What is the rate of a chemical reaction?

Rate and progress: do not confuse the two

When a chemical reaction takes place, it can be described using two distinct concepts: progress x, which measures ‘how much’ of the reaction has taken place, and rate, which measures ‘how quickly’ it is occurring at a given moment.

Defining reaction rate

The volumetric reaction rate is expressed as the derivative of the progress with respect to time, divided by the volume V of the reaction mixture:

v(t) = (1/V) * dx/dt

It is expressed in mol/L/s (or mol·L⁻¹·s⁻¹). The steeper the slope of the curve x(t), the faster the reaction is at that moment.

Monitoring a reaction over time

In practice, we often monitor a physical quantity related to the reaction progress (absorbance, conductivity, volume of gas evolved, etc.) over time, and then deduce x(t) from this. The curve x(t) is increasing, with a slope that gradually decreases: the reaction is rapid at the start, when the reactants are concentrated, and slows down as they are consumed.

The half-life t₁/₂

The half-life is the time required for the reaction progress to reach half its final value x_f, i.e. for x(t₁/₂) = x_f/2. It is a useful indicator for comparing the rates of two reactions without having to plot the entire curve.

Common misconception

A common misconception is to believe that a high reaction rate means the reaction is ‘more advanced’. These are two different things: a reaction may be fast at the start (high rate) but far from complete (low progress), and then slow down whilst continuing to progress towards its final state.