Chemical kinetics focuses on how quickly reactions occur. This page defines reaction rate, clarifies what “change per unit time” means in chemistry, and shows how rate is represented mathematically and graphically.

Core idea: what a reaction rate measures

A reaction proceeds as reactant particles are transformed into product particles, so measurable quantities (like amount in moles or concentration) change as time passes. The reaction rate turns that change into a single numerical description of “how fast.”

Rates are always tied to a clearly stated chemical species and a chosen measurement basis:

• Amount-based rate: uses moles, typically in a fixed-volume system or when tracking total moles directly.

• Concentration-based rate: uses molarity ($\mathrm{mol,L^{-1}}$), most common for solutions because concentrations reflect particle density in the reacting mixture.

Mathematical description of rate

When a rate is reported over a time interval, it is an average rate. Average rates depend on the chosen interval because the speed of many reactions changes as concentrations change.

A standard way to express an average rate for a single species $A$ is shown below. The sign convention matters: reactants are consumed (decrease), products are formed (increase).

To keep “rate” as a positive quantity for reactants, chemists often report rate of disappearance as $-\Delta[A]/\Delta t$ (because $\Delta[A]$ is negative when $A$ is consumed). For products, $\Delta[P]/\Delta t$ is typically positive.

Units and what they communicate

Common rate units depend on what is measured:

• Concentration-based rate: $\mathrm{mol,L^{-1},s^{-1}}$ (often written $\mathrm{M,s^{-1}}$)

• Amount-based rate: $\mathrm{mol,s^{-1}}$

Interpreting the unit is conceptual: $\mathrm{M,s^{-1}}$ tells you how many moles per litre are consumed or produced each second, on average over the interval used.

Rate at an instant (idea of instantaneous rate)

Many reactions slow down as reactants are depleted, so a single average rate may hide how the speed changes.

A concentration–time plot for the decomposition of $\mathrm{H_2O_2}$ with tangent lines drawn at two times. The instantaneous rate at each time is the (negative) slope of the tangent, illustrating why reactant rates are often reported as $-d[\mathrm{A}]/dt$ to keep rate positive. The right-triangle “rise/run” markers show how a tangent slope is estimated from the graph. Source

You can visualise this by plotting concentration (or amount) versus time:

• For a reactant, the curve typically slopes downward; the instantaneous rate relates to the steepness at that time.

• For a product, the curve typically slopes upward.

Instantaneous rate is a local concept: it is obtained by considering a very small time interval around the moment of interest (a tangent slope on the graph). In AP Chemistry, the key skill is interpreting what “steeper” or “less steep” means physically: steeper slope = faster change = larger magnitude of rate.

Choosing “amount” versus “concentration” carefully

The syllabus statement emphasises that rate can be defined using amount or concentration. The best choice depends on what stays controlled and what you can measure reliably:

• Use concentration when solution volume is essentially constant and mixing is uniform.

• Use amount when you track total moles directly (for example, from a mass change or a total-mole measurement).

In all cases, a reported rate should clearly indicate:

• the species being monitored (reactant or product),

• whether the rate is average (over an interval) or instantaneous (at a time),

• the units and time scale used.