The superscripts indicate that in this particular reaction, the reactants are ions, having a positive or negative charge (in this case, a single charge equal to that of an electron or proton). Note that both charge and the count of atoms must balance between the left hand and the right hand side of the reaction. In water, a certain proportion of the H2O molecules will decompose into the indicated ions, until the rate of recombination equals the rate of production.
The rate of a chemical reaction depends on the probability with which molecules of the reactants collide multiplied by the probability that they react upon collision. In simple cases, such as reactions between molecules in a gas or a dilute solution of molecules dissolved in a liquid, the chance of encounter of reactants is proportional to the product of the concentrations of the reactants. In chemical calculations, it is almost invariably most convenient to measure concentrations as molar concentrations, rather than mass concentrations. For liquid phase reactions between solutes, molar concentration and molar density (e.g Moles of solute per liter of solvent) are practically the same thing, since the density of the liquid varies little. For gases, it is often more convenient to represent the quantity of a substance in terms of its partial pressure instead of its mass or molar density.
It is commonly the case that the availability of a molecule to participate in reactions is not simply proportional to its concentration. This might happen, for example, because other molecules in a solution cluster around a solute molecule, partially shielding it from reactions. To deal with this, chemists have introduced the notion of activity, as a generalization of concentration. The represention of activity, when it is something other than a simple concentration, is particular to the class of reactions under consideration. To distinguish the activity of a substance, which is a number, from the abstract symbol denoting the substance itself, the activity is written in square brackets: [A] is the activity of substance A. However the activities are defined, the reaction rate is expressed as the product of all the activities multiplied by a rate coefficient. By convention, we'll call the rate coefficient k+ for the forward reaction and k- for the back reaction. Thus, the reaction rate for the forward reaction in Eq. 8.1 is R+ = k+[A][B]. The product of activities represents the probability of encounter of the two reactants, while the rate coefficient represents the probability of reaction given a collision. For the unary back-reaction involving decomposition of C, the rate at which the decomposition proceeds is proportional to the amount of substance C present, so we write R- = k-[C].
By way of example, let's consider the net of forward and back reactions in Eq. 8.1, in the simple case where the activities are just concentrations, in which case the reaction rates are the time-derivatives of the concentrations. The evolution of the concentrations is then given by
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