Integral trace

FIGURE 6.1 Integration of an EPR spectrum. The EPR derivative spectrum of the hydrated copper ion (trace A) is numerically integrated to its EPR absorption spectrum (trace B) and a second time integrated (trace C) to obtain the area under the absorption spectrum. Note that both the derivative and the absorption spectrum start and end at zero, while the doubly integrated spectrum levels off to a constant value the second-integral value. 

FIGURE 10.14 The NMR spectrum of ethylbenzene with integration trace. 

What does the integrator trace in Figure 10.22 tell you about the number of the different kinds of hydrogen present in the structure ... 

After answering problem 34, describe what the integrator trace would look like on this spectrum. 

The integration trace shows that the three peaks are in the ratio 1 2 3, left to right. This is what is expected with ethyl alcohol since there are one of one kind of hydrogen, two of another, and three of another. For ethyl methyl ether, a ratio of 3 2 3 would be expected. 

The integrator trace would show that the singlet is due to one hydrogen, the septet due to one hydrogen, and the doublet due to six hydrogens. 

This is equal to the height of step of the integration trace. 

Fig. 3.3 Expansion of a H spectrum of peracetylatcd glucose with integral traces...

Chemical shift (ppm) Integral trace in mm Proton ratio Multiplicity Assignment Remarks... 

The integration step — i.e., the vertical distance between the horizontal lines of the integration trace — is proportional to the number of protons represented by the particular absorption peak or multiplet of peaks. These steps give ratios, not absolute numbers of protons. The ratios actually represent areas under the peaks. 

Neither an integral trace (shown in blue in Figure 13-19) nor a digital integral can specifically indicate that methyl ferf-butyl ether has three methyl hydrogens and nine f erf-butyl hydrogens. Each simply shows that about three times as many hydrogens are represented by the peak at 81.2 as are represented by the peak at S3.2. We must interpret what the 3 1 ratio means in terms of the structure. 

To measure the heights of the rises in the integral trace, use a ruler to measure the integrals in millimeters. 

Integrated proton NMR spectrum of methyl ferf-butyl ether. In going over a peak, the integrator trace (blue) rises by an amount that is proportional to the area under the peak. 

Figure 13-20 shows the integrated spectrum of a compound with molecular formula QH CF. Because we know the molecular formula, we can use the integral trace to determine exactly how many protons are responsible for each peak. The integrator has moved a total of 32.5 mm vertically in integrating the 12 protons in the molecule. Each proton is represented by... 

Draw the integral trace expected for the NMR spectrum of fcrf-butyl acetoacetate, shown in Figure 13-17. 

An examination of the relative areas of the NMR lines or multiplets (resolved or unresolved) is often the best starting point for the interpretation of the spectrum. If the total number of protons in the molecule is known, the total area can be equated to it, and the number of hydrogen atoms in each portion of the spectrum established. The opposite procedure of assigning the smallest area to one or two protons and comparing other areas with this one is sometimes helpful, but it should be used with caution because appreciable error can be introduced in this way. Occasionally, lines so broad that they are unobservable in the spectrum itself can be detected in the integral trace. 

Transport balance or box models have been used by many workers in the past in efforts to understand the trace element and isotope characteristics of the Earth s major silicate reservoirs, i.e. continental crust, and upper and lower mantle (e.g. Jacobsen Wasserburg 1979 Zartman Haines 1988). Although simple mass balance calculations can be applied to present-day trace element concentrations and Pb, Nd and Hf isotope compositions of major reservoirs, e.g. continental crust and depleted mantle, to test the hypothesis that these reservoirs are complementary, transport balance models are needed to test ideas on their evolution in time. The reason is that the isotope ratio variations are the result of time-integrated trace element variations in the reservoir, modified by fluxes between them. Below, recent transport balance models in which the evolution of the continental crust is examined using Th-U-Pb (Kramers T olstikhin 1997) and... 

Figure L I3C-NMR spectrum of shale oil vacuum distillate polar fraction aliphatic region, TMS reference, methanol internal standard and integration trace (upper curve).

As Fig. 11 shows, there is some variability in the integrated trace-element contents of cores from central Long Island Sound. These sediments are not located near intense sources of trace metals nor are there major grain-size differences. As we will show later, the differences in both metal concentrations and inventories can be related primarily to the intensity and depth of biological mixing of the sediment column. 

Gibbs-Duhem Integration Tracing Coexistence Lines A. Concept Formalism... 

We could probably derive a couple of possible structures at this point. The NMR spectrum should provide confirmation. Using the integral traces on the spectrum, we should conclude that the peaks shown have the ratio 2 2 3 3 (downfield to upheld). These numbers add up to the 10 total hydrogen atoms in the formula. Now, using the splitting patterns on the peaks, we can determine the structure of the compound. It is ethyl propanoate. 

Use the integral trace to determine the relative numbers of different types of protons. 

The low-resolution NMR spectrum of anhydrous ethanol, showing peaks and Integration trace... 

Analysis of the integration line in the H NMR spectrum of 1-bromo-2,2-dimethylpropane. The peak at 3.3 ppm has a smaller integral trace than the peak at 1.0 ppm because the peak at 3.3 ppm is produced by two methylene protons, whereas the peak at 1.0 ppm is produced by nine methyl protons. 

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