Gibbs excess mass

Mn2 = 28 g/mol being the molar mass of nitrogen. An example for such measurements is given in Figure 1.12, [1.36]. It presents Gibbs excess masses of nitrogen adsorbed on reference material CRM BAM-PM-104 at 77 K (po = 1 atm) determined by the volumetric/manometric method in a closed system and without carrier gas. Data show hysteresis between the adsorption-... 

Differences in the volumetrically and gravimetrically measured Gibbs excess masses depicted in Fig. 1.24 are partly due to different activation procedures of the zeolite samples used in the experiments. This of course should be avoided, but as a matter of fact happened in our experiments and therefore is brought to reader s attention. 

We restrict this discussion to dispersions or mean square deviations (MSD) of the Gibbs excess masses of component i = 1...N of a... 

In Figure 2.14 the integral heats of adsorption (AH, cp. (2.36)) per unit mass of sorbent (m = 1 g) are shown as functions of the Gibbs excess mass of n-butane adsorbed. Data were taken for 4 temperatures. Measurements at T = 323 K were performed twice. Uncertainties of data are about three times the size of the graphical symbols presenting data points. The experiments performed with the GSC so far indicate that the sensitivity of measurements decreases with increasing temperature but increases with decreasing thermal conductivity of both the sorptive gas and the sensor gas used in the SGC. 

As has been outlined in Chap. 2 uncertainties or errors of measured data constitute an important part of any kind of experimental work and hence always should be considered [2.18], However, for sake of brevity we here provide the reader only with the formulae allowing one to calculate uncertainties or mean square deviations (MSD) (cj ge) of th Gibbs excess mass (m g) of an adsorbate which has been measured gravimetrically by using a two beam balance. This mass can be calculated from eq. (3.14) combined with eqs. (3.10) and (3.13). By using Gauss law ofpropagation of uncertainties we have... 

From (3.18), (3.19) one can recognize that the MSD of the Gibbs excess mass will increase with increasing numerical values of the reduced... 

The uncertainty of measurement represented by its dispersion or mean square deviation (MSD) of the Gibbs excess mass (o Qg) can be calculated from eq. (3.18) which results from eq. (3.14) or (3.34) by applying the Gauss... 

What has already been said at the end of Sect. 2.1.3 is also valid here To obtain accurate values of the Gibbs excess mass, it is essential to know system s parameters (g, V, ) and the sorptive gas density (p ) fairly accurately which means inequalities (Og / g) < 10 , (av / < lO , and... 

The Gibbs excess masses (m g ) have been calculated from experimental i2o data using numerical values of the sorbent s helium volume as given below... 

Figure 3.18. Gibbs excess mass () of nitrogen adsorbed on activated carbon NORIT R1 EXTRA at (298 K - 343 K) for pressures up to 50 MPa, [3.26],...

Figure 3.20. Gibbs excess mass ( = io + ) of carbon dioxide adsorbed on activated...

Here the volume of the adsorption chamber (Vac) etc. has to be determined -for example - from helium or nitrogen expansion experiments using a sample mass of well known volume (ballast or tare), cp. Chap. 2. For the volume of the sorbent mass and the adsorbed phase (V ) one has again to introduce a model assumption. We here restrict e discussion to the Gibbs excess mass of all components adsorbed. Hence we choose the so-called helium approximation for V ... 

Uncertainties of Gibbs excess masses (3.52) as represented by their mean square deviations (MSD) (a ) can be calculated by applying the Gauss Law of propagation of uncertainty of error to eqs. (3.51) and (3.52) respectively ... 

Gibbs excess masses (m j3E)ofa two component adsorbate which have been measured by the volumetric-gravimetric method, i. e. calculated by Eqs. (4.1)... 

From these expressions the Gibbs excess masses adsorbed can be calculated via the mass balances (4.45) as... 

Table 4.2. Gibbs excess masses and absolute masses of a CO2 / CH4 co-adsorbed phase on AC D47/3 at T = 293 K for pressures up to 1.4 MPa, [4.17]. For calculation of absolute masses adsorbed cp. also (2.7), (2.9), (2.31).

For sake of completeness we also mention the dispersion or uncertainty of Gibbs excess masses as given by eq. (4.71). Gauss law of propagation of uncertainty leads to the expression... 

Combining equations (5.25), (5.40) we have for the Gibbs excess mass adsorbed... 

We here present a formula allowing one to calculate numerically the dispersions or mean square deviation (MSD) of Gibbs excess masses of adsorbates which have been measured oscillometrically and... 

These numerical values of dispersions (Ox) provided one can expect relative uncertainties of Gibbs excess masses measured with the rational pendulum to be limited by (a GE/mQg)<2%. This is about the accuracy of standardized volumetric / manometric measurements, cp. Chap. 2. To realize accurate oscillometric measurements it is most important to determine the (A) and ( ) parameters related to the various oscillations of the pendulum as accurate as possible, cp. Eq. (5.39). For this it is necessary to choose an initial amplitude (uo) of about 2-3 times the size of (ai, but less than 60 ° as for higher values of (Uo) measurable deviations of the oscillation from ideal harmonic behavior occur. Also it is necessary to observe at least 10 periods within an oscillation if not more, to get reliable (A, co)-data. To ensure this, the use of diodes with characteristic detection times less than 0.1 ms is recommended [5.7]. 

Figure 5.7. Reduced masses (Hose, f grav) resulting from oscillometric and gravimetric adsorption measurements of He on activated carbon (Norit R1 Extra) at 293 K. Gibbs excess masses adsorbed (= 0, ) are calculated from (f2o c>...

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