Carbonate system species calculation

The alkalinity and DIC data were used to calculate the carbonate ion concentration and pH of the culture medium during the second half of the first experiment, and throughout the second experiment (Fig. 3). These calculations used the program C02SYS (Lewis Wallace 1998) with the carbonate dissociation constants of Roy et al. (1993), the calcite solubility of Mucci (1983), and the assumption that the boron/salinity ratio of the culture system water was equal to the seawater ratio. Because much of the culture system water in both years was Instant Ocean, it may not be correct to estimate the total borate concentration from the whole-ocean boron/salinity relationship. However, trends in the concentrations of carbonate system species during each year will be independent of the actual absolute total borate concentration. 

In this chapter I explained how isotope ratios may be calculated from equations that are closely related, but not identical, to the equations for the bulk species. Extra terms arise in the isotope equations because isotopic composition is most conveniently expressed in terms of ratios of concentrations. I illustrated the use of these equations in a calculation of the carbon isotopic composition of atmosphere, surface ocean, and deep ocean and in the response of isotope ratios to the combustion of fossil fuels. As an alternative application, I simulated the response of the carbon system in an evaporating lagoon to seasonal changes in biological productivity, temperature, and evaporation rate. With a simulation like the one presented here it is quite easy to explore the effects of various perturbations. Although not done here, it would be easy also to examine the sensitivity of the results to such parameters as water depth and salinity. 

Like the climate system of Chapter 7, this system yields nonzero elements of the sleq array only close to the diagonal. Much computation can be eliminated by modifying the solution subroutines, SLOPER and GAUSS. I presented the modified subroutines SLOPERND and GAUSSND, which differ from the equivalent routines of Chapter 7 in that they can accommodate an arbitrary number of interacting species. To illustrate how the computational method can be applied to more species, I added to the system a calculation of the stable carbon isotope ratio, solving finally for the three... 

The relative proportions of the different carbonic acid system species can be calculated using equilibrium constants. If thermodynamic constants are used, activities must be employed instead of concentrations. The activity of the ith dissolved species (a,) is related to its concentration (mj) by an activity coefficient... 

The rebound mechanism, though in a modified version, has been recently supported by theoretical calculations of KIF using the density functional theory (Yoshizawa et al., 2000). The calculations demonstrate that the transition state for the H-atom abstraction from ethane involves a linear [FeO.H...C] array a resultant radical species with a spin density of nearly one is bound to an iron-hydroxy complex, followed by recombination and release of product ethanol. According to the calculation of the reaction energy profile, the carbon radical species is not a stable reaction intermediate with a finite lifetime. The calculated KIF at 300 K is in the range of 7-13 in accord with experimental data and is predicted to be significantly dependent on temperature and substituents. It was also shown from femtosecond dynamic calculations in the FeOVCH4 system that the direct abstraction mechanism can occur in 100-200 fs. 

The dissolved carbonate system can be described by a number of parameters. Most geochemical models require the pH, which indicates the distribution among the carbonate species, and either the total dissolved carbonate content, the total alkalinity, or the concentrations of bicarbonate and carbonate to indicate the amount of carbonate present. From these data, models calculate the concentrations and thermodynamic activities of the various dissolved carbonate species. The total dissolved carbonate content is the sum of these concentrations. The activity of the carbonate ion is used in calculating the saturation indices of carbonate minerals. 

The relationship between alkalinity, Ct.coj and pH has been used by Deffeyes to construct a diagram relating alkalinity toCi-.coa cil a series of constant pH values. This diagram, shown in Fig. 4-21, can be used for a wide variety of calculations involving the addition and removal of various species from the carbonate system. 

The system evaporates UC2(g) as well as a small amount of UC4(g). Since the UC2(g)/U,g) pressure ratio is proportional to the carbon activity squared. Storms (1966a) was able to determine the carbon activity directly by measuring this ratio at various temperatures and compositions. Thus, the carbon activity was obtained without measuring any pure carbon specie. The result is compared to the uranium activity in Fig. 69 and Table 74. A curve for the carbon activity was calculated by a Gibbs-Duhem integration of the uranium activity curve and the result is compared to the direct measurements in the figure. 

These reactions are believed to proceed through a complex of the alkene with a singlet excited state of the aromatic compound (an exciplex). The alkene and aromatic ring are presumed to be oriented in such a manner that the alkene n system reacts with p orbitals on 1,3-carbons of the aromatic. The structure of the excited-state species has been probed in more detail using CAS-SCF ab initio calculations. ... 

The complexation of Pu(IV) with carbonate ions is investigated by solubility measurements of 238Pu02 in neutral to alkaline solutions containing sodium carbonate and bicarbonate. The total concentration of carbonate ions and pH are varied at the constant ionic strength (I = 1.0), in which the initial pH values are adjusted by altering the ratio of carbonate to bicarbonate ions. The oxidation state of dissolved species in equilibrium solutions are determined by absorption spectrophotometry and differential pulse polarography. The most stable oxidation state of Pu in carbonate solutions is found to be Pu(IV), which is present as hydroxocarbonate or carbonate species. The formation constants of these complexes are calculated on the basis of solubility data which are determined to be a function of two variable parameters the carbonate concentration and pH. The hydrolysis reactions of Pu(IV) in the present experimental system assessed by using the literature data are taken into account for calculation of the carbonate complexation. 

E. L. Shock (1990) provides a different interpretation of these results he criticizes that the redox state of the reaction mixture was not checked in the Miller/Bada experiments. Shock also states that simple thermodynamic calculations show that the Miller/Bada theory does not stand up. To use terms like instability and decomposition is not correct when chemical compounds (here amino acids) are present in aqueous solution under extreme conditions and are aiming at a metastable equilibrium. Shock considers that oxidized and metastable carbon and nitrogen compounds are of greater importance in hydrothermal systems than are reduced compounds. In the interior of the Earth, CO2 and N2 are in stable redox equilibrium with substances such as amino acids and carboxylic acids, while reduced compounds such as CH4 and NH3 are not. The explanation lies in the oxidation state of the lithosphere. Shock considers the two mineral systems FMQ and PPM discussed above as particularly important for the system seawater/basalt rock. The FMQ system acts as a buffer in the oceanic crust. At depths of around 1.3 km, the PPM system probably becomes active, i.e., N2 and CO2 are the dominant species in stable equilibrium conditions at temperatures above 548 K. When the temperature of hydrothermal solutions falls (below about 548 K), they probably pass through a stability field in which CH4 and NII3 predominate. If kinetic factors block the achievement of equilibrium, metastable compounds such as alkanes, carboxylic acids, alkyl benzenes and amino acids are formed between 423 and 293 K. 

Copper may exist in particulate, colloidal, and dissolved forms in seawater. In the absence of organic ligands, or particulate and colloidal species, carbonate and hydroxide complexes account for more than 98% of the inorganic copper in seawater [285,286]. The Cu2+ concentration can be calculated if pH, ionic strength, and the necessary stability constants are known [215,265-267]. In most natural systems, the presence of organic materials and sorptive surfaces... 

Like the climate system described in Chapter 7, this diagenetic system consists of a chain of identical reservoirs that are coupled only to adjacent reservoirs. Elements of the sleq array are nonzero close to the diagonal only. Unnecessary work can be avoided and computational speed increased by limiting the calculation to the nonzero elements. The climate system, however, has only one dependent variable, temperature, to be calculated in each reservoir. The band of nonzero elements in the sleq array is only three elements wide, corresponding to the connection between temperatures in the reservoir being calculated and in the two adjacent reservoirs. The diagenetic system here contains two dependent variables, total dissolved carbon and calcium ions, in each reservoir. The species are coupled to one another in each reservoir by carbonate dissolution and its dependence on the saturation state. They also are coupled by diffusion to their own concentrations in adjacent reservoirs. The method of solution that I shall develop in this section can be applied to any number of interacting species in a one-dimensional chain of identical reservoirs. 

Now I shall show how the nearly diagonal system can easily be modified to incorporate additional interacting species. In this illustration I shall add the calculation of the stable carbon isotope ratio specified by 813C. All of the parameters that affect the concentrations of carbon and calcium are left as in program SEDS03, so that the concentrations remain those that were plotted in Section 8.4. I shall not repeat the plots of the concentrations but present just the results for the isotope ratio. 

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