DAT Organic Chemistry: Reading Reaction Coordinate Diagrams

DAT High-Yield Concept

Axes Interpretation: Y-axis measures free energy ( $G$ ) or enthalpy ( $H$ ); X-axis plots reaction coordinate (progress of reaction).
Peaks vs. Valleys: Local maxima (peaks) represent transition states; local minima (valleys) represent reaction intermediates.
Counting Steps: Number of peaks equals the number of elementary steps. Number of intermediates equals $\text{peaks} - 1$ .
Thermodynamics vs. Kinetics: Height from reactants to peak determines activation energy ( $E_a$ , kinetics); energy difference between products and reactants determines enthalpy change ( $\Delta H$ , thermodynamics).
Exothermic vs. Endothermic: Products lower in energy than reactants indicates an exothermic reaction ( $\Delta H < 0$ ); products higher in energy indicates an endothermic reaction ( $\Delta H > 0$ ).

Reaction Coordinate Axes & Energy Terms

A reaction coordinate diagram displays energy changes as reactants transform into products. The vertical axis (y-axis) tracks potential energy, enthalpy ( $H$ ), or Gibbs free energy ( $G$ ). The horizontal axis (x-axis) represents the reaction coordinate, tracing continuous structural changes such as bond elongation, bond cleavage, and bond formation.

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

Key energetic terms read directly from the y-axis include:

Activation Energy ( $E_a$ ): The energy difference between reactants and the highest-energy transition state in a step. It determines reaction rate (kinetics).
Enthalpy Change ( $\Delta H$ ): The difference in energy between products and reactants ( $\Delta H = H_{\text{products}} - H_{\text{reactants}}$ ). It determines reaction equilibrium (thermodynamics).

Transition States Versus Intermediates

Distinguishing transition states from intermediates is a core DAT skill tested on organic reaction mechanisms.

Transition states are peaks, intermediates are valleys — A transition state is the top of a hill: bonds are half broken and half formed, nothing rests there, and it can never be bottled or isolated. An intermediate sits in a valley between two hills, so it is a real molecule with a real lifetime that can often be detected or even trapped. Counting the peaks counts the steps: two peaks, two steps.

Reaction Coordinate Diagram: Starting material or reactant A convert to product C via the transition state B. (Source: AimNature · CC BY-SA 3.0 · Wikimedia Commons)

Transition State (TS): A local maximum (peak) representing an activated complex with partially broken and partially formed bonds. It has an infinitely short lifetime (approx.

\pu{10^{-13} s}

) and cannot be isolated.

Reaction Intermediate: A local minimum (valley) representing a real chemical species with fully formed covalent bonds. It has local thermodynamic stability and a finite lifetime, meaning it can often be detected spectroscopically or trapped.

Worked Example: Distinguishing Transition States and Intermediates

Problem: An organic reaction energy profile exhibits two local energy peaks at $\pu{95 kJ/mol}$ and $\pu{65 kJ/mol}$ , separated by a single energy dip at $\pu{40 kJ/mol}$ . How many transition states and intermediates are present?

Step-by-Step Reasoning:

Identify energy maxima (peaks): Each peak corresponds to one transition state. With 2 peaks, there are 2 transition states.
Identify energy minima (valleys): Each dip between peaks corresponds to a reaction intermediate. With 1 dip, there is 1 intermediate.

Answer: 2 transition states and 1 intermediate.

Common Exam Trap: Treating transition states as isolable molecules. Transition states sit at energy maxima with partial bonds, whereas intermediates reside in energy valleys with fully formed bonds.

Single-Step Versus Multi-Step Profiles

Reactions proceed via concerted (single-step) or stepwise (multi-step) pathways:

Single-Step Profile: Contains exactly 1 peak (1 transition state) and 0 intermediates. Bond breaking and formation occur simultaneously. Example: Concerted $\ce{S_N2}$ nucleophilic substitution: $\ce{CH3Br + HO^- -> CH3OH + Br^-}$ .

Multi-Step Profile: Contains multiple peaks separated by valleys (intermediates). Example: Unimolecular substitution ( $\ce{S_N1}$ ) involving heterolytic cleavage to form a carbocation intermediate $\ce{(CH3)3CBr -> (CH3)3C^+ + Br^-}$ , followed by nucleophilic capture $\ce{(CH3)3C^+ + H2O -> (CH3)3C-OH2^+}$ .

The double-headed arrow shows the rate determining step for each chemical transformation depicted in the reaction co-ordinate diagram (Source: AimNature · CC BY-SA 3.0 · Wikimedia Commons)

Worked Example: Profile Step Identification

Problem: A reaction profile starts at $\pu{30 kJ/mol}$ , reaches a peak at $\pu{80 kJ/mol}$ , drops to $\pu{50 kJ/mol}$ , reaches a second peak at $\pu{100 kJ/mol}$ , and ends at $\pu{10 kJ/mol}$ . Classify the profile as single-step or multi-step and determine the number of elementary steps.

Step-by-Step Reasoning:

Count total peaks: There are 2 peaks (at $\pu{80 kJ/mol}$ and $\pu{100 kJ/mol}$ ).
Number of elementary steps = number of peaks = 2 steps.
Because steps > 1, the reaction profile is multi-step.

Answer: Multi-step profile with 2 elementary steps and 1 intermediate.

Common Exam Trap: Confusing overall activation energy with step activation energy. The barrier for step 2 is $\pu{100 kJ/mol} - \pu{50 kJ/mol} = \pu{50 kJ/mol}$ , not $\pu{100 kJ/mol} - \pu{30 kJ/mol}$ .

Exothermic and Endothermic Profiles

Relative positions of reactant and product energy levels reveal reaction thermochemistry:

Exothermic (Exergonic) Profile: Products are lower in energy than reactants ( $\Delta H < 0$ ). Heat/free energy is released.
Endothermic (Endergonic) Profile: Products are higher in energy than reactants ( $\Delta H > 0$ ). Heat/free energy is absorbed.

Property	Exothermic Reaction Profile	Endothermic Reaction Profile
Relative Energy	$E_{\text{products}} < E_{\text{reactants}}$	$E_{\text{products}} > E_{\text{reactants}}$
Sign of $\Delta H$	Negative ( $\Delta H < 0$ )	Positive ( $\Delta H > 0$ )
Forward vs. Reverse Barrier	$E_{a,\text{fwd}} < E_{a,\text{rev}}$	$E_{a,\text{fwd}} > E_{a,\text{rev}}$
Transition State Nature

References

Sources returned by Google Search grounding during lesson verification.

6.6: Reaction Coordinate Diagrams - Chemistry LibreTexts — chem.libretexts.org
14.3 Reaction Mechanisms, Catalysts, and Reaction Coordinate Diagrams - Chad's Prep — chadsprep.com

Reading Reaction Coordinate Diagrams

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