Carbonate equilibrium constant

The carbon-metal bonds of organolithium and organomagnesium compounds have appreciable carbamomc character Carbanions rank among the strongest bases that we 11 see m this text Their conjugate acids are hydrocarbons—very weak acids indeed The equilibrium constants for ionization of hydrocarbons are much smaller than the s for water and alcohols thus hydrocarbons have much larger pA s... 

The equilibrium constant for the overall reaction is related to an apparent equilibrium constant Ki for carbonic acid ionization by the expression... 

Thermodynamically, the formation of methane is favored at low temperatures. The equilibrium constant is 10 at 300 K and is 10 ° at 1000 K (113). High temperatures and catalysts ate needed to achieve appreciable rates of carbon gasification, however. This reaction was studied in the range 820—1020 K, and it was found that nickel catalysts speed the reaction by three to four orders of magnitude (114). The Hterature for the carbon-hydrogen reaction has been surveyed (115). 

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... 

When one of the elements is solid, as in tire case of carbon in the calculation of the partial pressures of tire gaseous species in the reaction between methane and air, CO(g) can be used as a basic element together widr hydrogen and oxygen molecules, and thus the calculation of the final partial pressure of methane must be evaluated using the equilibrium constant for CH4 formation... 

The magnitude of the anomeric effect depends on the nature of the substituent and decreases with increasing dielectric constant of the medium. The effect of the substituent can be seen by comparing the related 2-chloro- and 2-methoxy-substituted tetrahydropy-rans in entries 2 apd 3. The 2-chloro compound exhibits a significantly greater preference for the axial orientation than the 2-methoxy compound. Entry 3 also provides data relative to the effect of solvent polarity it is observed that the equilibrium constant is larger in carbon tetrachloride (e = 2.2) than in acetonitrile (e = 37.5). 

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. 

Figure 4-4. Vapor-solid equilibrium constants o) for carbon dioxide, b) for hydrogen sulfide. (From Gas Processors Suppliers Association, Bngineerinq Data Book, 10th Edition.)...

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

Unfortunately, hemoglobin forms a complex with carbon monoxide that is considerably more stable than oxyhemoglobin. The equilibrium constant for the reaction... 

Changes in free energy and the equilibrium constants for Reactions 1, 2, 3, and 4 are quite sensitive to temperature (Figures 2 and 3). These equilibrium constants were used to calculate the composition of the exit gas from the methanator by solving the coupled equilibrium relationships of Reactions 1 and 2 and mass conservation relationships by a Newton-Raphson technique it was assumed that carbon was not formed. Features of the computer program used were as follows (a) any pressure and temperature may be specified (b) an inert gas may be present (c) after... 

Reactions 1 and 3 are highly exothermic and therefore have equilibrium constants that decrease rapidly with temperature. Reaction 2 is moderately exothermic, and consequently its equilibrium constant shows a moderate decrease with temperature. Reaction 4 is moderately endothermic, and its equilibrium constant increases with increasing temperature. The relationship between temperature and equilibrium constant for these four reactions is depicted in Figure 1 where carbon is assumed to be graphite. Thermodynamic data were taken from Refs. 1 and 2. 

Whatever the exact form of carbon deposition may be, it must be recognized and taken into account in future calculations. The deposited material is called Dent carbon, and equilibrium constants based on its free energy are included in Figure 1. The deposition of carbon as Dent carbon was confirmed qualitatively by Pursley et al. (4). In other recently reported equilibrium calculations (5, 6, 7), it was assumed that... 

From these numbers, a large number of calculations of technical interest can be made. Further, if we divide the equilibrium constant of carbon dioxide by that of steam we obtain the equilibrium constant of the water-gas equilibrium ... 

Up to this point, we have focused on aqueous equilibria involving proton transfer. Now we apply the same principles to the equilibrium that exists between a solid salt and its dissolved ions in a saturated solution. We can use the equilibrium constant for the dissolution of a substance to predict the solubility of a salt and to control precipitate formation. These methods are used in the laboratory to separate and analyze mixtures of salts. They also have important practical applications in municipal wastewater treatment, the extraction of minerals from seawater, the formation and loss of bones and teeth, and the global carbon cycle. 

The stable 2-norbornyl cation has recently been shown to be a non-classical, unusually stabilized species. Olah et al. (1970) proved spectroscopically that this ion is a comer-protonated nortricyclene with a pentavalent carbon atom. The value for the carbonylation-decarbonyla-tion equilibrium constant K (= of the 2-norbomyl ion illustrates... 

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). 

Fig. 11-7 Distribution of dissolved carbon species in seawater as a function of pH. Average oceanic pH is about 8.2. The distribution is calculated for a temperature of 15°C and a salinity of 35%o. The equilibrium constants are from Mehrbach et al. (1973).

Alcohols are heterolysed into carbocations and water in the presence of the hydronium ion (6). From the equilibrium constant the free energy of heterolytic dissociation of the carbon-oxygen a bond, AGSe,(ROH + H30+), can be calculated. The AG°het(ROH + H3O+) value is related to the pi R+ of the carbocation by (26). 

This proton transfer reaction involves the second acidic hydrogen atom of carbonic acid, so the appropriate equilibrium constant is. a 2 > whose p is found in Appendix E p. a 2 — 10.33. Because this is a buffer solution, we apply the buffer equation ... 

The analysis can be made quantitative by writing the various equilibria and their values. The reactions can be added to obtain the net reaction that occurs when calcium carbonate is exposed to acidic water, and the equilibrium constant for the net reaction is the product of the individual. S eq values ... 

The equilibrium constant expression derived for calcium carbonate dissolving in acidic solution is a general one... 

Carbon dioxide fugacity fcOi- CO2 fugacity (/coa) of ore fluids is estimated based on CO2 concentration of fluid inclusions analyzed. By using equilibrium constant of the reaction, C02(g) + H2O = H2CO3, and assuming uh20 to be unity, /CO2 can be estimated. 

In this chapter, the definitions used by Perrin in his book on pA a prediction (which also includes a very convenient compilation of o values) will be used. One must be alert to the importance of the number of hydrogens directly attached to the carbonyl carbon several groups have pointed out that aldehydes and ketones give separate but parallel lines, with formaldehyde displaced by the same amount again. What this means is that given one equilibrium constant for an aldehyde (or ketone) one may estimate the equilibrium constant for other aldehydes (or ketones) from this value and p for the addition using a value from experiment, if available, or estimated if necessary. This assumes that there is no large difference in steric effects between the reference compound and the unknown of interest. 

Both these methods require equilibrium constants for the microscopic rate determining step, and a detailed mechanism for the reaction. The approaches can be illustrated by base and acid-catalyzed carbonyl hydration. For the base-catalyzed process, the most general mechanism is written as general base catalysis by hydroxide in the case of a relatively unreactive carbonyl compound, the proton transfer is probably complete at the transition state so that the reaction is in effect a simple addition of hydroxide. By MMT this is treated as a two-dimensional reaction proton transfer and C-0 bond formation, and requires two intrinsic barriers, for proton transfer and for C-0 bond formation. By NBT this is a three-dimensional reaction proton transfer, C-0 bond formation, and geometry change at carbon, and all three are taken as having no barrier. 

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