Carbonate system species concentration 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. 

Several computer-based techniques have been developed for more specific applications. Truesdell (45) describes a computer program for calculating equilibrium distributions in natural water systems, given concentrations and pH. Edwards, et al. (31, Z2) have developed computer programs for treating volatile weak electrolytes such as ammonia, carbon dioxide and hydrogen sulfide systems however, in their present state these programs (presumably) do not accommodate metallic species in solutions. 

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 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. 

Calculation of Carbonate Species Concentrations in Open and Closed Systems... 

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. 

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. 

The values predicted by the equilibrium calculations can be compared with exhaust concentrations observed in practical combustion systems. The major species (i.e., CO2, H2O, and O2) are well predicted by thermal equilibrium. In most of the temperature range covered in the figure, the fuel is fully oxidized. The fast chemistry assumption would also be sufficient to predict the exhaust concentrations of these species. The problem arises if the chemical equilibrium assumption is also used to estimate the concentration level of minor species, such as carbon monoxide, nitrogen oxides, and sulfur oxides. 

The concentration of any of these species depends on the total concentration of dissolved aluminum and on the pH, and this makes the system complex from the mathematical point of view and consequently, difficult to solve. To simplify the calculations, mass balances were applied only to a unique aluminum species (the total dissolved aluminum, TDA, instead of the several species considered) and to hydroxyl and protons. For each time step (of the differential equations-solving method), the different aluminum species and the resulting proton and hydroxyl concentration in each zone were recalculated using a pseudoequilibrium approach. To do this, the equilibrium equations (4.64)-(4.71), and the charge (4.72), the aluminum (4.73), and inorganic carbon (IC) balances (4.74) were considered in each zone (anodic, cathodic, and chemical), and a nonlinear iterative procedure (based on an optimization method) was applied to satisfy simultaneously all the equilibrium constants. In these equations (4.64)-(4.74), subindex z stands for the three zones in which the electrochemical reactor is divided (anodic, cathodic, and chemical). 

Carbonate Complexes. Of the many ligands which are known to complex plutonium, only those of primary environmental concern, that is, carbonate, sulfate, fluoride, chloride, nitrate, phosphate, citrate, tributyl phosphate (TBP), and ethylenediaminetet-raacetic acid (EDTA), will be discussed. Of these, none is more important in natural systems than carbonate, but data on its reactions with plutonium are meager, primarily because of competitive hydrolysis at the low acidities that must be used. No stability constants have been published on the carbonate complexes of plutonium(III) and plutonyl(V), and the data for the plutoni-um(IV) species are not credible. Results from studies on the solubility of plutonium(IV) oxalate in K2CO3 solutions of various concentrations have been interpreted to indicate the existence of complexes as high as Pu(C03) , a species that is most unlikely from both electrostatic and steric considerations. From the influence of K2CO3 concentration on the solubility of PuCOH) at an ionic strength of 10 M, the stability constant of the complex Pu(C03) was calculated (10) to be 9.1 X 10 at 20°. This value... 

In this sense we have already described in Chapters 4 and 7 the equilibrium of the CaC03(s)-H20-C02 system. Specifically, we have used equilibrium models to characterize the concentrations of the carbonate species as a function of pco2 and of pH. We have already shown (Example 7.8) that CaCOj in surface seawater is oversaturated and we calculated in Example 4.10 how the composition of seawater changes as a result of increasing the CO2 concentration in the atmosphere. 

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