where the subscripts c and s denote carbonates and silicates, respectively, and x is the fraction of the total drainage area due to each rock type. Further refinement, such as inclusion of the individual dissolution rates of limestones, dolostones, and different types of silicate rocks, is not justified for this simple computation.

By using the ranges of carbonate and silicate dissolution rates from Figure 2.7, and the preceding estimates of the carbonate outcrop area and the percentage contributions of rock types, the weathering rate W is

An upper bound of the weathering rate W from the preceding equation is 10-7, a value much greater than the mean chemical denudation rate of about 10-12 mol/cm2/s, shown in Figure 2.7 and Table 2.2.

In this computation, the same value of the S/A ratio was arbitrarily taken for the carbonate and silicate rocks. A more careful inspection of the numerical terms in the computation of W would show that the first term of the sum representing carbonate dissolution is the main contributor to the high value of W, which is further magnified by the surface-area ratio term S/A >>1. This contribution would have been reduced if the S/A value for rocks were small; for example, surface dissolution without water penetrating the rock is an approximation to dissolution of dense limestone or marble surfaces exposed to rain or running water (Reddy, 1988). However, theoretical and empirical estimates of the rock surface areas (S), the ratio S/A, and the volume of water flow through the rocks are such that regional or global estimates of the chemical denudation rates based on them have large margins of uncertainty.


Background — Alkalinity [Alk], Acidity [Acy], CO2, and pH

Observations of weathering in small drainage basins of streams and lakes exposed to acid rain, and experimental results from acid water leaching of soils in lysimeters show that variable, yet significant fractions of imported acidity, measured as [H]+, are neutralized by reactions of water with minerals (Likens et al., 1977; Henriksen, 1980; Wright, 1983, 1988; Folster, 1985; Paces, 1985; Colman and Dethier, 1986; Schnoor and Stumm, 1986; Berner and Berner, 1987; Drever, 1988; Norton et al., 1989; Velbel and Romero, 1989). These conclusions corroborate the older and broader ideas that crustal weathering is a chemical acid-base titration on a planetary scale (Sillen, 1961, p. 551; Stumm and Morgan, 1981; Holland, 1984).

Acidic streams and acidic lakes exist because neutralization reactions in some areas are not fast enough. Whenever waters react with carbonate and/or silicate rocks, consumption of the hydrogen ions from solution is balanced by releases of chemically equivalent amounts of other metal cations. The released cations may be transported away by flow or they may in part be stored in secondary minerals and vegetation of the drainage area, as discussed in an earlier section. More generally, H+ -sensitive reactions are those that produce changes in the alkalinity of the solution (function [Alk] defined below), and they result in concentration increases for cations derived from the reacting minerals.

One of the simpler definitions is that alkalinity is the acid neutralization capacity of a solution. A more specific definition is that alkalinity is the difference between the concentrations of the H+-independent cations and anions in solution. Extensive textbook-level discussions of alkalinity of natural waters are given by Stumm and Morgan (1981) and Drever (1988). The main ions in natural waters that are H+ dependent include the anions bicarbonate, carbonate, and hydroxyl. In certain continental waters, phosphate ions may also contribute to the alkalinity. In acidic waters, the positively charged aluminum hydroxide aqueous complexes add to the balance along with the hydrogen ion. Anions of organic acids may also be important in waters enriched in dissolved organic carbon.

In a simplified general case, alkalinity is the difference between the following anion and cation concentrations, given in equivalents per liter:

The preceding form of alkalinity, which is based on the carbonate, hydroxyl, and hydrogen ions, is also known as the carbonate alkalinity.

In acidic solutions, where concentrations of the bicarbonate, carbonate, and hydroxyl ions are negligibly low, the hydrogen ion is dominant and the values of [Alk] become negative. Thus for acidic solutions, the negative alkalinity is defined as acidity [Acy]:

-[Alk] = [Acy]. (2.21)

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