In the section about thermodynamics the Gibbs free energy was discussed as a way to determine if a given chemical reaction will happen spontaneously or not. However, the laws of thermodynamics cannot dictate how fast a given process will happen, only if the process will happen spontaneously. A chemical reaction can happen without any addition of energy to the system being needed, but take thousands of years to convert 10% of the reactants into product. If we want to discuss the speed at which chemical reactions occur, we need to enter the domain of chemical kinetics.
In this section on chemical kinetics, we will discuss the different rate laws that exist for different chemical reactions, find out how we can use these to calculate the concentration of reactants at a given point in time, touch on factors that affect the rate of reaction and finally discuss a very important equation in kinetics: the Arrhenius Law.
Chemical kinetics is the part of chemistry that tries to map the speed of chemical reactions as accurately as possible. Central to this is the general rate equation of a chemical reaction. The rate of a chemical reaction (v) is defined as the change in concentration of the reactants or products per second, and thus has the unit \(mol\cdot l^{-1}\cdot s^{-1}\). The function that expresses this reaction rate is therefore found by calculating the change function of the concentration of a reactant as a function of time.
The general rate equation of a chemical reaction is often noted as \(v=\frac{\Delta [A]}{\Delta t}\), where [A] represents the concentration of an arbitrary reaction product A. This abbreviated notation is used when the volume of the reactor remains constant. If the volume of the reactor changes over time, the correct form of the rate equation becomes: \(v=\frac{1}{V(t)}\cdot \frac{\Delta n_A}{\Delta t}\).
Here, V(t) represents the volume of the reactor as a function of time, and \(n_A\) represents the amount in moles of the substance at a specific moment in time. The rate equation can also be defined starting from the reactants, but then the general function is presented as \(v=-\frac{\Delta [A]}{\Delta t}\), because the change in the concentration of the reactants per second is always negative, while the reaction rate is always positive.
Let's take a look at a hypothetical chemical reaction: \[3A + 2B \rightarrow C + 4D\]Because the reaction rate must always be equal, even if you look at the change in concentration of different substances, the ratios of the stoichiometric coefficients in the equation must be taken into account. This would yield the following general formulas in this example:
\(v = \frac{\Delta [C]}{\Delta t} = \frac{1}{4}\cdot \frac{\Delta [D]}{\Delta t} \)\(= -\frac{1}{2}\cdot \frac{\Delta [B]}{\Delta t} = -\frac{1}{3}\cdot \frac{\Delta [A]}{\Delta t}\).
These functions clearly show that the concentration change per second of substance D, for example, is four times greater than that of substance C.
Written by Imre Bekkering