Calcite rate constants

Phosphate has been found to be an extremely strong inhibitor of carbonate reaction kinetics, even at micromolar concentrations. This constituent has been of considerable interest in seawater because of its variability in concentration. It has been observed that phosphate changes the critical undersaturation necessary for the onset of rapid calcite dissolution (e.g., Berner and Morse, 1974), and alters the empirical reaction order by approximately a factor of 6 in going from 0 to 10 mM orthophosphate solutions. Less influence was found on the log of the rate constant. Walter and Burton (1986) observed a smaller influence of phosphate on calcite... 

A detailed study of the chemistry of pore waters near the sediment-water interface of sediments from the equatorial Atlantic was conducted by Archer et al. (1989) using microelectrodes that were slowly lowered into the sediment. By modeling the resulting data they were able to confirm that calcite was dissolving above the saturation depth as a result of benthic oxidation of organic matter. The estimated in situ rate constant for calcite dissoluton was 1-100% day1. This rate constant is 10 to 100 times slower than the one used in previous models, which was based on experimental data. If the slower rate constant proves to be correct, then dissolution of calcite by benthic metabolic processes will be of major importance. 

Figure 13. Empirical reaction order and log of the rate constant for synthetic calcite dissolution in seawater as a function of phosphate concentration based on the data presented in Figure 12...

Figure 7. Langmuir isotherm plot of ko/(T o — k) against the reciprocal of the phosphate concentration, where ko is the calcite growth rate constant in the absence of phosphate and k is the rate constant in the presence of phosphate ( ) ko = 0.824 (n)ko = 1.205 (O)ko = 0.790. Adapted from Ref. 43.

Here k, k2, kj, are rate constants for reactions 11, 12, and 13, and 4 represents the rate constant for the precipitation of calcite. The values for these rate constants (mmolcm s ) are summarized as a function of temperature, T (K), in the following reactions ... 

Here, K2 is the dissociation constant for bicarbonate, Kc is the solubility product constant for calcite, ki is the rate constant for reaction (11), and the subscript (s) refers to concentrations in the surface adsorption layer. Chou et al. (1989) suggested a... 

In this equation, the rate constant k and the exponent were observed to vary for different samples of natural calcite. Here, fi = exp(AG/R7) and the equation can be rewritten as... 

There are several studies that have been successful in determining the dissolution rate at conditions near seawater saturation. Acker et al. (1987) was able to employ very precise determinations of pH to measure the rate of dissolution of a single pteropod shell at different pressures from 15 atm to 300 atm. Because his measurements were at different pressures and is a function of pressure, he was able to determine whether the rate constant is indeed a function of K p. He found that Equation (9) fit his data better than (10), suggesting that the constant is not pressure dependent and the former is a more accurate universal rate law. An exponent oin= 1.9 was obtained for this surface-controlled dissolution reaction and a partial molal volume. Ay, of —39 cm mol (very close to the mean of the values determined in laboratory experiments for calcite) best fit the data. 

Based on the rate equations of Plummer et al. (1979), we can compute that for groundwater pH s above 6 and 7 co, values less than 0.1 bar at 25°C and below, the solution rate of calcite far from equilibrium reduces toR = ky In other words, for these conditions (which are typical of many shallow groundwaters) the reaction is zero-order, as long as the surface area of the calcite is constant. This assumes no catalysis or inhibition of the rate by adsorbed substances. (Sc, Cu, and PO4 are strong inhibitors according to Sjoberg and Rickard 1984.) As equilibrium is approached, the rate equation becomes... 

Figure 2. Influence of pCOi on the rate of dissolution of calcite at constant pH (S.6-5.7). Adapted from the experimental results, Table 6, of Busenberg and Plummer (1986).

Many natural aquatic systems have a chemical composition close to saturation with respect to calcite or even dolomite. This is the case, for instance, for seawater, which is usually slightly oversaturated in the upper part of the water column and slightly undersaturated at greater depths. Under these conditions, the rates of both precipitation and dissolution contribute significantly to the overall rate of reaction. Even though the reaction paths may be very complex, there is a very direct and important link between the kinetic rate constants, according to which the rates of forward and reverse microscopic processes are equal for every elementary reaction. The fundamental aspect of this principle forms the essential aspect of the theory of irreversible thermodynamics (Frigogine, 1967). 

In the last decade, however, in-situ techniques have been developed to overcome these problems. Profiling lander systems were deployed to record the pore water microprofiles of oxygen, pH and pCOj, and Ca whereas benthic chambers were deployed to measure solute fluxes across the sediment-water interface directly. Very often, reactive-transport models are used to explain the interrelation between measured microprofiles, to predict overall calcite dissolution rates by defining the dissolution rate constants, and to distinguish between dissolution driven by organic matter oxidation and by the undersaturation of the bottom water. 

In contrast, the study of calcite dissolution kinetics in CaCOj-poor sedi-ments of the equatorial Atlantic, Adler et al. (2001) again favored higher reaction orders. In this sense, the observed dissolution rate constants are highly variable, which seems to be mainly dependent on differences in the physical (e.g. surface area) and chemical properties (high/low Mg-calcite) of the calcite mineral phase. 

Table 2.21 Calcite dissolution rate constants and activation energy.

Rate constant for calcite precipitation [d J Rate constant for calcite dissolution [mol dm d ]... 

The kinetic parameters for DOC biodegradation and solid carbonate precipita-tion/dissolution are given in Table 11.5. For calcite precipitation and dissolution rate constant were assigned for both solid carbonates. The simulation time was 100 years with a time step length of 10 d. 

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