Reactivity How fast? The rate of chemical change : R2.2.6 Reaction mechanisms and rate-determining steps IB DP Chemistry Study Notes - New Syllabus 2025
Reactivity How fast? The rate of chemical change – IB DP Chemistry- Study Notes
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Reactivity 2.2.6 – Reaction Mechanisms
Reactivity 2.2.6 – Reaction Mechanisms
What Are Elementary Steps?
Many chemical reactions do not occur in a single step. Instead, they proceed through a series of simpler reactions called elementary steps. Each elementary step represents a single molecular event, such as a collision between molecules that leads to bond-breaking and bond-making.
- An elementary step cannot be broken down further; it is a single kinetic event.
- The sum of all elementary steps gives the overall balanced chemical equation.
- Each elementary step has its own rate law, which is based directly on its molecularity (the number of species involved in the step).
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Reaction Mechanism
A reaction mechanism is the sequence of elementary steps that describes how a reaction proceeds from reactants to products.
Criteria for a Valid Mechanism:
- It must agree with the overall balanced chemical equation.
- It must be consistent with the experimentally determined rate law.
- It must correctly introduce and eliminate reaction intermediates.
Each step in the mechanism has its own rate constant and may produce or consume intermediates.
Rate-Determining Step (RDS)
The rate-determining step is the slowest elementary step in the reaction mechanism. It acts as a bottleneck that limits the rate at which the overall reaction can proceed.
- The rate of the entire reaction is governed by the RDS.
- The rate law for the overall reaction is usually based on the molecularity of the RDS.
- If the RDS involves an intermediate, earlier fast steps may be used to express it in terms of reactants.
Characteristics of the Rate-Determining Step
| Feature | Description |
|---|---|
| Slowest Step | Limits the speed of the entire reaction pathway |
| Controls Rate Law | Only species involved in the RDS appear in the rate expression |
| May Involve Intermediates | If RDS is not the first step, intermediates from earlier steps may influence the rate |
Example: Reaction of Nitrogen Dioxide
Consider the overall reaction:
\( \text{2NO}_2 \rightarrow \text{2NO} + \text{O}_2 \)
Proposed mechanism:
- \( \text{NO}_2 + \text{NO}_2 \rightarrow \text{NO}_3 + \text{NO} \) (slow)
- \( \text{NO}_3 + \text{NO}_2 \rightarrow \text{NO} + \text{O}_2 + \text{NO}_2 \) (fast)
Analysis:
- The first step is the rate-determining step (RDS), which is slow.
- The intermediate \( \text{NO}_3 \) is produced in the first step and consumed in the second step.
- Because the slow step involves two \( \text{NO}_2 \) molecules, the rate law is: \( \text{rate} = k[\text{NO}_2]^2 \)
Important Notes:
- Reaction mechanisms are hypothetical and must match both the overall balanced equation and the experimental rate law.
- The RDS is not always the first step—it can occur anywhere in the mechanism.
Reaction Intermediates
A reaction intermediate is a species that is formed in one step of the mechanism and consumed in a subsequent step. It does not appear in the overall balanced chemical equation.
Characteristics:
- They are real species with finite lifetimes (though often short).
- They can sometimes be detected experimentally.
- They are produced and then used up within the mechanism.
Example: In the reaction:
\( \text{2NO}_2 \rightarrow \text{2NO} + \text{O}_2 \)
Mechanism:
- \( \text{NO}_2 + \text{NO}_2 \rightarrow \text{NO}_3 + \text{NO} \) (slow)
- \( \text{NO}_3 + \text{NO}_2 \rightarrow \text{NO} + \text{O}_2 + \text{NO}_2 \) (fast)
Intermediate: \( \text{NO}_3 \) is formed in Step 1 and consumed in Step 2.
Transition States
A transition state is the high-energy arrangement of atoms that exists momentarily at the peak of the energy barrier during a reaction step.
Properties:
- Extremely unstable – exists for a fraction of a second.
- Cannot be isolated or observed directly.
- Represents the point of maximum energy on the reaction coordinate.
Important: Each elementary step has its own transition state.
Comparison: Intermediates vs. Transition States
| Property | Reaction Intermediate | Transition State |
|---|---|---|
| Existence | Stable enough to exist briefly | Exists momentarily (no finite lifetime) |
| Detectable | May be detected or isolated | Cannot be isolated or directly observed |
| Energy | Lower energy than transition state | Highest energy point on reaction coordinate |
| Position on energy diagram | Valley between two peaks | Peak (activation barrier) |
Energy Profiles of Single-Step and Multi-Step Reactions
1. Single-Step Reaction Energy Profile
A single-step reaction proceeds through a single elementary step and has only one transition state. There are no intermediates.
Key Features:
- Reactants start at the initial energy level.
- Transition State is the peak of the curve – a high-energy unstable configuration.
- Products end at a higher (endothermic) or lower (exothermic) energy level.
- Activation Energy (Ea) is the energy difference between the reactants and the transition state.
- ΔH (Enthalpy Change) is the difference in energy between reactants and products.
2. Multi-Step Reaction Energy Profile
A multi-step reaction occurs via two or more elementary steps, each with its own transition state. Intermediates appear between the steps.
Key Features:
- Each peak represents a transition state.
- Each valley between peaks represents a reaction intermediate.
- The rate-determining step is the one with the highest activation energy (tallest peak).
- Total ΔH is the energy difference between the reactants and final products.
Example:
In the reaction:
\( \text{NO}_2 + \text{CO} \rightarrow \text{NO} + \text{CO}_2 \)
The experimentally determined rate equation is:
\( \text{rate} = k[\text{NO}_2]^2 \)
The proposed mechanism is:
- \( \text{NO}_2 + \text{NO}_2 \rightarrow \text{NO}_3 + \text{NO} \) (slow)
- \( \text{NO}_3 + \text{CO} \rightarrow \text{NO}_2 + \text{CO}_2 \) (fast)
Determine the Rate-Determining Step.
▶️Answer/Explanation
- The slow first step involves two molecules of \( \text{NO}_2 \), which matches the order in the rate law: second order with respect to \( \text{NO}_2 \).
- This confirms that Step 1 is the rate-determining step.
- \( \text{NO}_3 \) is formed and consumed – it’s a reaction intermediate.
Example:
The acid-catalyzed hydration of ethene:
\( \text{CH}_2 = \text{CH}_2 + \text{H}_2\text{O} \xrightarrow{\text{H}^+} \text{CH}_3\text{CH}_2\text{OH} \)
Mechanism:
- \( \text{CH}_2 = \text{CH}_2 + \text{H}^+ \rightarrow \text{CH}_3\text{CH}_2^+ \) (slow)
- \( \text{CH}_3\text{CH}_2^+ + \text{H}_2\text{O} \rightarrow \text{CH}_3\text{CH}_2\text{OH}_2^+ \) (fast)
- \( \text{CH}_3\text{CH}_2\text{OH}_2^+ \rightarrow \text{CH}_3\text{CH}_2\text{OH} + \text{H}^+ \) (fast)
Describe its energy profile.
▶️Answer/Explanation
- The rate-determining step is Step 1, involving the formation of the carbocation.
- The carbocation \( \text{CH}_3\text{CH}_2^+ \) is a reaction intermediate.
- The reaction follows a three-step mechanism with only the first being slow.
- Energy profile would show three steps with the first peak being the highest.
Example :
The following timeline shows a multi-step reaction mechanism:- Step 1: \( \text{A} + \text{B} \rightarrow \text{C} \) (slow)
- Step 2: \( \text{C} + \text{D} \rightarrow \text{E} \) (fast)
- Step 3: \( \text{E} \rightarrow \text{F} + \text{G} \) (fast)
▶️Answer/Explanation
- Rate-determining step: Step 1, because it is slow.
- Intermediate(s): C and E. Both are formed in one step and consumed in a later step, not in the overall equation.
- Overall reaction: Add all three steps and cancel intermediates:
\( \text{A} + \text{B} + \text{D} \rightarrow \text{F} + \text{G} \) - Transition states: One for each step, occurring at the peak of each energy barrier (not directly shown but implied).