Linear least squares analysis adsorption isotherms

Experimental Verification of Adsorption Isotherms and Linear Least-Squares Analysis. If gas A is exposed to a very high surface area solid catalyst (i.e., sslOO m /g) in a closed chamber, then a sensitive electronic balance should provide measurements of the increase in catalyst mass at a given gas pressure pa as active sites become occupied. A flow control valve is necessary to maintain constant pressure pa while measurements are made, because adsorption of gas molecules on the catalytic surface will cause a decrease in gas pressure if additional gas is not introduced into the system. Knowledge of the gas density at STP conditions and the additional mass of gas from the flow control valve required to maintain constant pressure pa allows one to calculate the volume of adsorbed gas per initial mass of catalyst, va- Experiments are repeated at different gas pressures. The raw data correspond to pa va pairs that can be modeled via the Langmuir isotherm to extract two important parameters of the adsorption process. 

Since there are three equilibrium constants (i.e., Ka, Kb, and / eq.Rxi) and one kinetic rate constant that one seeks to determine via linear least-squares analysis, it is necessary to have an independent measurement of either Ka or via adsorption studies on the same high-surface-area catalyst in a pulverized state. For example, if this catalyst is exposed to pure gas A and Ka is determined via linear least-squares analysis of its adsorption isotherm, then some of the other temperature-dependent parameters in the Hougen-Watson model are calcnlated as follows from ao, ai and a2. 

Briefly describe linear least-squares analysis of adsorption data that conform to the BET isotherm. 

Adsorption of DPM from seawater by humic acid was recorded and the value of Kads was determined by a simple least squares analysis of the linear portion of the isotherm to be 1.11 for a 150 ppm suspension of humic acid in seawater (Table II). This low value of Kads is not unexpected, since one would expect the interaction between the neutral nonpolar DPM molecule and the suspended humic acid to be due to a rather weak molecular attraction. 

Adsorption and desorption data points are presented in Figures 2-4 and are well matched with linear, least-squares fit isotherms, namely, 6 vs. Ceq plots. Linear isotherms are expected for situations having low surface coverage such as ours (seen in very low values of 6 exhibited by the data), where the probability of adsorbate-adsorbate interactions (aggregation) is small. It is conceivable that actual variation of 0 with Ceq may be more complex than a linear function however, data scatter is such that more detailed analysis of adsorption-desorption data is not justified. In any case, linearity, as characterized by I.T slope on the log-log plots, fits the data quite well. These plots are required for presentation of data that span six orders of magnitude in each direction. 

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See also in sourсe #XX -- [ , , , ]

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