8.2: Reaction Rates

In science, when we talk about a rate we mean the change in a quantity over time. A few non-chemical examples include: certain investments with an interest rate, which is the increase in the principle over time (if the rate is negative, then it means that the amount of principle is decreasing over time—not a good investment!); your speed, which is the rate at which you travel down the road, given in miles per hour (or kilometers per hour); a child’s growth rate, which might be an inch or two per year (while the elderly might shrink at a different rate); and the growth rate of some plants, like kudzu, which can grow at a rate of 12 inches per day. The units of rate are an amount divided by a period of time. This might seem too obvious to dwell on, but it is worth noting that most real processes do not have a constant rate of change; rates themselves can and do change. This is one reason why calculus is useful in chemistry: it provides the mathematical tools needed to deal with changing rates, like those associated with planetary motions, falling bodies, and (it turns out) chemical reactions.

If we apply the idea of an amount divided by a period of time to the speed of a chemical reaction, what can we measure to determine a reaction’s rate? What units tell us the amount present, in the same way that miles and meters measure distance? We can’t use mass, because reactions occur between particles (atoms, molecules, ions), which have different masses. We must use the unit that tells us how many particles of a particular type there are—moles. Furthermore, because most reactions (particularly the ones involved in biological and environmental systems) occur in aqueous solutions or in the atmosphere, we usually use units of concentration—molarity (M, mol/L)—to describe the amount of a substance taking part in or produced by a reaction. Typically, the concentration of substance A₂ is written [A₂], and the rate of a reaction can be described as the change in concentration of a reactant or product over a unit of time. So, Δ[A₂]/Δt or [A₂]₂ –[A₂]₁ / t₂ –t₁, where [A₂]₂ is the concentration at time t₂, and [A₂]₁ is the concentration at time t₂ (assuming that t₂ occurs later in time than t₁).