Ratios activity

Equation A2.4.126 shows that the EMF increases by 0.059/z V for each decade change in the activity ratio in the two solutions. 

Owing to the stability of the uranyl carbonate complex, uranium is universally present in seawater at an average concentration of ca. 3.2/rgL with a daughter/parent activity ratio U) of 1.14. " In particulate matter and bottom sediments that are roughly 1 x 10 " years old, the ratio should approach unity (secular equilibrium). The principal source of dissolved uranium to the ocean is from physicochemical weathering on the continents and subsequent transport by rivers. Potentially significant oceanic U sinks include anoxic basins, organic rich sediments, phosphorites and oceanic basalts, metalliferous sediments, carbonate sediments, and saltwater marshes. " ... 

The activities of two catalysts, C150-1-01 and another commercial catalyst, were compared (Table XVIII). Catalyst activity was determined (a) from the literature data using their kinetics, and (b) by Equation 5. Then the same procedure was followed for the C150-1-01 catalyst using typical data. The activity ratios are presented in Table XVIII. 

The best growth-PG activity ratio is thus obtained with this later concentration. 

The activity of CoSx-MoSx/NaY (2. IMo/SC) is shown in Fig.5 for the HYD of butadiene as a function of the Co/Mo atomic ratio. The HYD activity decreased slightly on the addition of Co up to Co/Mo = ca. 1, followed by a steep decrease at a further incorporation of Co. The HYD/HDS activity ratio decreased with increasing Co content and reached the ratio for CoSx/NaY at the Co/Mo atomic ratio of the maximum HDS activity (Fig.3). The product selectivity in the HYD of butadiene shifted from t-2-butene rich distribution to 1-butene rich one on the addition of Co, as presented in Fig.6. It is worthy of noting that at the Co/Mo ratio of the maximum HDS activity, the butene distribution is close to that for CoSx/NaY. It should be noted, however, that these product distributions are not the initial distributions of the HYD over the catalyst but the distributions modified by successive isomerization reactions. It was found that MoSx/NaY showed high isomerization activities of butenes even in the... 

Figure 5. HYD activity ( ) and HYD/HDS activity ratio ( ) of CoSx-MoSx/NaY (2.1 Mo/SC) as a function of the Co/Mo atomic ratio.

Historically, indicator electrodes have been metals which form a redox couple with the analyte, such as a Ag electrode for the determination of Ag", or a chemically inert metal which responds to the activity ratio of a soluble redox couple, such as a Pt electrode for Fe /Fe. Whereas simple indicator electrodes of this type perform well for the analysis of relatively pure samples, they are often subjwt to interferen< when apphed to complex samples such as those of biological origin. 

Fig. 2.3 was constructed using a K2-3 value at 250°C extrapolated from high-temperature data by Orville (1963), liyama (1965) and Hemley (1967). Ion activity coefficients were computed using the extended Debye-Hiickel equation of Helgeson (1969). The values of effective ionic radius were taken from Garrels and Christ (1965). In the calculation of ion activity coefficients, ionic strength is regarded as 0.5 im i ++mci-) (= mc -)- The activity ratio, an-f/aAb, is assumed to be unity. 

Fig. 2.11. The temperature dependence of cation/proton activity ratios of geothermal well discharges in Japan. The lines in the figure are recalculated temperature dependences of cation/proton ratios in Icelandic geothermal waters. The dashed curve in B represents the reaction 1.5 K-feldspar + H+ = 0.5 K-mica + 3 quartz (or chalcedony) + K+ (Chiba, 1991). Open circle Takigami, open triangle Kakkonda, open square Okuaizu, solid circle Kirishima, solid triangle Sumikawa, solid square Nigoiikawa.

This situation, when the activity of the higher atomic number nuclide, the parent, is equal to the activity in the next step in the chain, the daughter, is known as radioactive equilibrium (also referred to as secular equilibrium). Thus, secular equilibrium between a parent and a daughter implies an activity ratio of 1. 

Processes that fractionate nuclides within a chain produce parent-daughter disequilibrium the return to equilibrium then allows quantification of time. Because of the prescribed decay behavior, U-series disequilibria can be used for geochronology or for examining the rates and time scales of any dynamic processes which induces fractionation. In many cases, the direction of disequilibrium (activity ratios above or below one) provides a powerful means of tracing specific processes. 

One of the behaviors of the system not easy to grasp is why the return to equilibrium is mostly controlled by the half-life of the daughter nuclide This can be investigated by considering the Ra/ °Th system ( °Th decays to form Ra with a half-life of 1599 years). If fractionation by some process results in an activity ratio greater than 1 at time t = 0, the equation describing the return to equilibrium, as shown above, is ... 

If we now take into account the fact that since A,Ra A,xh, this equation can be rewritten using activity ratios as ... 

Figure 3. Parent daughter disequilibrium will return to equilibrium over a known time scale related to the half-life of the daughter nuclide. To return to within 5% of an activity ratio of 1 requires a time period equal to five times the half-life of the daughter nuclide. Because of the wide variety of half-lives within the U-decay-series, these systems can be used to constrain the time scales of processes from single years up to 1 Ma.

Figure 4. Return to secular equilibrium of activity ratio with no initial Ra. The return to...

In the introduction we asserted that it was important to use the correct partition coefficients when interpreting U-series data. Both the ratio of daughter and parent partition coefficients and their absolute values are important. Small errors in the ratio can propagate to quite large errors in predictions of activity ratios even when the source material is assumed to have a parent-daughter ratio of unity (i.e., in radioactive... 

N2)q and (N2/Ni)q represent the initial activity and activity ratio, respectively, just after the fractionation between parenf and daughter nuclides. 

Figure 1. (a) Schematic representation of the evolution by radioactive decay of the daughter-parent (N2/N1) activity ratio as a function of time t after an initial fractionation at time 0. The initial (N2/Ni)o activity ratio is arbitrarily set at 2. Time t is reported as t/T2, where T2 is the half-life of the daughter nuclide. Radioactive equilibrium is nearly reached after about 5 T2. (b) Evolution of (N2/N1) activity ratios for various parent-daughter pairs as a function of time since fractionation (after Williams 1987). Note that the different shape of the curves in (a) and (b) is a consequence of the logarithmic scale on the x axis in (b). 

Figure 2. ( °Th/ Th) vs. isochron diagram (parentheses denote activity ratios). In this...

Although precise ages generally cannot be deduced from U-series data on single silicate volcanic samples (because of the unknown initial value of the (N2/N1) activity ratio) it was nevertheless very significant to discover the ubiquity of °Th- U disequilibria (constraining the transfer time of the magmas to less than 350 ka), and later on... 

T = [(N2) - (N2)] / X2 [(N2) - (Ni)] or T = [(N2/Ni) -(N2/Ni)] / X2 [(N2/N1) - 1], where parentheses denote activities or activity ratios (note that (Ni) = (Ni) because of the long half-life of the parent nuclide and the absence of crystal fractionation). If the (N2/N1) ratio is known, then the residence time can be calculated from the measurement of the (N2/N1) ratio in lavas erupted from the central conduit. An eccentric eruption, whose magma has bypassed the reservoir, may provide a value for the (N2/N1) ratio. 

Time evolution of ( °Pb/ Ra)L activity ratios in the degassed lava can be drawn for... 

Figure 17. Time-evolution of ( °Pb/ Ra)L activity ratios in the degassed magma for different values of the magma chamber renewal rate ( )o/M (figures on curves). Curves are drawn from the equation (Gauthier and Condomines 1999) ...

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