Carbon equilibrium constant

Table 13.1 Temperature dependence of some important carbonate equilibrium constants. 

Figure 4.5. Aqueous carbonate equilibrium constant Pcoz- Water is equilibrated with the atmosphere pco2 10 atm), and the pH is adjusted with strong base or strong acid. Equations 7-9 with the constants (25°C) pATn = 1.5, pAT, = 6.3, pAT2 = 10.25, and pAT (hydration of CO2) = -2.8 have been used. The pure CO2 solution is characterized by the proton condition [H ] = [HCO ] + 2[C03 ] + [OH ] (see point P) and the equilibrium concentrations -log[H J = -log[HCO ] = 5.65 log[C02aq] = -log[H2C03 ] = 5.0 -log[H2C03] = 7.8 and -log[C03 ] = 8.5.

The pH and carbonate species distribution for waters from different locations in the ocean (Table 4.4) are calculated by using data for At and DIG and the equilibrium constants. The equilibrium equations were solved with the computer program of Lewis and Wallace (1998) using the carbonate equilibrium constants fCj and K 2 of... 

TABLE 4-7 Temperature Dependence of Some Important Carbonate Equilibrium Constants... 

The pressure dependence of the various carbonate equilibrium constants is less well defined than the temperature dependence, with the result that less attention has been devoted to empirical equations for the pressure dependence of pH. Millero (1979) quotes the following equation for the NBS pH scale as a function of pressure P ... 

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... 

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