Stability experimental uncertainties

A set of experiments was performed at variable droplet sizes. The graph in Fig. 4.7 shows the dependence of the normalized (by Kint/a) osmotic resistance as a function of the oil volume fraction. The normalized values fall onto a single curve within reasonable experimental uncertainty. The results were compared to the normalized data obtained by Mason et al. [7] in the presence of surfactants. These latter are represented as a solid line that corresponds to the best fit to the experimental points (Eq. (4.18)). It is worth noting that the normalized pressures in solid-stabilized emulsions are much larger than the ones obtained in the presence of surfactants. 

This is encouragingly small, especially considering the experimental uncertainty for the dioxime enthalpy of formation, althongh we have no real idea how mnch repnlsion or stabilization we might expect from vicinal dioxime gronps. (We likewise lack snch information for vicinally substituted alicycUc diones—there are literature enthalpy of formation data for 1,3- and 1,4- but not 1,2-cyclohexanedione there are also data for 2,3-pentanedione but not 1,2-cyclopentanedione.) Consider now the reaction 33. 

There are no thermochemical data for the bromophenols. For the iodophenols, there are enthalpy data only for the solid phases. Our estimation procedure, using the enthalpy of formation of iodobenzene and the OH/H exchange increment, predicts —86 kJ moG. How the iodophenols could be stabilized by ca 10 kJ moG is not clear, except that the experimental uncertainty is somewhat large and we know very little about the solid phase. 

The enthalpy of formation of solid 4-acetyl-l,3-benzenediol may be estimated from the enthalpy of formation of solid acetophenone and twice the OH/H exchange increment to be —565 kJ mol . The destabilization of less than 10 kJ moH may be due to uncertainty in the estimation of the enthalpy of formation of acetophenone and experimental uncertainty in the measurement of the diol. We would have expected resonance stabilization by the favorably situated acetyl and hydroxyl groups. The experimental enthalpy of formation is consistent with those of the acetylphenols, discussed in an earlier section. Their predicted values, estimated now by deoxygenating the diol, are both —370 kJ mol , close to the —361 kJ mol found as the average of the 2- and 4-hydroxy species. 

Ahyd// was measured in glacial acetic acid and corrected by a separate heat of solution measurement. The value given is for the liquid - liquid reaction. Experimental uncertainty is large for alkynes and ene-ynes because experimental error increases linearly with Ahyd77. The ene-yne conjugation stabilization relative to propyne and 2-butene is small, —96.0 —(—97.3) = 1.3 kcal mol 1 = 5.4 kJ mol"1, that is, Ahy(JH is smaller in magnitude by this amount than it would be for a hypothetical molecule with no conjugation interaction. 

Ahyd// was measured in acetic acid solution. No experimental uncertainty was given. The unexpectedly large Ahy(,//of l,l,4,4-tetramethylcyclodec-7(8)-ene, (Z), which causes the usual E, Z stability relationship in cycloalkenes to be reversed, is brought about by strain. The conformation of the cyclodecane ring of 1,1,4,4-tetramethylcyclodec-7(8)-ene, (Z) forces a methyl group into the energetically... 

Measurements by photographic photometry require careful calibration due to the nonlinear response of photographic plates saturation effects can lead to erroneous values. Line profiles can be recorded photoelectrically, if the stability of the source intensity and the wavelength scanning mechanism are adequate. Often individual rotational lines are composed of incompletely resolved spin or hyperfine multiplet components. The contribution to the linewidth from such unresolved components can vary with J (or TV). In order to obtain the FWHM of an individual component, it is necessary to construct a model for the observed lineshape that takes into account calculated level splitttings and transition intensities. An average of the widths for two lines corresponding to predissociated levels of the same parity and J -value (for example the P and R lines of a 1II — 1E+ transition) can minimize experimental uncertainties. A theoretical Lorentzian shape is assumed here for simplicity, but in some cases, as explained in Section 7.9, interference effects with the continuum can result in asymmetric Fano-type lineshapes. 

The hnished product will be subjected to inspection and rigorous testing for identity, uniformity, residual water content, stability, sterility and potency. In addition, all analytical techniques employed in testing these attributes will themselves have been subjected for reliability, reproducibility, experimental uncertainty limits. The biotechnological revolution has resulted in the appearance of ever more rehned and sensitive analytical techniques, mainly novel types of spectroscopy and coupled techniques, based on mass spectrometry, known usually by complex acronyms, e.g. MALDI-TOE-MS (Matrix-Assisted-Laser-Z)esorption-71me-of-Tlight-Mass Spectrometry). Some of the available analytical procedures are treated in more detail in the next chapter. 

The W3 method provides a mean absolute error of 0.8 kJ/mol for 30 molecules, with the worst case having an error of 2kJ/mol, and these values can be compared with the average experimental error of 0.6kJ/mol for the same set of data. It can be noted that the experimental data were carefully selected to have small experimental uncertainties, a more typical experimental error is 5-lOkJ/mol. Such explicit extrapolation procedures are thus capable of yielding results with accuracies comparable to experimental methods, and may soon surpass experiments as the preferred method for obtaining geometry and stability data for small- and medium-sized systems. 

It is clear from the discussion earlier that in almost all cases where stability constants are obtained by fitting a function to some experimental points where there is more than one variable, the constants will be partially interdependent. Essentially this means that if the stability constant uncertainties are used, for example, for a speciation uncertainty calculation, then it will not be correct to use them as independent uncertainties (refer to Figure 3.13). 

Table 3.3 shows some stability constants for hard and soft types of metal ligand complexes. The constants are experimental values [1,2] and, as such, contain some uncertainties. Nevertheless they support well the HSAB principle. 

By combining the various observations obtained from the G-T diagrams in different P conditions, we can build up a P-P diagram plotting the stability fields of the various polymorphs, as shown in figure 2.5. The solid dots in figures 2.4 and 2.5 mark the phase transition limits and the triple point, and conform to the experimental results of Richardson et al. (1969) (A, R, B, C ) and Holdaway (1971) (A, H, B, C). The dashed zone defines the uncertainty field in the... 

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