Carbonate system equilibrium constants

In order to solve the equations and determine pH and the concentrations of the species that make up the alkalinity, the apparent equilibrium constants, F, must be accurately known. These constants have been evaluated and re-evaluated in seawater over the past 50 y. The pH scales and methods of measuring pH during these experiments have been different, and this has complicated comparisons of the data until recently, when many have been converted to a common scale. Equations for the best fit to carbonate system equilibrium constants as a function of temperature and salinity are presented by Luecker et al. (2000), DoE (1994) and Millero (1995) (see Appendix 4.2). 

The component reactions in eqn. (2) are very fast, and the system exists in equilibrium. Additional carbon dioxide entering the sea is thus quickly converted into anions, distributing carbon atoms between the dissolved gas phase, carbonate and bicarbonate ions. This storage capacity is clear when the apparent equilibrium constants for the two reactions in eqn. (2) are examined, namely... 

The other C=N systems included in Scheme 8.2 are more stable to aqueous hydrolysis than are the imines. For many of these compounds, the equilibrium constants for formation are high, even in aqueous solution. The additional stability can be attributed to the participation of the atom adjacent to the nitrogen in delocalized bonding. This resonance interaction tends to increase electron density at the sp carbon and reduces its reactivity toward nucleophiles. 

Dissolved inorganic carbon is present as three main species which are H2CO3, HCOs and CO. Analytically we have to approach the carbonate system through measurements of pH, total CO2 or DIC, alkalinity (Aik), and PcOj- In an open carbonate system there are six unknown species H", OH , PcOj/ H2CO3, HCOs, and CO . The four equilibrium constants connecting these species are K, Ki, Kh, and fCw. The values of these equilibrium constants vary with T, P, and S (Millero, 1995). To solve for the six rmknowns we need to measure two of the four analytical parameters (Stumm and Morgan, 1996). Direct measurement of Pco is the best approach, but if that is not possible then the most accurate and precise pair (Dickson, 1993) is Total CO2 by the coulometric method Johnson et al., 1993) and pH by the colorimetric method (Clayton et ah, 1995). 

The temperature experiment can be expected to show only the effects of the temperature dependence of the equilibrium constants in the carbonate system. Other possible consequences of changing temperature are not included in the simulation. Figure 6-7 shows little response by the calcium... 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

Equilibrium constants for formation of iron(III) complexes of several oxoanions, of phosphorus, arsenic, sulfur, and selenium, have been reported. The kinetics and mechanism of complex formation in the iron(III)-phosphate system in the presence of a large excess of iron(III) involve the formation of a tetranuclear complex, proposed to be [Fc4(P04)(0H)2(H20)i6]. The high stability of iron(III)-phosphate complexes has prompted suggestions that iron-containing mixed hydroxide or hydroxy-carbonate formulations be tested for treatment of hyperphosphatemia. " ... 

The formation of RSSR from RS and RS species is particularly relevant in the present context because it is the reverse of the electro-induced radical anion cleavage (equation 76). Actually, the formation of RSSR from reaction (79) is as well studied as the reaction between aryl carbon radicals and anionic nucleophiles, the fundamental step of the SrnI. Equilibrium constants in the range 10 -10 M for reaction (79) were determined for a number of alkyl-type systems in water, although the corresponding values for aryl-type systems are smaller. The rate constants... 

The mass-action equations have been written in the same form as those given by Marynowski et al. (6) so that the equilibrium constants can be used directly. (Should more accurate data become available, the equilibrium yields calculated here will require revision.) The fourth equation, which applies to the heterogeneous equilibrium between carbon and nitrogen, is included for completeness but is unnecessary for the general solution. It can be shown that when the total pressure of the system is F, the partial pressure of cyanogen radicals is given by the equation ... 

When the system is heterogeneous—i.e., the temperature and pressure are such that solid carbon exists in equilibrium with its vapor, the value of Pci is uniquely determined by the temperature and can be calculated directly from the equilibrium constant Ki. Hence in a heterogeneous system, the partial pressure of cyanogen radicals and of cyanogen depend only on the temperature... 

Literally hundreds of complex equilibria like this can be combined to model what happens to metals in aqueous systems. Numerous speciation models exist for this application that include all of the necessary equilibrium constants. Several of these models include surface complexation reactions that take place at the particle-water interface. Unlike the partitioning of hydrophobic organic contaminants into organic carbon, metals actually form ionic and covalent bonds with surface ligands such as sulfhydryl groups on metal sulfides and oxide groups on the hydrous oxides of manganese and iron. Metals also can be biotransformed to more toxic species (e.g., conversion of elemental mercury to methyl-mercury by anaerobic bacteria), less toxic species (oxidation of tributyl tin to elemental tin), or temporarily immobilized (e.g., via microbial reduction of sulfate to sulfide, which then precipitates as an insoluble metal sulfide mineral). 

The absorption rate of carbon dioxide increases in the presence of amines or ammonia. Therefore, the reaction kinetics of NH3 and C02 has been considered in the model equations, too. The rate constant as a function of the temperature has been determined according to Ref. 136. The coefficients for the calculation of the chemical equilibrium constants in this system of volatile weak electrolytes are taken from Ref. 137. 

Since thermodynamics deals with systems at equilibrium, time is not a thermodynamic coordinate. One can calculate, for example, that if benzene(equilibrium with hydrogen(g) and carbon(s) at 298.15 K, then there would be very little benzene present since the equilibrium constant for the formation of benzene is 1.67 x 10-22. The equilibrium constant for the formation of diamond(s) from carbon(s, graphite) at 298.15 K is 0.310 that is, graphite is more stable than diamond. As a final example, the equilibrium constant for the following reaction at 298.15 K is 2.24 x 10-37 ... 

When dissolved in a solvent, some solutes combine with the solvent to form solvated species. The two outstanding examples in aqueous solution are carbon dioxide to form COz(aq) (carbonic acid) and ammonia to form NH3(aq) (ammonium hydroxide). In many cases the equilibrium constant for the reaction is unknown or not known with sufficient accuracy for thermodynamic purposes. Conventions have been established for treating such systems thermodynamically. Here we discuss the carbon dioxide-water... 

The right-hand sides of Equations (3.3) and (3.11) imply consideration has been given of all the weak acids in saltwater. The ions of other compounds are taken into account through the dependence of equilibrium constants on salinity or chlorine content. The characteristic parameter of equilibrium in the carbonate system is a variable ... 

The partial pressure of C02 dissolved in surface waters is proportional to its concentration in the water and inversely proportional to its solubility. This dependence is established by solving the system of Equations (3.12) and (3.13), which describe the functioning of the ocean carbonate system. For the quantitative solution of this system we can use, for instance, the secant method. As a result, we obtain [C02] and P . Based on data on the temperature dependence of the equilibrium constants for the respective chemical reactions, we find ... 

Carbonate equilibria in an open system. What is the pH of water in equilibrium with atmospheric C02 gas To answer such a question involves a knowledge of acid-base chemistry, the use of Henry s Law constant for the solubility of carbon dioxide and the use of the ENE to calculate the proton concentration of the equilibrium solution. The details of the equilibrium constants used are detailed below. 

Kametani and co-workers (43, 44) have used 13C NMR to study the effect of C-1 substituents on the stereochemistry of the quinolizidine system in this group of alkaloids. In O-methylcapaurine (73), which has a methoxy group at C-l, the quinolizidine system was considered to be in the cis form. This conclusion was based on the upheld shift of C-6. Comparison of 73 with 71 and 72 revealed some interesting differences. C-5, C-6, C-8, and C-l3 were all shielded in the cis form of the 13-methyltetrahydroprotoberberines relative to the trans form but only C-6 and C-l3 were affected in 73. Carbon-14 in 73 was shifted upheld relative to 72 in a manner analogous to that found for C-l in compound 72, and this steric shielding is probably greater than any chemical shift change associated with cis-trans interconversion. C-5 and C-8 of 73 did not show any upheld shift as they did in the 13-methyl compounds. These results indicated a difference in the cis conformation of the two types of compounds and it has been proposed that this was caused by different cis-trans equilibrium. constants (28, 48). 

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... 

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