To this point we have measured reaction progress parametrically in terms of the reaction progress variable ξ, which is dimensionless. When in Chapter 11 we reacted feldspar with water, for example, we tied reaction progress to the amount of feldspar that had reacted and expressed our results along that coordinate. Studying reactions in this way is in many cases perfectly acceptable. But what if we want to know how much time it took to reach a certain point along the reaction path? Or, when modeling the reaction of granite with rainwater, how can we set the relative rates at which the various minerals in the granite dissolve? In such cases, we need to incorporate reaction rate laws from the field of geochemical kinetics. The differences between the study of thermodynamics and kinetics might be illustrated (e.g., Lasaga, 198la) by the analogy of rainfall on a mountain. On the mountaintop, the rainwater contains a considerable amount of potential energy. With time, it flows downhill, losing energy (to be precise, losing hydraulic potential, the mechanical energy content of a unit mass of water; Hubbert, 1940), until it eventually reaches the ocean, its lowest possible energy level. The thermodynamic interpretation of the process is obvious: the water seeks to minimize its energy content. But how long will it take for the rainfall to reach the ocean? The rain might enter a swift mountain stream, flow into a river, and soon reach the sea. It might infiltrate the subsurface and migrate slowly through deep aquifers until it discharges in a distant valley, thousands of years later. Or, perhaps it will find a faster route through a fracture network or flow through an open drill hole. There are many pathways, just as there are many mechanisms by which a chemical reaction can proceed. Clearly, the questions addressed by geochemical kinetics are more difficult to answer than are those posed in thermodynamics. In geochemical kinetics, the rates at which reactions proceed are given (in units such as moles/sec or moles/yr) by rate laws, as discussed in the next section. Kinetic theory can be applied to study reactions among the species in solution.
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