Ratio data

Ratio data is continuous data that does not have zero as an arbitrary placeholder. The zero on this scale represents an actual absence of that characteristic. For example, zero accidents recorded for a period of time means no accident cases existed. Ratio data is the only scale in which magnitude between values on the scale exists. If one group had 10 accidents and the other five, then it is correct to say that the first group had twice as many accidents as the second. Examples of ratio data that the safety professional would use include any characteristics that are counted, such as the number of accidents, the number of days away from work, etc. 

The preceding section described a method of determining molecular formulas using data from high-resolution mass spectrometers. Another method of determining molecular formulas is to examine the relative intensities of the peaks due to the molecular ion and related ions that bear one or more 

SELECTED COMPARISONS OF MOLECULAR WEIGHTS AND PRECISE MASSES 

The example of ethane (C2H6) can illustrate the determination of a molecular formula from a comparison of the intensities of mass spectral peaks of the molecular ion and the ions bearing heavier isotopes. Ethane has a molecular weight of 30 when it contains the most common isotopes of carbon and hydrogen. Its molecular ion peak should appear at a position in the spectrum corresponding to miz = 30. Occasionally, however, a sample of ethane yields a molecule in which one of the carbon atoms is a heavy isotope of carbon, C. This molecule would appear in the mass spectrum at m/z = 31. The relative abundance of in nature is 1.08% of the atoms. In the tremendous number of molecules in a sample of ethane gas, one of the carbon atoms of ethane will turn out to be a atom 1.08% of the time. Since there are two carbon atoms in the molecule, an ethane with mass 31 will turn up (2 x 1.08) or 2.16% of the time. Thus, we would expect to observe a peak at mIz = 31 with an intensity of 2.16% of the molecular ion peak intensity at miz = 30. This mass 31 peak is called the Af + 1 peak since its mass is one unit higher than that of the molecular ion. You may notice that a particle of mass 31 could form in another manner. If a deuterium atom, H, replaced one of the hydrogen 

A peak that appears two mass units higher than the mass of the molecular ion peak is called the M + 2 peak. The intensity of the M + 2 peak of ethane is only 0.01% of the intensity of the molecular ion peak. The contribution due to two deuterium atoms replacing hydrogen atoms would be (0.016 x 0.016)/100 = 0.00000256%, a negligible amount. To assist in the determination of the ratios of molecular ion, M +, and M +2 peaks, Table 8.5 lists the natural abundances of some common elements and their isotopes. In this table, the relative abundances of the isotopes of each element are calculated by setting the abundances of the most common isotopes equal to 100. 

To demonstrate how the intensities of the M + 1 and M + 2 peaks provide a unique value for a given molecular formula, consider two molecules of mass 42, propene (CsHg) and diazomethane (CH2N2). For propene, the intensity of the M + 1 peak should be (3 x 1.08) -r (6 x 0.016) = 3.34%, and the intensity of the M h- 2 peak should be 0.05%. The natural abundance of isotopes of nitrogen is 0.38% of the abundance of atoms. In diazomethane, we expect the relative intensity of the M H-1 peak to be 1.08 h- (2 x 0.016) + (2 x 0.38) = 1.87% of the intensity of the molecular ion peak, and the intensity of the M h- 2 peak would be 0.01% of the intensity of the molecular ion peak. Table 8.6 summarizes these intensity ratios. It shows that the two molecules have nearly the same molecular weight, but the relative intensities of the M + 1 and M + 2 peaks that they yield are quite different. 

You may notice that a particle of mass 31 could form in another manner. If a deuterium atom, H, replaced one of the hydrogen atoms of ethane, the molecule would also have a mass of 31. The natural abundance of deuterium is only 0.016% of the abundance of atoms. The intensity of the M+ peak would be (6 x 0.016) or 0.096% of the intensity of the molecular ion peak, if we consider only contributions due to deuterium. When we add these contributions to those of we obtain the observed intensity of the M + 1 peak, which is 2.26% of the intensity of the molecular ion peak. 

NATURAL ABUNDANCES OF COMMON ELEMENTS AND THEIR ISOTOPES 

The formula for calculating the approximate intensity of the Af + 2 peak is as follows. 

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To demonstrate how the intensities of the Af + 1 and M + 2 peaks provide a unique value for a given molecular formula, consider two molecules of mass 42, propene (CsHe) and diazomethane 

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Fuel costs vaiy widely from one area to another because of the cost of the fuel itself and the cost of transportation. Any meaningful cost comparison between fuels requires current costs based on such factors as the amounts used at a particular geographical location, utilization efficiencies or energy-ratio data for the equipment involved, and the effects of Torm v ue. Although the costs given in Table 27-9 do not apply to specific locations, they give fuel-cost trends. 

Not including error correlations where significant (say >0.3) in isotope-ratio data tables ... 

Comparison of GCE model parameters with production ratio data from the literature Tq = 9.9 3.5 Gyr. The high uncertainty reflects the difficulties of estimating theoretically the production ratio of r-process elements, whose production sites are not well known. 

Fig. 1. Element ratio data for Galactic field stars (dots) compiled by Venn et al. (2004). [The open squares are stars in dSph galaxies.] The important point to notice here is the very small scatter in element abundances for Galactic field stars at any given [Fe/H] value, over 4dex in [Fe/H].

Coplen, T. B. (1996) New guidelines for reporting stable hydrogen, carbon, and oxygen isotope ratio data. Geochimica et Cosmochimica Acta 60, 3359. 

Hammers, W.E., Meurs, G.J., De Ligny, C.L. (1982) Correlations between liquid chromatographic capacity ratio data on Lichrosorb RP-18 and partition coefficients in the octanol-water system. J. Chromatogr. 247, 1-13. 

The ratio data were normalized by assuming that the highest ratio measured was i0Be/9Be — 10(In fact, the 9Be(n,y/0Be cross section is only known to 10%.) The diagonal line represents the response of a perfectly linear system, and the dashed horizontal line gives the present limit of sensitivity. 

Baxter, M.J. and Gale, N.H. (1998). Testing for multivariate normality via univariate tests a case study using lead isotope ratio data. Journal of Applied Statistics 25 671-683. 

Die-swell and draw-resonance ratio data for these polymers are presented in Table 13.2 and Table 13.3, respectively. According to these results, the influence of branching and molecular weight is significant. The extremely large increase in... 

TRIMEB/allene molar ratio. Data relative to the allene proton of llOa-f are summarized in Table 43. 

A test of the hypothesis that the linear trends in Figures 10-12 are due to mixing comes from comparisons with oxygen isotopes. It has been conventional wisdom that Mg does not correlate in detail with O excesses in primitive chondrite components, including CAIs. However, combining the new highly precise MC-ICPMS data with isotope ratio data for the... 

Figure 3.2 Burning rate and area ratio data from black powder propellant.

In the case of naphthalene, transitions to the two lowest excited states (again, often indicated with Lb and La) are two-photon forbidden, as in benzene. However, due to vibronic coupling, the Lb band is visible in the 2PA spectrum of naphthalene in the 575-650 nm region (see Fig. 5), while La gains intensity in the IPA spectrum and peaks around 275 nm [44-46], but is basically absent from the 2PA spectrum this is again in line with predictions based on the pseudoparity of the states. Polarization ratio data were used to aid the band assignment. A weak 0-0 peak of the Lb band can actually be seen in the 2PA spectrum (at 630.5 nm for naphthalene in cyclohexane [45] and at 631.8 nm in carbon tetrachloride [47]), probably because of local perturbation of the symmetry due to the solvent environment or other effects [44,45]. The 2PA... 

FIG. 4.12 Viscosity of dispersions of some nonspherical particles (a) intrinsic viscosity as a function of the axial ratio a/b for oblate and prolate ellipsoids of revolution according to the Simha theory (redrawn with permission of Hiemenz 1984) (b) experimental values of relative viscosity versus volume fraction for tobacco mosaic virus particles of different a/b ratios (data from M. A. Lauffer, J. Am. Chem. Soc., 66, 1188 (1944)). 

Based on the successful laboratory soil microcosm experiment, the most heavily contaminated soil was excavated from the surface (2 m) layerand treated ex situ. The soil was placed in an enclosed rectangular bed and its moisture content maintained at 15% (w/w). The soil was aerated with an agricultural spading machine. Surfactant, organic nutrients, and inorganic nutrients were applied to maintain an optimum C N P ratio (data not presented). The isolated microorganisms were inoculated into the soil as dilute suspensions on five separate occasions. 

The above empirical equation can be derived theoretically, and the deviation of the experimentally observed Ce isotope ratio data from Curve I illustrates the extent to which the tropospheric atmosphere is not instantly and uniformly mixed this enables us to follow the eastward movement of the nuclear debris around the world... 

It is concluded tentatively from these preliminary 210Bi/210Pb ratio data that tropospheric aerosols have a much shorter atmospheric residence time than is generally appreciated. If so, both natural aerosols and radioactive fallout observed at tropospheric levels will not be well mixed zonally but for the most part will be deposited within a few... 

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