Chemical Kinetics

1. Introduction

Chemical kinetics is the branch of chemistry that studies the rate (speed) of chemical reactions, the factors that affect the rate, and the mechanism (the sequence of elementary steps) by which reactants change into products. Thermodynamics tells us whether a reaction can happen; kinetics tells us how fast it happens.

Reactions range from almost instantaneous (ionic precipitation, neutralisation) to extremely slow (rusting of iron, weathering of rocks). Kinetics lets us control industrial reactions and understand reaction pathways.

---

2. Rate of Reaction

The rate of reaction is the change in concentration of a reactant or product per unit time. For

$$ \ce{A -> B} $$

:

$$ \begin{aligned} \text{Rate} &= -\frac{d[\ce{A}]}{dt} \ &= +\frac{d[\ce{B}]}{dt} \end{aligned} $$

The minus sign shows that $[\ce{A}]$ decreases. Units are usually $\text{mol L}^{-1}\text{s}^{-1}$.

For a general reaction

$$ \ce{aA + bB -> cC + dD} $$

, the single unique rate is:

$$ \begin{aligned} \text{Rate} &= -\frac{1}{a}\frac{d[\ce{A}]}{dt} \ &= -\frac{1}{b}\frac{d[\ce{B}]}{dt} \ &= +\frac{1}{c}\frac{d[\ce{C}]}{dt} \ &= +\frac{1}{d}\frac{d[\ce{D}]}{dt} \end{aligned} $$

• Average rate: change in concentration over a finite time interval, $\dfrac{\Delta[\ce{A}]}{\Delta t}$.
• Instantaneous rate: rate at a particular instant, the slope of the tangent to the concentration-time curve ($\Delta t \to 0$).

---

3. Rate Law and Rate Constant

The rate law (rate expression) relates the rate to the molar concentrations of the reactants raised to some powers, found only by experiment:

$$\text{Rate} = k[\ce{A}]^x[\ce{B}]^y$$

• $k$ is the rate constant (specific reaction rate): numerically equal to the rate when all concentrations are unity. It depends on temperature and the catalyst but not on concentration.
• The powers $x$ and $y$ are found experimentally and need not equal the stoichiometric coefficients.

Unit of $k$ depends on the overall order $n$:

$$k \text{ has units } (\text{mol L}^{-1})^{1-n},\text{s}^{-1}$$

So for a zero-order reaction $k$ is $\text{mol L}^{-1}\text{s}^{-1}$; first order $\text{s}^{-1}$; second order $\text{L mol}^{-1}\text{s}^{-1}$.

---