Calcite surface, calculated solution

The enhancing and inhibiting effect of sulfite can be modeled as a shift in equilibrium at the calcite surface. Thus, the equilibrium [CaCOg0] is reduced by increased [CaS03°], much like a solid solution at the CaCOj surface. Using the general mass transfer model, the solution composition at the CaCO surface was calculated from the experimental rate data. 

Thus, CaS03° concentration quantitatively reduces the equilibrium solubility of CaC03°, probably by forming a solid solution or adsorption layer at the calcite surface. For [CaS03°] less than 0.05 mM, [CaC03°] at the surface is equal to its normal equilibrium value, 6.80 x 10 m. The calculated rate is obtained by successive trial and error with 8 until the above solid solution equilibrium is satisfied. 

Figure 22. (A) The specular reflectivity of the calcite-water interface (squares), with similar data for a calcite surface in contact with a 5 mM solution of stearic acid in methanol (The calcite-water data are offset vertically by a factor of 10, for clarity). The measurements were performed in a transmission cell. The solid lines are best-fit structure factor calculations for selected models. The thick solid line through the stearate data is optimized for an extended stearate molecule adsoibed on top of the calcite surface, as shown in (B). The thin solid line through the stearate data is optimized for the carboxylic head group substituting for surface carbonate ions of the calcite lattice. (B) Best-fit model for the stearate monolayer adsorbed on calcite.

The mass transfer by convection and diffusion within the channel is precisely calculable. Numerical methods are used to fit measured concentrations at the detector electrode to the fluid flow in the cell, and to the reaction kinetics at the surface and in solution [24]. The technique was extensively developed during a study of the dissolution of calcite in dilute aqueous acid [25], and has latterly been applied to a number of organic reactions. 

Speleothem precipitation rates from thin water films open to the cave atmosphere are controlled by three processes (Baker and Smart, 1995 Baker et al., 1998) 1) chemical reactions at the calcite-solution interface as described by the rate equations of Plummer et al. (1978) through which precipitation rates can be calculated when the concentrations of reactants are known 2) mass transport of reactants through the solution towards or away from the speleothem surface and 3) the rate-limiting reaction H" + HCO = H2O + CO2, through which CO2 is released into the cave atmosphere. Buhmann and Dreybrodt (1985a,b) have solved the transport equations taking into consideration these three mechanisms in order to obtain precipitation rates. For speleothems, Eq.3 can approximate these processes within 10% ... 

The apparently most consistent set of data was obtained from soil site 19. These data suggest that essentially all solution of Ca is occurring at the soil— rock interface. Ca content of samples taken from a depth of 0.64 m ranged from 12 to 22 mg/1 while samples taken on the same days from a lysometer at the soU—rock interface 1.20 m below the surface ranged from 76 to 89 mg/1. No calcite could be detected in soil samples from various depths, and it is believed that aU of the Ca in the shallower samples was derived from upward diffusion. Values of Sq calculated for the six samples obtained from the lysometer installed at the soil-T ock interface were 0.66, 0.44, 0.66,... 

Moreover, numerical solutions of Eq. 11 for calcite, quartz, and feldspars show that after a short transient period (a few minutes for calcite), the rate of dissolution remains roughly constant. Our calculations (see Table 4) indicate that during this steady-state period the overall dissolution rate should increase by a factor of only 3 or 4 at maximum due to two competing effects decreasing surface strain energy and increasing surface area, as dislocation cores dissolve ind widen. 

When mineral particles are contacted with water, they will undergo dissolution, the extent of which is dependent upon the type and concentration of chemicals in solution. The dissolved mineral species can undergo further reactions such as hydrolysis, complexation, adsorption and even surface or bulk precipitation. The complex equilibria involving all such reactions can be expected to determine the interfacial properties of the particles and their flotation behavior. The concentration of each dissolved mineral species can be calculated from various solution equilibria of the minerals. The calculated results are plotted as log C-pH diagram. The equilibria in selected salt-type mineral systems with special reference to calcite and apatite are examined below. 

The dissolution of limestone is a very slow process. For instance, Kennard and Knill (1968) quoted mean rates of surface lowering of limestone areas in the British Isles that ranged from 0.041 to 0.099 mm annually, and Sowers (1996) suggested rates of 0.025 to 0.040 mm a for the eastern United States. More recently, Trudgill and Viles (1998) quoted calculated erosion rates of calcite of 0.06 to 0.11 mm a- at pH 5.5, and 2.18 to 2.69 mm a at pH 4.0. Nevertheless, solution may be accelerated by man-made changes in the groundwater conditions or by a change in the character of the surface water that drains into limestone. 

The adsorption isotherm of organic solutions of stearic acid onto the calcite form of calcium carbonate has been determined by workers such as Suess [16]. This work has shown that mono-layer coverage is obtained when the area occupied per molecule is around 0.21 nm, which implies that orientation is in this case again perpendicular to the surface. It has also been calculated by Suess that this coverage level corresponds well with the density of calcium atoms in the surface of the inorganic substrate. Thus it is seen that fatty acids, like stearic acid, provide a very good match for the surface of calcite, thereby probably explaining the widespread use of such treatments with calcium carbonate fillers. 

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