DAT General Chemistry: Activation Energy and Reaction-Coordinate Diagrams

DAT High-Yield Concept

Activation Energy ( $E_{\text{a}}$ ): The minimum energy threshold colliding reactant molecules must possess to undergo a chemical transformation ( $E_{\text{a}} > \pu{0 kJ/mol}$ ).
Transition State (Activated Complex): The maximum potential energy point along a reaction coordinate, featuring partial bonds; it cannot be isolated due to extreme instability.
Thermodynamic vs. Kinetic Relationship: Enthalpy change equals forward minus reverse activation energy ( $\Delta H_{\text{rxn}} = E_{\text{a, fwd}} - E_{\text{a, rev}}$ ).
Catalysts: Lower both $E_{\text{a, fwd}}$ and $E_{\text{a, rev}}$ equally by providing an alternate reaction pathway, accelerating rate without altering overall $\Delta H_{\text{rxn}}$ or equilibrium position.

1. Reaction-Coordinate Diagrams & Activation Energy

A reaction-coordinate diagram tracks the potential energy of a chemical system as reactants transform into products along a theoretical pathway called the reaction coordinate (or reaction progress). On the y-axis, potential energy is plotted, while the x-axis represents the extent of bond reorganization.

Activation Energy ( $E_{\text{a}}$ ): The energy barrier between reactants and the highest energy point along the pathway. Reactants must absorb at least this amount of kinetic energy during collisions to react.

A simple reaction coordinate diagram (Source: Chem540grp1f08 · CC BY-SA 3.0 · Wikimedia Commons)

The activation energy determines reaction kinetics: higher barriers correspond to smaller rate constants and slower overall reaction rates. Temperature increases boost kinetic energy distributions, enabling a larger fraction of reactant species to overcome $E_{\text{a}}$ .

2. Transition States as Energy Maxima

At the highest peak of a reaction coordinate diagram sits the transition state (or activated complex). At this position, chemical bonds are in the process of breaking and forming simultaneously. Because it represents a potential energy maximum, the transition state is dynamic, possesses an infinitesimal lifetime ( $\approx \pu{10^{-15} s}$ ), and cannot be isolated or stored.

It is crucial on the DAT to distinguish a transition state from a reaction intermediate. While a transition state sits at a peak (energy maximum), a reaction intermediate sits at a valley (local energy minimum) between two transition states in a multi-step mechanism.

Feature	Transition State (Activated Complex)	Reaction Intermediate
Position on Diagram	Energy maximum (peak)	Local energy minimum (valley)
Bonding State	Partial bonds breaking/forming	Fully formed chemical bonds
Isolability	Cannot be isolated	Sometimes isolable or detectable
Lifetime	$\approx \pu{10^{-15} s}$ (transient)	Measurable lifetime

3. Forward and Reverse Activation Energy

Chemical reactions can proceed in both forward and reverse directions. The energy required to reach the transition state differs depending on whether starting from reactants or products:

Forward Activation Energy ( $E_{\text{a, fwd}}$ ): Energy difference between the transition state and reactants ( $E_{\text{a, fwd}} = E_{\text{TS}} - E_{\text{reactants}}$ ).
Reverse Activation Energy ( $E_{\text{a, rev}}$ ): Energy difference between the transition state and products ( $E_{\text{a, rev}} = E_{\text{TS}} - E_{\text{products}}$ ).

The overall enthalpy change of the reaction ( $\Delta H_{\text{rxn}}$ ) links these two kinetics values:

\Delta H_{\text{rxn}} = E_{\text{a, fwd}} - E_{\text{a, rev}}

In an exothermic reaction ( $\Delta H_{\text{rxn}} < \pu{0 kJ/mol}$ ), products sit at lower energy than reactants, making $E_{\text{a, fwd}} < E_{\text{a, rev}}$ . In an endothermic reaction ( $\Delta H_{\text{rxn}} > \pu{0 kJ/mol}$ ), products sit at higher energy, making $E_{\text{a, fwd}} > E_{\text{a, rev}}$ .

Forward and reverse activation energies differ by delta H — Forward and reverse reactions pass over the very same transition state, so their activation energies are measured from different starting levels up to one shared peak. Subtracting them gives the enthalpy change: forward barrier minus reverse barrier. When the forward barrier is the smaller of the two the reaction is exothermic, as drawn here, and when it is the larger one the reaction is endothermic. The barrier height controls the rate while the difference between the two levels controls the energy released or absorbed, and the two are independent of each other.

Worked Example: Energy Diagram Calculations

Problem: Consider the reaction $\ce{A + B -> C + D}$ . The initial energy of reactants $\ce{A + B}$ is $\pu{40 kJ/mol}$ , the transition state energy is $\pu{110 kJ/mol}$ , and the product energy of $\ce{C + D}$ is $\pu{15 kJ/mol}$ . Calculate $E_{\text{a, fwd}}$ , $E_{\text{a, rev}}$ , and $\Delta H_{\text{rxn}}$ .

Step 1: Forward Activation Energy

E_{\text{a, fwd}} = E_{\text{TS}} - E_{\text{reactants}} = \pu{110 kJ/mol} - \pu{40 kJ/mol} = \pu{70 kJ/mol}

Step 2: Reverse Activation Energy

E_{\text{a, rev}} = E_{\text{TS}} - E_{\text{products}} = \pu{110 kJ/mol} - \pu{15 kJ/mol} = \pu{95 kJ/mol}

Step 3: Enthalpy of Reaction

\Delta H_{\text{rxn}} = E_{\text{products}} - E_{\text{reactants}} = \pu{15 kJ/mol} - \pu{40 kJ/mol} = -\pu{25 kJ/mol}

Verification: $\Delta H_{\text{rxn}} = E_{\text{a, fwd}} - E_{\text{a, rev}} = \pu{70 kJ/mol} - \pu{95 kJ/mol} = -\pu{25 kJ/mol}$

DAT Exam Trap: Do not measure activation energy from the zero line on the y-axis. Activation energy is always the relative difference from the starting baseline (reactants or products) up to the peak!

4. Catalysts and Reaction Pathways

A catalyst increases reaction rate by providing an alternative mechanism with a lower activation energy transition state. Importantly, catalysts lower both $E_{\text{a, fwd}}$ and $E_{\text{a, rev}}$ by the exact same numerical amount.

Because reactant and product energy levels remain untouched by a catalyst, the reaction enthalpy change ( $\Delta H_{\text{rxn}}$ ), Gibbs free energy change ( $\Delta G_{\text{rxn}}$ ), and equilibrium constant ( $K_{\text{eq}}$ ) do not change. Catalysts speed up how quickly equilibrium is achieved without changing the equilibrium position.

DAT Mnemonic for Catalysts: CATALYST = Cuts Activation barrier, Time Accelerated, Leaves Yield & Starting/final Thermodynamics unchanged!

Critical Thinking Questions

If a forward reaction has $E_{\text{a, fwd}} = \pu{45 kJ/mol}$ and $\Delta H_{\text{rxn}} = +\pu{15 kJ/mol}$ , what is the activation energy for the reverse reaction? Is the reverse reaction endothermic or exothermic?
Why is it impossible for a physical catalyst to lower $E_{\text{a, fwd}}$ without also lowering $E_{\text{a, rev}}$ ?
In a two-step mechanism with two transition states and one intermediate, which step determines the overall reaction rate, and how is its transition state identified on a reaction coordinate diagram?

References

Sources returned by Google Search grounding during lesson verification.

6.6: Reaction Coordinate Diagrams - Chemistry LibreTexts — chem.libretexts.org
Learn: Activation energy (article) - Khan Academy — khanacademy.org

Activation Energy and Reaction-Coordinate Diagrams

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