Reaction Mechanism

Core Concepts

In the upcoming article, we will discuss the Reaction Mechanism how it works based on molecularity, which is about how things come together in a reaction. We’ll also cover Unimolecular, Bimolecular, and Termolecular reactions, which are different ways things combine. We’ll look at Rate-Limiting Step and Determining Rate Law, which help us understand how fast a reaction goes. Lastly, we’ll explore the Pre-Equilibrium Approach, a method to guess what will happen in reactions.

Topics Covered in Other Articles

What is a reaction mechanism?

A reaction mechanism is a detailed and organized picture of the series of tiny changes that happen when chemicals react. It looks closely at the exact steps and changes that occur as starting materials turn into new things. This detailed description includes the making and breaking of connections between chemicals, the movement of electrons, and how atoms and molecules work together. A reaction mechanism is a helpful tool for scientists to understand how reactions happen on the inside, guess what will result from them, and control how they happen under different conditions.

In order to create a mechanism for a reaction we use a curved-arrow notation to show the direction of electron flow. To demonstrate curved-arrow notation, let’s consider the following reaction of hydrogen chloride with water, where we can see the overall reaction and its respective reaction mechanism (step-by-step):

Reaction

Molecularity

Molecularity refers to the number of particles or parts that join together in a specific basic chemical reaction. It helps us figure out how many pieces come together to start it. Molecularity can be different, like unimolecular (one part), bimolecular (two parts), or termolecular (three parts), depending on how many pieces take part in the reaction. This idea helps chemists understand how chemical reactions work and how they happen.

Unimolecular Reaction Mechanism

An unimolecular reaction refers to a process where a single starting material undergoes a rearrangement, resulting in the formation of one or more product molecules. These reactions focus on how one substance transforms into different substances through isomerization, dissociation, or decomposition.

$A \rightarrow \text{Products}$

The unimolecular reaction uses the following rate law: $\text{rate}= k[A]$

Chemical bonds require energy to break during reactions, examples of unimolecular reactions are ring opening, racemization and cis-trans isomerization. The next illustration shows the result of the decomposition of C₄H₈, where an activation energy of 261 kJ per mole is required for this reaction to take place.

This energy causes molecular distortions, leading to the formation of activated complexes that eventually undergo decomposition to generate products. In this case the rate of decomposition is directly proportional to the concentration of C₄H₈. By doubling the concentration, the number of reactive molecules and the reaction rate also double.

Bimolecular Reaction Mechanism

A bimolecular reaction involves the collision of two particles, which can be the same molecule or different molecules. The term “bimolecular” stems from the fact that two reactants come together to form products.

The rate of a bimolecular reaction is determined by the multiplication of the concentrations of both participating species, leading to their classification as second-order reactions.

There exist two categories of bimolecular reactions:

In the first type two reactant molecules are distinct,

$A+B \rightarrow \text{Products}$

here the rate law is initial-rate in A and initial-rate in B:

$\text{rate}=k[A][B]$

And in the second type two identical molecules collide and react:

$2A\rightarrow \text{Products}$

and the rate law is second-order with respect to A:

$\text{rate}=k[A][A]=k[A]^{2}$

Termolecular Reaction Mechanism

A termolecular reaction is a process that requires the simultaneous collision of three atoms, molecules, or ions. These reactions are extremely uncommon due to the minuscule likelihood of three particles colliding concurrently, contrasting the more prevalent two-particle collisions. Nonetheless, there exist a few recognized instances of termolecular elementary reactions.

In such reactions, the convergence of the three species becomes crucial, necessitating the precise alignment, synchronicity, and adequate energy for the reaction to manifest. The overall molecularity of a termolecular reaction is three, with the order of reaction for each species reflecting the number of colliding particles from that species in the termolecular collision,

$A + B + C \rightarrow \text{Products}$

And its rate law would be:

$\text{rate}= k[A][B][C]$

Rate-Limiting Step

In chemistry, the rate-limiting step refers to the slowest step in a reaction mechanism that determines the overall rate of the reaction. It plays a crucial role in understanding the kinetics of a chemical reaction. To illustrate this concept of a rate-limiting step, imagine a system of four funnels through which water is being poured. Funnels 1, 2, and 4 are of similar size, while funnel 3 is much smaller.

In this scenario, the rate of water flow throughout the system is limited by the diameter of the smallest funnel. If the smaller funnel were replaced with a larger or equivalent-sized funnel, the water flow would increase significantly. Conversely, if funnel 1, 2 or 4 was replaced by a larger funnel, flow rate would not increase because funnel 3 still slows the rate. Therefore, if we have a mechanism consisting of two elementary steps where the first step is slower than the second, we identify the first step as the rate-limiting step.

Rate Law

The rate law represents the relationship between the concentration of reactants and the rate of the reaction. Importantly, the rate law must not include any intermediates. Intermediates are substances that one step produces and another step consumes, but they do not appear in the overall balanced chemical equation.

For a reaction mechanism to be valid, it must satisfy certain conditions:

Conservation of Reaction Equation: The sum of the elementary steps in a mechanism should be equivalent to the overall chemical reaction. For example in the following reaction mechanism:

$\begin{align*} {CO + NO_{2} &\rightarrow CO_{2} + NO} \\ {NO_{2} + NO_{2} &\rightarrow NO_{3} + NO \text{(slow)}} \\ {NO_{3} + CO &\rightarrow NO_{2} + CO_{2} \text{(fast)}} \end{align*}$

Consistency with Experimentally Observed Rate Law: The rate law predicted by the mechanism should agree with the rate law observed experimentally.

In the given reaction mechanism, NO₃ is identified as the only reaction intermediate since NO₂ cancels out with another NO₂ molecule to form the balanced equation. Thus, it is crucial that the rate law for this reaction does not contain NO₃ in any form.

Determining Rate Law

The rate law for a reaction with a slow initial step (as is the case in the provided mechanism) is relatively easier to determine compared to mechanisms with fast initial steps. This rate law is derived based on the collision of two NO₂ molecules to form the products. Notably, the rate law for the rate-limiting step does not contain any intermediates, including NO3. Therefore, the overall rate law for the reaction is:

$\text{rate}= k[NO_{2}]^{2}$

This equation represents the rate law for the entire reaction.

Pre-Equilibrium Approach

We use the pre-equilibrium approximation when dealing with more complex reactions that involve multiple steps. It simplifies the determination of the rate law by assuming that the reaction before the rate-limiting slow step reaches equilibrium. For this we substitute the concentration of the intermediate species in the rate law with an equivalent value derived from the equilibrium constant (K), simplifying the rate law and obtain a more manageable expression that reflects the overall reaction kinetics accurately.

How it works

To illustrate this, let’s consider a specific mechanism involving two steps. In the first step, the reaction proceeds rapidly to attain equilibrium:

$NO + Br_{2} \rightleftarrows NOBr_{2} \text{(fast)}$

After that, the second step, known as the rate-determining step, occurs at a slower rate:

$NOBr_{2} + NO \rightarrow 2NOBr \text{(slow)}$

Here’s how we can apply the pre-equilibrium approximation to derive the rate law for this reaction:

The rate law for the fast equilibrium step can be written as $k_{1}[NO][Br_{2}] = k_{-1}[NOBr_{2}]$ , where k₁ and k_-1 are the forward and reverse rate constants, respectively.
By solving for [NOBr₂], we find that $[NOBr_{2}] = \frac{k_{1}[NO][Br_{2}]}{k_{-1}}$ .
Substituting the expression for [NOBr₂] into the rate law for the slow step (rate-determining step), we obtain $\text{rate} = k_{2}[NO]\frac{k_{1}[NO][Br_{2}]}{k_{-1}}$ .
Simplifying the expression further, we have $\text{rate} = \frac{k_{1}k_{2}[NO]^{2}[Br_{2}]}{k_{-1}}$ .
Finally, combining the rate constants $\frac{k_{1}k_{2}}{k_{-1}}$ into a single rate constant k, we arrive at the rate law: $\text{rate} = k[NO]^{2}[Br_{2}]$ .

It’s important to know that the exponents in the rate law are not determined only by the coefficients in the equation, but by the individual steps of the mechanism. Also, it assumes that the intermediate species, like NOBr₂in this case, is consumed in equilibrium before the slowest step of the reaction. Therefore, the concentration of the intermediate doesn’t influence the rate law.

To confirm the proposed mechanism and rate law, we compare it with the experimentally determined overall rate law. If they match, it provides more evidence that the chosen mechanism is reasonable and accurately explains the observed reaction kinetics.