Reaction Kinetics

A chemical reaction does not finish in an instant. The rate of reaction is the change in concentration of a reactant or a product per unit time, and for a species $X$ it is written as $\text{rate} = \frac{\Delta [X]}{\Delta t}$. Because concentration is measured in $\text{mol dm}^{-3}$ and time usually in seconds, the rate carries the units $\text{mol dm}^{-3}\text{ s}^{-1}$; in a gas-phase reaction the concentration term is often replaced by a pressure. For the simple change $A \rightarrow B$, the rate can be followed either as the disappearance of $A$, $-\frac{\Delta [A]}{\Delta t}$, where the minus sign keeps the rate positive, or as the appearance of $B$, $+\frac{\Delta [B]}{\Delta t}$.

The rate is not constant during a reaction. Plot concentration against time and the curve is steepest at the start, where the reactants are most concentrated, then flattens as they are used up. The average rate over a chosen interval is the change in concentration divided by the interval, while the instantaneous rate is the slope of the tangent drawn at that instant. Because the slope is greatest near the beginning, the instantaneous rate is highest at the start and falls as the reaction proceeds. When the equation has coefficients the rate is shared among the species: for $2A + 2B \rightarrow 3C$ the one rate of reaction is $-\frac{1}{2}\frac{\Delta [A]}{\Delta t} = -\frac{1}{2}\frac{\Delta [B]}{\Delta t} = +\frac{1}{3}\frac{\Delta [C]}{\Delta t}$.

Chemical kinetics is the name for the whole study, the rate of a reaction, its mechanism, and the factors that change its speed. Where a reaction makes or removes ions, the rate can be followed by watching the change in electrical conductivity, because the ion concentration governs how well the solution conducts. This is the standard way to follow a reaction between ions, as opposed to watching a colour fade or reading a pressure gauge.