Error due to the volume change

These two aspects shall be discussed briefly at this juncture. 

In a situation wherein two immiscible solvents are employed in an extraction, the volumes of the two individual phases after attainment of equilibrium may be appreciably different in comparison to the initial volumes of the solvents used. Therefore, a number of procedures have been adopted to avoid error due to the volume change incurred thereby, namely  

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The titration vessel was purged with nitrogen to eliminate CO 2. From the volume and molarity of added base and the mass of titrated DOC, the content of acidic functional groups can be calculated. Carboxylic acid content was calculated from the amount of base added until the end-point was reached. Phenolic acid content was calculated as twice the difference in titrant required to change the pH of the titrate from 8 to 10, since it was assumed that at pH 10 only half the phenolic groups were dissociated. A solution of a concentration of 20 mgL" as DOC NOM were titrated. The error due to the salt content of NOM is likely to be high. 

Information is available on the design of pyknometer bulbs, meniscus correction,3 errors due to change of volume of the bulb with time (1 in 10 ),... 

A blank contains the reagents and solvents used in a determination, but no analyte. Often, many of the sample constituents are added to simulate the analyte environment, often called the sample matrix. In a blank determination, all steps of the analysis are performed on the blank material. The results are then applied to correct the sample measurements. Blank determinations reveal errors due to interfering contaminants from the reagents and vessels used in the analysis. Blanks are also used to correct titration data for the volume of reagent needed to cause color change in an indicator. 

The latter expression clearly shows that Hartree-Fock wave functions are not properly correlated they allow two electrons of opposite spin to simultaneously occupy a same elementary volume of an atomic or molecular space. Consequently, two-electron properties which are completely determined by the second-order density matrix cannot be correctly evaluated at the Hartree-Fock level and, a fortiori, from approximate SCF wave functions. On the contrary, satisfactory values of one-electron properties may be generally provided by those functions, at least in the case of closed-shell systems. However, due to the large contribution of pair correlation, the energy changes associated with the so-called isodes-mic processes (Hehre et al., 1970) can be reasonably well predicted at the Hartree-Fock level and also using SCF wave functions. Indeed, in that case, correlation errors approximately balance each other. 

Figure 6 Partitioning of LiCl between water and 1-octanol at 25°C, as taken from ref. [2l6]. The lithium distribution ratios Du were determined at 1 1 initial phase ratio by use of ion chromatography (IC), inductively coupled plasma (ICP) atomic emission spectrometry, and Li NMR spectrometry. A correction was made for the slight volume changes due to the mutual solubility of 1-octanol and water. Error bars are indicated only for the ICP data, which were the least precise data obtained by the three techniques. The solid curved line represents the equilibrium model calculated by SXLSQl using the values of log/Cs= = —6.85 and logX, = — 2.74 (Table 12). The dashed curved line is an extrapolation of the model to indicate the approach to the calculated asymptotic value of the distribution ratio at infinite dilution (3.76 X 10...

Identically this hold to be true for Ti (15 for ZSM-5), Fe (11 for ZSM5, 12 for ZSM-23) Zr (23 for ZSM-5 with u.c. volume varying from 5.345 to 5.380 nn with 0.5 Zr per u.c., etc. However it appears that this does not actually held true for Al in ZSM-5 (Fig. 1 left). This is probably due to the fact that water content was depending in Al content and that u.c. volume depends on water content as it will be described below. This makes that many data in the litterature are questionable when ambient atmosphere has not been well defined as outgassing at a given temperature or under a given water pressure. This holds particularly true since substitution may lead to more or less hydrophilic materials. Moreover when isomorphous substitution corresponds to a maximum of a few percents as for ti or Fe in MFI structure, the u.c. volume changes are within experimental error. 

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