Data in Table

Estimate the surface tension of n-decane at 20°C using Eq. 11-39 and data in Table II-4. 

The data in Table III-2 have been determined for the surface tension of isooctane-benzene solutions at 30°C. Calculate Ff, F, F, and F for various concentrations and plot these quantities versus the mole fraction of the solution. Assume ideal solutions. 

The existence of this situation (for nonporous solids) explains why the ratio test discussed above and exemplified by the data in Table XVII-3 works so well. Essentially, any isotherm fitting data in the multilayer region must contain a parameter that will be found to be proportional to surface area. In fact, this observation explains the success of Ae point B method (as in Fig. XVII-7) and other single-point methods, since for any P/P value in the characteristic isotherm region, the measured n is related to the surface area of the solid by a proportionality constant that is independent of the nature of the solid. 

The data in Tables 4.2 and 4.3 refer to ions in aqueous acid solution for cations, this means effectively [MlHjO), ]" species. However, we have already seen that the hydrated cations of elements such as aluminium or iron undergo hydrolysis when the pH is increased (p. 46). We may then assume (correctly), that the redox potential of the system... 

The data in Table 7.1 show that, as expected, density, ionic radius, and atomic radius increase with increasing atomic number. However, we should also note the marked differences in m.p. and liquid range of boron compared with the other Group III elements here we have the first indication of the very large difference in properties between boron and the other elements in the group. Boron is in fact a non-metal, whilst the remaining elements are metals with closely related properties. 

Phosphine is a colourless gas at room temperature, boiling point 183K. with an unpleasant odour it is extremely poisonous. Like ammonia, phosphine has an essentially tetrahedral structure with one position occupied by a lone pair of electrons. Phosphorus, however, is a larger atom than nitrogen and the lone pair of electrons on the phosphorus are much less concentrated in space. Thus phosphine has a very much smaller dipole moment than ammonia. Hence phosphine is not associated (like ammonia) in the liquid state (see data in Table 9.2) and it is only sparingly soluble in water. 

The second subject is concerned with cis and (runs isomers. The tratu isomer has the higher Xma. value (except for azobenzene) and the larger mai. This will be apparent from the data in Table XIII. 

Comparison of the water-induced acceleration of the reaction of 2.4a with the corresponding effect on 2.4g is interesting, since 2.4g contains an ionic group remote from the reaction centre. The question arises whether this group has an influence on the acceleration of the Diels-Alder reaction by water. Comparison of the data in Table 2.1 demonstrates that this is not the case. The acceleration upon going from ethanol to water amounts a factor 105 ( 10) for 2.4a versus 110 ( 11) for 2.4g. Apparently, the introduction of a hydrophilic group remote from the reaction centre has no effect on the aqueous acceleration of the Diels-Alder reaction. 

To the best of our knowledge the data in Table 3.2 constitute the first example of enantio selectivity in a chiral Lewis-acid catalysed organic transformation in aqueous solution. Note that for the majority of enantioselective Lewis-acid catalysed reactions, all traces of water have to be removed from the... 

In order to interpret the data in Table 5.1 in a quantitative fashion, we analysed the kinetics in terms of the pseudophase model (Figure 5.2). For the limiting cases of essentially complete binding of the dienophile to the micelle (5.If in SDS and 5.1g in CTAB solution) the following expression can be derived (see Appendix 5.2) ... 

Reference for the Gaussian 98 software used to generate the data in Table 15.3... 

A more unusual fact observed in thiazole chemistiy is that also the other positions (4 and 5) are activated toward the nucleophilic substitution, as found independently by Metzger and coworkers (46) and by Todesco and coworkers (30, 47). Some kinetic data are reported in Table V-2. As the data in Table V-2 indicate, no simple relationship between nucleophilic reactivity and charge density, or other parameters available from more or less sophisticated calculation methods, can be applied. As a... 

Which IS the stronger acid H2O or H2S Which is the stronger I base HO or HS Check your predictions against the data in Table 1 7 j... 

The thermocouple reference data in Tables 11.55 to 11.63 give the thermoelectric voltage in millivolts with the reference junction at 0°C. Note that the temperature for a given entry is obtained by adding the corresponding temperature in the top row to that in the left-hand column, regardless of whether the latter is positive or negative. 

One way to characterize the data in Table 4.1 is to assume that the masses of individual pennies are scattered around a central value that provides the best estimate of a penny s true mass. Two common ways to report this estimate of central tendency are the mean and the median. 

The range provides information about the total variability in the data set, but does not provide any information about the distribution of individual measurements. The range for the data in Table 4.1 is the difference between 3.198 g and 3.056 g thus... 

What are the standard deviation, the relative standard deviation, and the percent relative standard deviation for the data in Table 4.1 ... 

The data in Table 4.1 were obtained using a calibrated balance, certified by the manufacturer to have a tolerance of less than 0.002 g. Suppose the Treasury Department reports that the mass of a 1998 U.S. penny is approximately 2.5 g. Since the mass of every penny in Table 4.1 exceeds the reported mass by an amount significantly greater than the balance s tolerance, we can safely conclude that the error in this analysis is not due to equipment error. The actual source of the error is revealed later in this chapter. 

To evaluate the effect of indeterminate error on the data in Table 4.1, ten replicate determinations of the mass of a single penny were made, with results shown in Table 4.7. The standard deviation for the data in Table 4.1 is 0.051, and it is 0.0024 for the data in Table 4.7. The significantly better precision when determining the mass of a single penny suggests that the precision of this analysis is not limited by the balance used to measure mass, but is due to a significant variability in the masses of individual pennies. 

Consider, for example, the data in Table 4.1 for the mass of a penny. Reporting only the mean is insufficient because it fails to indicate the uncertainty in measuring a penny s mass. Including the standard deviation, or other measure of spread, provides the necessary information about the uncertainty in measuring mass. Nevertheless, the central tendency and spread together do not provide a definitive statement about a penny s true mass. If you are not convinced that this is true, ask yourself how obtaining the mass of an additional penny will change the mean and standard deviation. 

In most circumstances, populations are so large that it is not feasible to analyze every member of the population. This is certainly true for the population of circulating U.S. pennies. Instead, we select and analyze a limited subset, or sample, of the population. The data in Tables 4.1 and 4.10, for example, give results for two samples drawn at random from the larger population of all U.S. pennies currently in circulation. 

The data in Table 4.12 are best displayed as a histogram, in which the frequency of occurrence for equal intervals of data is plotted versus the midpoint of each interval. Table 4.13 and figure 4.8 show a frequency table and histogram for the data in Table 4.12. Note that the histogram was constructed such that the mean value for the data set is centered within its interval. In addition, a normal distribution curve using X and to estimate p, and is superimposed on the histogram. 

The difference between retaining a null hypothesis and proving the null hypothesis is important. To appreciate this point, let us return to our example on determining the mass of a penny. After looking at the data in Table 4.12, you might pose the following null and alternative hypotheses... 

A multiple-point standardization presents a more difficult problem. Consider the data in Table 5.1 for a multiple-point external standardization. What is the best estimate of the relationship between Smeas and Cs It is tempting to treat this data as five separate single-point standardizations, determining k for each standard and reporting the mean value. Despite its simplicity, this is not an appropriate way to treat a multiple-point standardization. 

How do we find the best estimate for the relationship between the measured signal and the concentration of analyte in a multiple-point standardization Figure 5.8 shows the data in Table 5.1 plotted as a normal calibration curve. Although the data appear to fall along a straight line, the actual calibration curve is not intuitively obvious. The process of mathematically determining the best equation for the calibration curve is called regression. 

Normal calibration curve for the hypothetical data in Table 5.1, showing the regression line. 

To calculate the standard deviation for the analyte s concentration, we must determine the values for y and E(x - x). The former is just the average signal for the standards used to construct the calibration curve. From the data in Table 5.1, we easily calculate that y is 30.385. Calculating E(x - x) looks formidable, but we can simplify the calculation by recognizing that this sum of squares term is simply the numerator in a standard deviation equation thus,... 

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