Dead space calculating

This method is smiple but experimentally more cumbersome than the volumetric method and involves the use of a vacuum microbalance or beam balance [22], The solid is suspended from one ann of a balance and its increase in weight when adsorption occurs is measured directly. The dead space calculation is thereby avoided entirely but a buoyancy correction is required to obtain accurate data. Nowadays this method is rarely used. 

The cooling effect of the channel walls on flame parameters is effective for narrow channels. This influence is illustrated in Figure 6.1.3, in the form of the dead-space curve. When the walls are <4 mm apart, the dead space becomes rapidly wider. This is accompanied by falling laminar burning velocity and probably lowering of the local reaction temperature. For wider charmels, the propagation velocity w is proportional to the effective flame-front area, which can be readily calculated. On analysis of Figures 6.1.2b and 6.1.3, it is evident that the curvature of the flame is a function of... 

Alveolar ventilation. Alveolar ventilation is less than the total ventilation because the last portion of each tidal volume remains in the conducting airways therefore, that air does not participate in gas exchange. As mentioned at the beginning of the chapter, the volume of the conducting airways is referred to as anatomical dead space. The calculation of alveolar ventilation includes the tidal volume adjusted for anatomical dead space and includes only air that actually reaches the respiratory zone ... 

It is calculated by measuring the nitrogen concentration in expired gas after a single breath of 100% oxygen. The nitrogen wash-out test is the same method used to measure anatomical dead space. Closing volume increases with age and reaches the standing FRC at 70 years and the supine FRC at 40 years. 

The physiological dead space can be calculated using the Bohr equation. 

The three-way stopcock is opened to connect the burette and sample tube, and volume and pressure are measured again. Since the dead space is known, the (final) number of moles of gas can be calculated. The difference between the initial and final number of moles gives the number of moles adsorbed. 

The total accessible pore volume may be measured by the amount of adsorbate at the saturation pressure of the adsorptive, calculated as liquid volume, provided the adsorption on the external surface can be neglected or can be evaluated. The accessible pore volume may be different for molecules of different sizes. A method which is not subject to the effect of the external surface is the determination of the dead space by means of a non-sorbable gas (normally helium) in conjunction with the determination of the bulk volume of the adsorbent by means of a non-wetting liquid or by geometrical measurements. 

We can now develop the necessary equations for calculating the amount adsorbed from the p Fdata obtained during a run. Let us denote the known volume of the gas burette by Vb(= Vi + V2+ Fjor F2 + 14 as the case may be) and its temperature by 7g. Since the sample bulb is not completely filled by the solid adsorbent, we must also consider the so-called dead-space volume occupied by gas. Let us denote this volume by I4 and consider it to be at a single temperature T. If the burette is filled with gas at an initial pressure Pi and then stopcock B is opened, the pressure will drop to a new equilibrium value pi. The number of moles adsorbed is... 

Stepwise measurements using any of both methods can be remarkably shortened by extrapolation of the equilibrium values. Evaluation of the kinetic curves allow conclusions on the mechanism of adsorption [15]. Results of buoyancy or dead space calibration may be used to calculate the sample density. 

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]. 

A column operated at 80°C contains 2.64 g of C24H5Q as stationary phase column inlet pressure is 907 mm Hg and outlet pressure 726 mm. Observed retention volume of benzene is 285.0 ml, column dead space is 10.6 ml, and vapor pressure of pure benzene at 80°C is 760 mm. Calculate the activity coefficient for benzene, with and without the correction for the second virial coefficient Bn. Assume a value of — 1500cm /mole for for benzene-benzene interaction, neglecting solute-gas and gas-gas interactions. 

The pressure was measured using a borosilicate glass Bourdon gage which was sensitive to 0.1 mm. of mercury as a null instrument to a mercury manometer. The final pressure was measured after the reaction vessel had been heated above 200° C. for 8 hours or longer. The maximum dead space of 14 cc. was efficiently flushed with oxygen at the start of each experiment and was duly corrected for in the calculation (2) of the ozone concentrations. The hollow-bore vacuum stopcocks used in the system were lubricated with Halocarbon (high temperature grade) stopcock lubricant. The usual precautions were taken to minimize the amount of mercury vapor in the system. 

We have shown that the experimentally measured heat exchange is direcdy connected to the integral heat of adsorption at constant temperamre. The experimental data needed to perform the calculation are Q, the number of moles adsorbed at two pressures, these pressures and the volume of the adsorption cell (the so-called dead space). 

The pressure required to counterbalance internal headspace pressures may be determined empirically (Figure 8) or calculated from theoretical modelling, [f done empirically, some care should be taken in relation to the amount of dead space in the system connecting the vessel under study to the pressure gauge, if erroneous results are to be avoided. This is particularly important for small headspaces and large dead spaces. 

Figure 1 shows a plot of pressure increase against time for an experiment at 189.2° with 14.9 mm. of formic acid decomposing on a 31.3-mg. high-vacuum film, and values calculated from Equations (1), (2), and (3) with appropriate constants. The exact dependence of pressure increase on the time is somewhat obscured at the end of the reaction by diffusion of formic acid vapor, partly present as dimer in the cooler portion of the apparatus, into the reaction flask from the dead space of the spoon gauge. 

The CO diffusing capacity, DLCO, is calculated by measuring the difference in alveolar CO concentrations at the beginning and end of a period of breath holding. The test begins by having die patient exhale completely to RV and then inspiring rapidly to TLC a breath of gas with a known CO concentration. After a 10-second breath-hold, the patient exhales rapidly (Fig. 21.14). The initial portion of this exhalation is discarded, as it contains gas from die dead space, and a portion of the subsequently exhaled gas, assumed to be well-mixed alveolar gas, is analyzed for CO content The initial alveolar concentration of CO is not the inspired concentration, as the inspired gas is diluted... 

Suitable manifold dead spaces. The system dead volume in theory should be as small as possible but in reality it should be carefully evaluated, especially for static volumetric systems. The volumes of adsorbed gas are calculated by the pressure difference between the experiment (with a reactive gas) and the blank (dead volume calibration with an inert gas) the smaller the dead volume, the higher the difference in pressure and more precise is the adsorbed volume calculation. On the contrary, by decreasing the system dead space the gas dose to be injected should be decreased accordingly to avoid the risk of injecting too much gas that might overtake the necessary amount to form a monolayer or, in the best case, to produce an isotherm with few experimental data points. In fact, when the injection volume is too small it is very difficult to calibrate it with the required precision. 

For drive systems with constant middle-position of the piston when stroke-adjusted, T e can be calculated from the compressibility of the discharge and the hydraulic fluid Xf 3Ch the relative dead spaces Edf = Vdf/Vp and dh = Vdh/Vp, the modulus of elasticity X of the working chamber, the pressure differential Ap and the stroke setting hp [14] (Vp is the chamber volume). 

For well designed pumps X is normally close to zero, i.e. the pump is of rigid construction so tjE can be calculated directly from pump and fluid data. This calculation shows that the relative dead spaces df and 8dh should be minimised to achieve good volumetric efficiency. Furthermore as the slip factor should approach tjs 1 (valves should be tight and operate with no slip [15]) the volumetric efficiency can be obtained directly from the indicator diagram (Figure 9.12) and the table beneath it. The diagram shows the relation between the decompression stroke h (from 3 to 4) and the compression stroke /i2 (from 1 to 2) and the table enables Joukowsky-shock, volumetric efficiency, shock factor and piston velocity to be calculated. 

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... 

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. 

---