In an abiotic weathering regime, the H2O-CO2 equilibria and kinetic dependence of CaMg silicates on pH will determine the rate of chemical weathering of these silicates for a given reactive surface area, at specified temperature and flushing rate (runoff). The relevant equilibria are:
(A second dissociation of HCO~ to H+ and CO3 2 will be neglected because the equilibrium constant is much smaller; see Plummer andBusenberg 1982) Thus, in a system with continuous reaction with water saturated with carbon dioxide and open to the atmosphere,
For these conditions, aHCO- = aH+, thus, aH+ = (K1K2 pCO2)05,
Hence, aH+ varies with pCO0 5. Note that a is the thermodynamic activity of the chemical species.
The rate of dissolution of CaMg silicates varies with (aH+)n, where 0 ^ n < 1; n has been determined for common rock-forming silicates (for pH <7, corresponding to the conditions to be modeled). For inosilicates, n varies from 0.2 (diopside) to 0.99 (augite) (Brantley and Chen 1995), for neosil-icates 1.0 (e.g., olivine; Sverdrup 1990), for tectosilicates, particularly plagio-clase less calcic than anorthite 0.5 (anorthite, n = 1) (Blum and Stillings 1995). Assuming n = 0.5 gives a = 0.25 (Berner 1992) in the following expression: dissolution rate varies with (Pab/Po)a.
A more rigorous treatment would require the weighted average of n derived from the relative abundances and dissolution rates of CaMg silicates in the exposed continental crust. Given the experimental range of n for these minerals, a probably falls between 0.25 and 0.5 for an open weathering regime. As Berner (1992) pointed out, the open regime would likely occur in weathering above the water table, with continuous resupply ofwater saturated with carbon dioxide. A closed weathering regime, occurring below the water table, is postulated to result in a = 1 because the rate of dissolution would then depend directly on the carbon dioxide concentration of percolating rain water consumed faster than resupply from soil gas or incoming rain water.
What would be the effective a for an abiotic land surface? For bare, soil-free, relatively impermeable plutonic and metamorphic rocks, most of the chemical weathering could well take place in an open system regime with 0.25 < a < 0.5. Weathering of porous volcanics and sediments might entail a range of a depending on where most dissolution takes place, above or below the water table (e.g., apparently, a is close to 1 for spring waters draining basalts in Iceland; see Gislason and Eugster 1987). Other possible influences on dissolution include buildup of bicarbonate in soils, corresponding to a < 0.5, but at higher pH, near 7, hence in the minimum region of dissolution. For most rock-forming silicates the dissolution rates increase as pH drops below about 5 and increases above about 8; thus, a dissolution minimum exists around neutrality (White and Brantley 1995). In alkaline solutions, dissolution occurs by OH~ complexing with surface cations.
Berner (1992) pointed out that an abiotic land surface would likely be much drier, with windblown alkaline dust neutralizing rain acidity, again tending to minimize dissolution, requiring still higher atmospheric pCO2 for a stronger greenhouse effect, hence higher surface temperatures, for attaining a weathering sink equal to the volcanic/metamorphic source. In addition, "... to avoid unreasonably high CO2 levels, and excessive global warming, one is forced to choose the closed-system, linear-feedback option . . . There are additional complications in a barren world. One is that the absence of plants would vastly change evapotranspiration. . . . Because of a lack of evaporation there would be lower cloudiness and much less rainfall over the continents . . . leading to large-scale desertification and thus, lower rates of weathering" (Berner 1992, p. 3227). As we will see in subsequent chapters, these arguments are consistent with just such a high atmospheric pCO2 (and temperature) regime on Archean/early Proterozoic continental surfaces, with limited microbial colonization. An open system weathering regime is not an implausible approximation for this scenario.
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