Kinetics of an elementary reaction

Chemical reaction kinetics: Basic principles

Kinetics of an elementary reaction

Here we look at the kinetics of the overall reaction $a\,\text{A}+b\,\text{B}+\cdots\longrightarrow \text{reaction products}$ Under the assumption that it is an elementary reaction and not a summary of a complex reaction mechanism one uses on the basis of a collision model for molecules the following formula for the reaction rate $r$ in terms of concentrations: $r = k\, [\text{A}]^a[\text{B}]^b\cdots\text,$ where the constant $k$ is the reaction rate constant. The constant is often written above or below the reaction arrow. This is also known as the application of the law of mass action. The stoichiometric coefficients $a, b, \ldots$ determine the order of the elementary reaction: $\text{order of the reaction} =a + b+ \cdots$ In other words, the order of the elementary reaction is equal to the sum of the stoichiometric coefficients of the reactants.

In general, we assume for a reaction $a\,\text{A}+b\,\text{B}+\cdots\longrightarrow \text{reaction products}$ the rate law $r = k\, [\text{A}]^\alpha[\text{B}]^\beta\cdots$ for certain numbers $\alpha$ , $\beta$ , etc. These numbers do not have to be equal to $a$ , $b$ , and so on; this is only the case for an elementary reaction. The order of the reaction is equal to $\alpha+\beta+\cdots$ .

An example of a non-elementary reaction is the gas reaction in which acetaldehyde is decomposed to form methane and carbon monoxide $\text{CH}_3\text{CHO}\longrightarrow \text{CH}_4+\text{CO}$ The empirical rate law for this reaction is $r=k\,[\text{CH}_3\text{CHO}]^{\frac{3}{2}}$

The order of the chemical reaction $2\text{NO} + \text{O}_2 \stackrel{k}{\longrightarrow} 2\text{NO}_2$ is equal to 3. $\frac{\dd[\text{NO}]}{\dd t}=-2r,\quad \frac{\dd[\text{O}_2]}{\dd t}=-r,\quad \frac{\dd[\text{NO}_2]}{\dd t}=2r$ with $r=k\, [\text{NO}]^2 [\text{O}_2]$

The assumption of an elementary reaction is essential in the above. For example, when $\text{A}+\text{B}\longrightarrow \text{C}+\text{D}$ is an elementary reaction, then the reaction rate $r$ is given by $r=k\, [\text{A}]\,[\text{B}]$ In contrast, when you experimentally only find proportionality of the reaction and the concentration of species $A$ , this can mean the following:

There is an excess of substance B so that the concentration thereof hardly changes.
There is in reality a reaction mechanism, for example $\begin{aligned}\text{A}&\longrightarrow \text{C}+\text{T}\\ \text{T}+\text{B}&\longrightarrow \text{D}\end{aligned}$ where T is an intermediate product of the first reaction that, in the presence of B, is converted in the second reaction to product D. If the second reaction takes place much faster than the first, then the kinetics is almost completely determined by the first reaction, and thus first-order kinetics applies.