Isotopes linear relationship

This equation shows that on a plot of (N2/Ni)g versus e , the volcanics erupted from this reservoir should define a straight line whose y intercept (at e = 0, i.e., in the future at 0 = -00) is 1 (radioactive equilibrium, cf Fig. 3). A linear relationship is also obtained if isotope ratios, like ( °Th7 Th)e, are reported versus e (see Fig. 11 in Condomines et al. 1988). This latter diagram is similar to the well known isotope... 

It was shown quite early (Gamier et al., 1971) and confirmed later (Ruasse and Motallebi, 1988), from solvent isotope effects (kMeoH/ mcod) on the rates of 1-pentene bromination and from a linear relationship (53) between these... 

The linear relationship of the isotope ratios of hydrogen and oxygen with a slope of 8 in rain and snow was discovered by Craig [74] to be... 

The importance of oxygen and hydrogen isotope ratios in the water cycle was first demonstrated by Dansgaard (1964), who showed that a simple linear relationship exists between < 180 in precipitation and the average annual air temperature. Through the isotopic analysis of a large number of meteoric water samples (rainfall and surface water) collected at different latitudes, Craig (1961) had previously demonstrated that a simple relationship existed between <5180 and < D in precipitation ... 

Extreme values of concentrations occur for the fraction on the right-hand side being equal to 0 (pure contaminant melt) and 1 (no contamination). These relationships show a fairly simple behavior of the AFC model the isotopic ratio (Ci2/Cil)liq should be linearly correlated with the inverse of the element concentration Cm,11, a property which it shares with all bulk mixing models. Such a linear relationship, initially suggested by Briqueu and Lancelot (1979) from the evidence of a numerical solution, was demonstrated by Fleck and Criss (1985) and Taylor and Sheppard (1986). The present analytical solution will help the reader to work out tests on geological cases. 

Figure 5A shows experimentally derived profiles of pH vs rate for reactions in H2O and D2O [30, 50, 71]. The magnitude of the apparent isotope effect (ratio of rate constants in H2O and D2O) is 4.4 and the profiles appear to support the possibility that a proton is transferred from (Mg -bound) water molecules. However, careful analysis led us to conclude that a metal ion binds directly to the 5 -oxygen. Since the concentration of the deproto-nated 2 -oxygen in H2O should be higher than that in D2O at a fixed pH, we must take into account this difference in pKa, namely ApKa (=pKa °-pKa ), when we analyze the solvent isotope effect of D2O [30, 50, 68, 71]. We can estimate the pKa in D2O from the pKa in H2O using the linear relationship shown in Fig. 5B [30, 68, 73-75]. If the pKa for a Mg -bound water molecule in H2O is 11.4, the ApKa is calculated to be 0.65 (solid line in Fig. 5B). Then, the pKa in D2O should be 12.0. Demonstrating the absence of an intrinsic isotope effect (kH2o/kD20=l)> the resultant theoretical curves closely fit the experimental data, with an approximate 4-fold difference in...

Another factor that is of great importance for the observed sulfur isotope variations of natural sulfides is whether sulfate reduction takes place in an open or closed system. An open system has an infinite reservoir of sulfate in which continuous removal from the source produces no detectable loss of material. Typical examples are the Black Sea and local oceanic deeps. In such cases, H2S is extremely depleted in " S while consumption and change in " S remain negligible for the sulfate. In a closed system, the preferential loss of the lighter isotope from the reservoir has a feedback on the isotopic composition of the unreacted source material. The changes in the " S-content of residual sulfate and of the H2S are modeled in Fig. 2.21, which shows that 5 S-values of the residual sulfate steadily increase with sulfate consumption (a linear relationship on the log-normal plot). The curve for the derivative H2S is parallel to the sulfate curve at a distance which depends on the magnitude of... 

A compilation of studies throughout the world s mountain belts has revealed a consistent and linear relationship between change in the isotopic composition of precipitation and change in elevation (Poage and Chamberlain 2001). The isotopic composition of precipitation decreases linearly with increasing elevation by about 0.28%c/100 m in most regions of the world except in the Himalayas and at elevations above 5,000 m. 

However, Ichikawa et al. [12] found a linear relationship between Tc and Ro-o, which is common to several KDP-type crystals, irrespective of whether they are deuterated or not. This finding suggests that the difference in Ro-o between KDP and DKDP (J o-o = 2.50 A for KDP and Rq-q = 2.52 A for DKDP at room temperature [10]) or the geometric isotope effect, rather than the difference in tunneling frequencies, causes the isotope effect on Tc. 

Later on, the role of each effect was examined more precisely by high-pressure neutron diffraction measurements on KDP and DKDP [13,14]. The linear relationship between Tc and Rq-q was confirmed in both KDP and DKDP for Tc > 50 K and the same slope dTc/dJ o-o was found in both crystals. However, the line in DKDP was found to be shifted from the line in KDP by about 40 K toward higher values. This result indicates that only part of 40 K 37%) of the whole isotope effect - Tf = 107 K) is caused by... 

A graphical examination of the data for meta substitution in toluene is presented as Fig. 8. The deviations from a precise linear relationship are larger than for the reactions at the para position of toluene. As for para substitution, the largest discrepancies are detected for the nitration and isotopic exchange reactions, indicated in Fig. 8 by broken circles. 

The poorly variable isotopic composition of the Lentia rocks favours a derivation of rhyolites from mafic-intermediate parents by dominant fractional crystallisation. However, there are linear relationships for many inter-element variations, which suggest mixing between acid and mafic magmas (De Astis et al. 1997). 

Only Pj is negligible (labeled IS with a sufficient mass increment to avoid interference of naturally abundant isotopes on its measuring channel). Under these circumstances, a linear relationship will be obtained also ... 

Because the phosphonate-phosphate rearrangement requires P-C bond breakage and formation of the P-O bond kinetic isotope studies by means of 13C NMR were chosen.50 13C KIEs were derived from NMR analysis of substrate-o-nitro-benzaldehyde or product-phosphate. Samples of aldehyde were prepared using the dead-end method. To the solution of phosphite 3 and triethylamine in acetonitrile an excess of aldehyde was added and solution was heated at 65°C to complete conversion of phosphonate 4 to phosphate 5 monitored by 31P NMR. The aldehyde conversions 0.2-0.8 were calculated from the balance of concentrations. The changes of 13C composition were determined for carbonyl carbon atom using signal of meta aryl carbon as an internal standard. KIE 1.0223(14) was calculated from the slope of linear relationship of isotopic ratio R and fraction of reaction,... 

Presumably less nucleophilically assisted solvolyses could show higher a-deuterium isotope effects, and there is a linear relationship between the magnitude of nucleophilic solvent assistance (Table 2) and the a-deuterium isotope effect for solvolyses of 2-propyl sulpho-nates (Fig. 7). Another measure of nucleophilic assistance is the ratio k2 (OH )/, where k2 is the second-order rate constant for nucleophilic attack by OH and kx is the first-order rate constant for reaction with the solvent water, and a linear correlation was obtained by plotting the ratio versus the experimentally observed isotope effects for methyl and trideuteriomethyl sulphonates, chlorides, bromides and iodides (Hartman and Robertson, 1960). Using fractionation factors the latter correlation may also be explained by a leaving group effect on initial state vibrational frequencies (Hartshorn and Shiner, 1972), but there seems to be no sound evidence to support the view that Sn2 reactions must give a-deuterium isotope effects of 1-06 or less. 

The positive one-bond isotope effects on nitrogen are larger for the Z isomer than for the E isomer, also due to intramolecular hydrogen bonding. A linear relationship has been found between 2AC(ND) and SH of NH for both E and Z isomers. The Z isomers show the narrower 15N resonances (line-widths) also as a result of hydrogen bonding. 

At temperatures higher than 100 °C, In wl-v does not show a linear relationship with 1/T however, the logarithm of the oxygen isotope fractionation factor, lna L-v( 0), does show a linear relationship with 1/T, up to the critical temperature. 

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