Rate of a reaction

Some reactions are over in a flash, like an explosion; others, like rusting, take months. Chemical kinetics studies how fast reactions go and what changes their speed.

The rate of a reaction is the change in concentration per unit time. As a reaction runs, the reactants disappear and the products appear:

• Rate of disappearance of a reactant R = –Δ[R]/Δt. The minus sign is there because [R] goes down, and a rate is always positive.
• Rate of appearance of a product P = +Δ[P]/Δt.

The units are concentration per time: mol L⁻¹ s⁻¹. For gases, pressure can be used instead of concentration, giving atm s⁻¹.

When the equation has numbers in front, divide each change by its number so that every way of writing the rate gives the same answer. For aA + bB → cC:

Rate = –(1/a) Δ[A]/Δt = –(1/b) Δ[B]/Δt = +(1/c) Δ[C]/Δt

This equality is very useful: if you know how fast one substance changes, you can work out the others.

Two kinds of rate:

• The average rate is measured over a stretch of time (Δ means 'change over an interval').
• The instantaneous rate is the rate at one moment. On a graph of concentration against time it is the slope of the tangent drawn at that moment, written d[R]/dt.

The reactant curve falls, and gets flatter as time goes on: a reaction usually slows down, because there is less reactant left to react.

The rate depends on the concentration of the reactants, the temperature, the presence of a catalyst, and the nature of the reactants themselves.