R2.2.7 Energy profiles and transition states (Higher Level Only)

Energy Profiles: Visualizing Activation Energy and Reaction Steps

Understanding Energy Profiles

As discussed earlier, an energy profile is a graphical representation of the energy changes that occur as a chemical reaction progresses.
It provides valuable insights into the reaction mechanism by illustrating the energy of reactants, products, and intermediate stages.

Note

The horizontal axis represents the reaction coordinate, which tracks the progress of the reaction from reactants to products.
The vertical axis represents the potential energy of the system.

Key Features of Energy Profiles

Reactants and Products:
- The starting point on the graph represents the energy of the reactants.
- The endpoint represents the energy of the products.
For exothermic reactions, the products are lower in energy than the reactants ( $Δ H < 0$ , energy is released).
For endothermic reactions, the products are higher in energy than the reactants ( $Δ H > 0$ , energy is absorbed).

Transition State:
- The transition state is the highest energy point along the reaction pathway.
- It represents a fleeting, unstable arrangement of atoms where bonds are partially broken and formed.

Hint

This is shown as a peak on the energy profile.

Activation Energy ( $E_{a}$ ):
- The activation energy is the energy required to reach the transition state from the reactants.
- It is represented as the energy difference between the reactants and the peak of the graph.
Rate-Determining Step:
- For reactions that occur in multiple steps, the rate-determining step is the slowest step, characterized by the highest activation energy.
- This step acts as a bottleneck, limiting the overall reaction rate.

Single-Step Reactions

In a single-step reaction, the energy profile is relatively simple:

It features one transition state (a single peak).
There are no intermediates—only reactants and products.

Example

Consider the reaction:
$A + B \to C + D$
If this reaction is exothermic ( $Δ H < 0$ ), the energy profile will show:

Reactants at a higher energy level than products.
A single peak representing the activation energy.

Example

Combustion of Hydrogen

The reaction:
$2 H_{2} (g) + O_{2} (g) \to 2 H_{2} O (g)$
is a single-step exothermic reaction. Its energy profile would show:

A single peak, representing the activation energy.
Products ( $H_{2} O$ ) at a lower energy level than reactants ( $H_{2}$ and $O_{2}$ ).

In this reaction:

The activation energy ( $E_{a}$ ) corresponds to the energy needed to break the $H - H$ and $O - O$ bonds.
The transition state represents the point where new bonds between hydrogen and oxygen are partially formed.

Multistep Reactions

Many reactions proceed through multiple steps, each with its own transition state and intermediate.
The energy profile for such a reaction is more complex, featuring:
- Multiple peaks, each corresponding to a transition state.
- Intermediates, which are more stable than the transition states but less stable than the reactants or products.

Identifying the Rate-Determining Step

In multistep reactions, the rate-determining step is the step with the highest activation energy. This step determines the overall reaction rate.

Example

Reaction of Nitrogen Dioxide with Carbon Monoxide

The reaction:
$N O_{2} (g) + C O (g) \to N O (g) + C O_{2} (g)$
proceeds in two steps:

$N O_{2} + N O_{2} \to N O_{3} + N O$ (slow, rate-determining step).
$N O_{3} + C O \to N O_{2} + C O_{2}$ (fast step).

The energy profile for this reaction shows:

Two peaks (two transition states).
An intermediate ( $N O_{3}$ ) between the peaks.
The first peak is higher than the second, confirming that the first step is the rate-determining step.

Energy profiles for a multistep exothermic reaction.

Tip

The number of peaks in an energy profile corresponds to the number of transition states, which equals the number of elementary steps in the reaction mechanism.

Interpreting Energy Profiles in Context

Energy profiles are not just theoretical—they are practical tools for analyzing reaction mechanisms and optimizing reaction conditions. For instance:

Catalysts:
- A catalyst lowers the activation energy by providing an alternative reaction pathway.
- On an energy profile, this appears as a lower peak, while the overall energy change ( $Δ H$ ) remains unchanged.
Temperature Effects:
- Increasing the temperature gives reactant molecules more kinetic energy, increasing their ability to overcome the activation energy barrier.

Common Mistake

Students often confuse intermediates with transition states. Remember, intermediates are relatively stable species that can sometimes be isolated, while transition states are fleeting and cannot be directly observed.

Reflection

Self review

Sketch the energy profile for the following reaction:
$A + B \to C + D (Δ H = - 50 k J m o l^{- 1}, E_{a} = 75 k J m o l^{- 1}$ )
Label the reactants, products, transition state, activation energy, and enthalpy change.
For a two-step reaction, the activation energy of the first step is 120 $k J m o l^{- 1}$ , and the activation energy of the second step is 80 $k J m o l^{- 1}$ . Which step is the rate-determining step? Sketch the energy profile for this reaction.
How does a catalyst affect the energy profile of a reaction? Sketch an energy profile showing both catalyzed and uncatalyzed pathways.

Theory of Knowledge

The transition state is a theoretical concept that cannot be directly observed.

How does this limitation affect our understanding of reaction mechanisms?
To what extent can indirect evidence, such as energy profiles, provide certainty in science?

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