## 4 Discussion  
### Quantitation of JCS  
As satisfactory fits and reasonable NMR parameters were obtained, we could investigate trends in the experimental spectra and NMR parameters. First, as the ratio of H-F changed, the relative peak intensities at each Larmor frequency also changed. This was qualitatively described by the scaling factor used for each spectrum (see Figures 3 and 4). For a majority of samples, the number of H was greater than the number of F per molecule and the \({}^{19}\)F regions of the spectra were scaled. As the number of F increased, the scaling factor for F decreased from \(\approx\)31 for monofluorobenzene to 2.37 for 1,2,4-trifluorobenzene. In a similar manner, the \({}^{1}\)H spectra were scaled when the number of empirical F surpassed the number of empirical H. The \({}^{1}\)H scaling factor increased from 2.39 to 12.67 as the number of H decreased from 2 to 1. While a qualitative assessment of the empirical formula may be derived from the scaling factors, a more quantitative assessment may be made _via_ peak area integration for \({}^{19}\)F and \({}^{1}\)H. The total integrated area of each nucleus corresponds to the relative ratios of \({}^{1}\)H-\({}^{19}\)F. The integrated areas are given in Table 4 for both the experimental and the simulated spectra. As expected, as the relative amount of \({}^{19}\)F increased in the molecule, the \({}^{1}\)H-\({}^{19}\)F ratio decreased. The three difluorobenzene compounds serve as a model system for comparison, since the splitting patterns of each spectra are unique, but the empirical formulas remains the same. The scaling factors from Figure 4 gave the false appearance of three drastically different \({}^{1}\)H-\({}^{19}\)F ratios. Furthermore, the scaling factor for 1,4-difluorobenzene (2.37) was similar to the scaling factor for 1,2,4-trifluorobenzene (2.85). However, integration of the difluorobenzene peak areas resulted in similar \({}^{1}\)H-\({}^{19}\)F ratios, which were substantially different from the \({}^{1}\)H-\({}^{19}\)F ratios of all the other compounds (Table 4). Despite the consistency, relatively large errors were observed from peak integration, even when using simulated spectra that were free from noise and lacked tuned detection circuit scaling of the resonances (Table 4). This was because the \({}^{19}\)F and \({}^{1}\)H were collected simultaneously, at the same field, and require a receptivity correction. Constant field receptivity (\(\Xi\)) is defined as  
\[\Xi=\chi\gamma^{3}I(I+1) \tag{5}\]  
where \(\chi\) is the natural abundance of the NMR active nuclei [59]. If \({}^{19}\)F and \({}^{1}\)H are both 100% abundant and \(I=\) 1/2, then \(\Xi\) of the nuclei depends solely on the \(\gamma^{3}\) term. Therefore, the observed \({}^{19}\)F area will be 83.3% of the observed \({}^{1}\)H area. Normalizing the peak areas for receptivity and comparing the \({}^{1}\)H-\({}^{19}\)F peak ratios yielded results that were within 22% of the correct stoichiometry (Table 4). Thus, pseudo-empirical formulas may be obtained from quantitation of JCS. Normalization by the receptivity was a considerable improvement; however, even for simulated spectra there was a 4%-7% error. This error may originate from truncation of the FID when compounds have different relaxation times. Since most of the compounds were simulated with the same relaxation rates for \({}^{19}\)F and \({}^{1}\)H (Table 1), other factors may have affected quantitation at LF, and this will be more thoroughly investigated in future work. Additionally, other errors associated with the experimental data may have arisen from errors introduced during processing (phasing and baseline correction), from noise during data acquisition, and from incomplete thermal polarization between scans.