenic conditions. The adsorption temperature can be kept constant within 0.03 K at 20 K. Adsorption isotherms are obtained by gas adsorption manometry. This method is based on the measurement of the gas pressure in a calibrated, constant volume, at a known temperature. The dead space volume was calculated from a helium calibration measurement at the temperature of interest. Thermal transpiration effect was calibrated according to the work by Takaishi and Sensui [41]. 

In (24-35) the term V /4 is influenced by many factors [Equation (24-14)], but mainly reflects the characteristics of a particular column and its mode of operation. This plate-munber factor is described in the preceding sections (24-2 and 24-3). The factors of relative retention and partition ratio in (24-35) depend on the solutes, the nature of the mobile and stationary phases, and the temperature. The factor A /(l -I- k) also strongly depends on the dead-space volume in a column. Figure 24-8 illustrates how it varies according to the dead-space volume per gram of stationary phase. When the specific retention volume of a solute is relatively low and a column... 

NOTE While the hair is digesting, become familiar with the atomic absorption instrument and obtain the values needed to prepare the calibration curve. It is very important that the dead space volume in the apparatus is the same for both the standards and the samples. Be sure to make any final additions or dilutions to assure this. 

For the dead-space volume phase, the material balance is... 

Normally F2 is at a different temperature from Fj so the total volume cannot be measured correctly. However, an effective volume called the dead space, F, can be measured. This quantity will then be used in subsequent calculations. To determine the dead space, one first does a calibration of the system without a sample with T2 and (temperatures of F2 and Fj) at the operating temperature anticipated. The adsorbing gas is admitted to the calibrated volume area F, (through valve G) with the valve to F2 (C) closed. The pressure measurement, P, is taken. The valve C is then opened and a second pressure measurement, Pp is taken. The dead space volume is given by... 

Prior to gas adsorption, it is common practice to pretreat or condition the catalyst surface. Frequently high temperatures, about 500°C, are employed. Therefore, a sample furnace is an essential part of the apparatus. After pretreatment, evacuation at pretreatment temperature, and cooling to adsorption temperature, it is necessary to determine the dead space volume (the volume in the sample tube which the adsorbate would occupy provided no adsorption occurred). Helium is most often used for this purpose. After evacuation, the adsorbate is added to the manifold and its pressure noted. Subsequently, it is expanded into the sample chamber, and adsorption, if any, commences. The pressure is monitored until no further variation with time is noted. The pressure over the sample can then be increased via a gas burette and readings again taken until equilibrium is established. When there is no longer gas uptake by the sample with increasing pressure, the desirable portion of the isotherm is complete, and the total volume adsorbed, expressed at S.T.P. per gram, can be determined. This procedure must be repeated for the support. The volume adsorbed at any pressure is subtracted from the volume adsorbed on the supported catalyst at the same pressure. Further details can be found in the books by Hayward and Trapnell (1964) and by Anderson (1968). 

In all the volumetric methods the basic principles are the same. The adsorbate is degassed under vacuum to remove surface contamination. Helium is next admitted into a burette of known volume and its pressure and temperature measured so that the amount at STP can be calculated. The sample tube is immersed in liquid nitrogen and helium admitted. The residual amount in the burette is determined and the amount expanded into the sample tube determined. Since helium does not adsorb on to the solid, this volume is termed the dead space volume and it is found to be linearly dependent on pressure, l e helium is removed and the procedure repeated with nitrogen. When the nitrogen expands into the sample tube, it splits into thi parts, residual in the burette, dead space which can be calculated from the previously found dead space factor, and adsorbed. The process is repeated at increasing pressures and the amount adsorbed determined as a function of relative pressure. 

In most low pressure measurements the correction for unadsorbed gas is negligible so that no effort needs to be made to minimize the dead space volume. 

CF is a correction factor applied for gender, is the dead space volume, composed of the extrathoracic and the tracheobronehiolar volumes. It is approximated to 147 and 118 cm for male and female adults (168). The deposited fraction in the alveolar region (DEa) is... 

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