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3.9.2 Law of mass action

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Let's attempt to understand the implications of eqn. 3.85. Consider the dissociation of carbonic acid, an important geologic reaction:


For this particular case, eqn. 3.85 is expressed as:


The right side of the equation is a quotient, the product of the activities of the products divided by the product of the activities of the reactants and is called the reaction quotient. At equilibrium, the reaction quotient is equal to the equilibrium constant. The equilibrium constant therefore allows us to predict the relative amounts of products and reactants that will be present when a system reaches equilibrium.

Suppose now that we prepare a beaker of carbonic acid solution; it is not hard to prepare: we just allow pure water to equilibrate with the atmosphere. Let's simplify things by assuming that this is an ideal solution. This allows us to replace activities with concentrations (the concentration units will dictate how we define the equilibrium constant; see below). When the solution has reached equilibrium, just enough carbonic acid will have dissociated so that the reaction quotient will be equal to the equilibrium constant. Now let's add some H+ ions, perhaps by adding a little HCl. The value of the reaction quotient increases above that of the equilibrium constant and the system is no longer in equilibrium. Systems will always respond to disturbances by moving toward equilibrium (how fast they respond is another matter, and one that we will address in Chapter 5). The system will respond by adjusting the concentrations of the three species until equilibrium is again achieved; in this case, hydrogen and bicarbonate ions will combine to form carbonic acid until the reaction quotient again equals the equilibrium constant. We can also see that had we reduced the number of hydrogen ions in the solution (perhaps by adding a base), the reaction would have been driven the other way (i.e., hydrogen ions would be produced by dissociation). Equation 3.85 is known as the law of mass action, which we can state more generally: Changing the concentration of one species in a system at equilibrium will cause a reaction in a direction that minimizes that change.

Geochemistry

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