Isotopic balance equation

This section considers the scalar and isotopic balance equations in general, with attention to the source terms for scalars and isotopes which arise in vegetation canopies. After general principles are set out in Section 2.1, the Eulerian framework is described in Section... 

In the case of equivalent exchangeable oxygen atoms (Ne), the time dependence of the gas phase isotopic fraction, a(t), is well described by an exponential function. By using the isotope balance equation 2Na +N al = 2Na + N OC = (2N(where is the initial value of, y-isotope fraction at equilibrimn), the variable as can be excluded from... 

TPIE experiments also allow a semi-quantitative characterisation of the oxygen mobility. Thus, the depth of isotope penetration from the gas phase into the oxide in the course of TPIE can be characterized by the value Nx determined by the isotope balance equation in the closed system ... 

If no KIE is present, the contribution of the derivative atom to the measured 8 value of the derivatised compound can be calculated using a simple mass balance equation (14.2), where n is number of moles of the isotope of interest, F is the fractional abundance of the isotope of interest, c refers to the compound of interest, d refers to the derivative group and... 

Bowers and Taylor (1985) were the first to incorporate isotope fractionation into a reaction model. They used a modified version of EQ3/EQ6 (Wolery, 1979) to study the convection of hydrothermal fluids through the oceanic crust, along midocean ridges. Their calculation method is based on evaluating mass balance equations, as described in this chapter. 

Lee and Bethke (1996) presented an alternative technique, also based on mass balance equations, in which the reaction modeler can segregate minerals from isotopic exchange. By segregating the minerals, the model traces the effects of the isotope fractionation that would result from dissolution and precipitation reactions alone. Not unexpectedly, segregated models differ broadly in their results from reaction models that assume isotopic equilibrium. 

Integrating isotope fractionation into the reaction path calculation is a matter of applying the mass balance equations while tracing over the course of the reaction path the system s total isotopic composition. Much of the effort in programming an isotope model consists of devising a careful accounting of the mass of each isotope. 

Once we have computed the total isotopic compositions, we calculate the compositions of the reference species using the mass balance equations (Eqns. 19.13, 19.20, 19.21, 19.22). We can then use the isotopic compositions of the reference species to calculate the compositions of the other species (Eqns. 19.10, 19.14, 19.15, 19.16) and the unsegregated minerals (Eqns. 19.11,19.17,19.18, 19.19). 

The combined effects of a +2.9%o equilibrium fractionation between Fe(III)aq and Fe(II)jq, and a +2.0%o fractionation between Fe(Ill)aq and ferrihydrite upon precipitation is illustrated in Figure 10. Although a k ki ratio of 5 appears to fit the fractionations measured by Bullen et al. (2001) (Fig. 10), we note that at these relatively low kjk ratios. Equation (16) cannot be used, but instead the calculations are made using an incremental approach and simple isotope mass-balance equations (e.g., Eqn. 12). As the kjki ratio increases to 20, Equation (16) may... 

The first attempts to quantify isotope exchange processes between water and rocks were made by Taylor (1974). By using a simple closed-system material balance equation these authors were able to calculate cumulative fluid/rock ratios. 

As the number of equations needed for isotope balances is large, it is important to use a condensed notation to describe the carbon transitions in a reaction. In the case of isotope balancing based on fractional enrichments, the balances can be expressed using so-called atom-mapping matrices [17]. The principle of using atom-mapping matrices is illustrated by considering an example where the carbon transitions in the first reactions in the Krebs cycle are shown (Fig. 3). 

When a diet consists of two isotopically distinct food sources for which the 6 C values are known, it becomes possible to estimate the relative proportions of each by applying an isotopic mass balance equation ... 

The calculation of past CO2 levels using GEOCARB begins with the iterative solution of equations (11) and (12) and a parallel mass balance equation for carbon isotopes to yield fluxes that are consistent with the carbonate... 

You need to be familiar with the use of exponential numbers in calculations and how to use your calculator. You should know how to calculate relative formula masses and be familiar with isotopes and the meaning of isotopic composition. You should also know how to balance equations. 

Boron is used in control rods in nuclear power reactors because it is a good neutron absorber. When the isotope °B captures a neutron, an alpha particle (helium nucleus) is emitted. What other atom is formed Write a balanced equation. 

The radioactive potassium-40 isotope decays to argon-40 with a half-life of 1.2 X 10 yr. (a) Write a balanced equation for the reaction, (b) A sample of moon rock is found to contain 18 percent potassium-40 and 82 percent argon by mass. Calculate the age of the rock in years. 

A nuclear equation can be used to represent the process of radioactive decay. In radioactive decay an isotope breaks down, producing a new isotope, smaller particles, andjor energy. The concept of mass balance, required when writing chemical equations, is also essential for nuclear equations. When writing a balanced equation, remember that ... 

Consider the decay of one isotope of uranium, 9 U, into thorium and an alpha particle. Because an alpha particle is lost in this process, this decay is called alpha decay. Examine the balanced equation for this nuclear reaction ... 

Seaborgium-263 (Sg Z = 106) was the first isotope of this element synthesized. It was made, together with four neutrons, by bombarding californium-249 with oxygen-18. It then decayed by three a emissions. Write balanced equations for the synthesis and three decay steps of " Sg. 

The mass balance equation for stable isotope transport... 

The change of mass (or moles) of oxygen isotope within the small cube with volume dV can alternatively be calculated from the change of mass, dm, of the system. Mass gain or loss of can be calculated by multiplying the concentration of by the volume of the system, dV. Hence we obtain for the basic mass balance equation ... 

Note that the concentration gain of an isotope in the system is equal to the negative of the change in flux of this isotope. The dV terms can be dropped to yield the basic mass balance equation for stable isotope transport (or any other element) ... 

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