You're staring at a graph with a couple of curved lines, some labels like ΔG‡ and ΔG°, and maybe a reaction coordinate arrow at the bottom. And you're wondering: what am I actually looking at?
Free energy diagrams show up everywhere — general chemistry, biochemistry, physical chemistry, even materials science. But most people don't. They're one of those things professors assume you just get after seeing them twice. They memorize the shapes for the exam and move on But it adds up..
Here's the thing: once you actually understand what the axes mean and what the peaks and valleys represent, these diagrams become one of the most useful tools in your mental toolkit. You can look at a reaction and see why it's slow, why it's favorable, whether a catalyst helps, and where the bottleneck is.
Let's walk through it properly.
What Is a Free Energy Diagram
At its core, a free energy diagram — sometimes called a reaction coordinate diagram or energy profile — is a plot of Gibbs free energy (G) versus the progress of a reaction. The horizontal axis isn't time. On the flip side, it's not distance. It's reaction coordinate, a vague but useful concept that tracks the transformation from reactants to products through all the intermediate geometries That's the whole idea..
Most guides skip this. Don't.
The vertical axis is Gibbs free energy, usually in kJ/mol or kcal/mol. Lower is more stable. Higher is less stable Small thing, real impact. Took long enough..
Reactants sit on the left. Products sit on the right. In between? That's where it gets interesting.
The key features you'll see every time
Reactants and products — their relative vertical positions tell you ΔG° for the overall reaction. If products are lower, the reaction is exergonic (spontaneous under standard conditions). If they're higher, it's endergonic. Simple.
Transition states — the peaks. Each peak represents a high-energy, unstable arrangement of atoms that exists for a fraction of a picosecond. You can't isolate a transition state. It's not an intermediate. It's the top of the hill.
Intermediates — the valleys between peaks. These are real, detectable species (sometimes). They have finite lifetimes. They're local minima on the energy surface.
Activation free energy (ΔG‡) — the vertical distance from a stable species (reactant or intermediate) to the next transition state. This is what controls rate. Not the overall ΔG°. The barrier height That's the whole idea..
Single-step vs. multi-step
A one-step reaction has one peak. On top of that, three steps? Three peaks, two valleys. Two steps? Two peaks and one intermediate valley. The number of peaks equals the number of elementary steps.
This is where a lot of students get tripped up. And only the highest transition state relative to the starting material determines the overall rate. " Nope. They see a diagram with two humps and think "two transition states, so two rate-determining steps.The others matter for other reasons — selectivity, intermediate buildup, catalyst design — but not for the overall rate constant.
Why It Matters / Why People Care
You might be thinking: okay, it's a graph. Why do I keep seeing it in every chemistry class since freshman year?
Because thermodynamics tells you if a reaction happens. Kinetics tells you how fast. And free energy diagrams show you both on the same plot The details matter here..
The ΔG° vs. ΔG‡ confusion
This is the single biggest misconception. Students see a reaction with a large negative ΔG° and assume it's fast. They see a positive ΔG° and assume it's impossible. Neither is true No workaround needed..
Diamond turning into graphite has a negative ΔG°. It's thermodynamically favorable. But the activation barrier is enormous. Plus, at room temperature, it's effectively frozen. Your engagement ring isn't turning into pencil lead anytime soon.
Conversely, some reactions with positive ΔG° can be driven forward by coupling, concentration changes, or continuous removal of products. The diagram doesn't change — but the conditions do Took long enough..
Catalysts only lower peaks
A catalyst provides an alternative pathway with lower activation barriers. That's why the reactants and products stay at the same energy. On the diagram, you see new peaks that are lower than the uncatalyzed ones. The equilibrium constant doesn't change. On top of that, δG° doesn't change. Only the rate changes.
This is why enzymes are so powerful. They stabilize transition states — not intermediates, not reactants — transition states. The diagram makes this visual: the peak drops, the valley might shift, but the endpoints are fixed Practical, not theoretical..
Selectivity lives in the differences
Two competing pathways from the same intermediate? Consider this: the diagram shows you exactly which product forms faster. Plus, lower barrier = major product. Even if the other product is more stable (lower on the diagram), if its barrier is higher, you get kinetic control.
People argue about this. Here's where I land on it.
This is why reaction conditions matter. Low temperature, short reaction time — you trap the kinetic product. High temperature, long time — the system equilibrates to the thermodynamic product. Day to day, the diagram doesn't change. Your position on it does And that's really what it comes down to. But it adds up..
How to Read One Like a Pro
Don't just look at the shape. Ask questions. Every feature on that graph answers something.
Start with the endpoints
Where are reactants? Where are products? What's ΔG°? Is it negative? By how much? A ΔG° of -5 kJ/mol is barely favorable. -50 kJ/mol is strongly favorable. The magnitude matters for equilibrium position Practical, not theoretical..
Count the peaks
Each peak = one elementary step. On top of that, if you're proposing a mechanism, your diagram must match the number of steps. Three peaks but you only wrote two steps? Your mechanism is wrong Small thing, real impact. Simple as that..
Find the highest transition state
Measure from the starting reactants to each peak. In practice, the tallest one? That's your rate-determining step (RDS). Not the step with the highest barrier from its own intermediate — the highest absolute barrier from reactants And that's really what it comes down to. Turns out it matters..
This trips people up constantly. Step 1 has ΔG‡ = 80 kJ/mol. Step 2 has ΔG‡ = 60 kJ/mol from its intermediate, but that intermediate sits at +40 kJ/mol. So the absolute barrier for step 2 is 100 kJ/mol. On top of that, step 2 is rate-determining. The diagram makes this obvious if you measure from the bottom left.
Check for intermediates
Are there valleys? How deep? That said, a shallow valley means a short-lived intermediate. A deep valley means a stable intermediate that might accumulate, be isolated, or cause side reactions Less friction, more output..
If an intermediate is lower than reactants, the first step is exergonic. If it's higher, the first step is endergonic — and that intermediate will be present in tiny amounts at equilibrium.
Look at the reverse barriers
The barrier for the reverse reaction is just the forward barrier minus ΔG° for that step. If a step is highly exergonic, its reverse barrier is huge. That step is essentially irreversible. This matters for mechanism — you can't assume microscopic reversibility if the reverse barrier is 150 kJ/mol.
Common Mistakes / What Most People Get Wrong
I've graded hundreds of exams with free energy diagram questions. The same errors show up every time.
Mistake 1: Confusing transition states with intermediates
Transition states are maxima. You cannot have an intermediate at a peak. Intermediates are minima. You cannot have a transition state sitting in a valley. This sounds obvious until you're drawing one under time pressure.
Mistake 2: Drawing the RDS as the highest peak from its intermediate
As explained above — measure from reactants. Now, always from reactants. The rate-determining step is the one with the highest absolute activation energy.
Mistake 3: Assuming ΔG° determines rate
$\Delta G^\circ$ tells you about the equilibrium—how much product you'll have once the reaction is finished. It says nothing about how fast you'll get there. This leads to a reaction can be incredibly favorable ($\Delta G^\circ = -200 \text{ kJ/mol}$) but still take a thousand years to occur if the activation energy ($\Delta G^\ddagger$) is too high. Conversely, a reaction can be slightly unfavorable but occur instantly if the barrier is negligible. Never use the "downhill" nature of the overall reaction to justify its speed.
Mistake 4: Neglecting the "Energy Debt" of endergonic steps
Students often look at a multi-step mechanism and see a massive downhill drop at the end, assuming the reaction is easy. They forget that if an intermediate sits at a very high energy level, the system must "pay" a massive energy tax to reach it. Even if the final product is stable, the bottleneck created by that high-energy intermediate or its preceding transition state dictates the reality of the reaction kinetics.
Mistake 5: Misinterpreting "flat" regions
If you see a very shallow valley or a nearly flat plateau between two peaks, don't assume there is no intermediate. It simply means the intermediate is highly reactive and sits very close in energy to the transition states. In these cases, the "intermediate" might be a transient species that exists for only a vibration or two, but it is still conceptually distinct from the transition state.
Summary Checklist
When you are presented with a free energy diagram, do not just glance at it. Run through this mental checklist to ensure you aren't falling into the common traps:
- Thermodynamics: Compare the energy of the reactants to the products. Is the overall reaction exergonic or endergonic?
- Kinetics: Find the highest point on the entire graph relative to the starting material. That is your bottleneck.
- Mechanism: Count the peaks to ensure they match the number of elementary steps described.
- Stability: Identify the valleys to locate intermediates and assess their relative stability.
- Reversibility: Look at the height of the peaks relative to the products to see if the reverse reaction is even a physical possibility.
Mastering free energy diagrams is about moving beyond seeing "lines on a graph" and starting to see a physical map of molecular struggle. Every peak is a hurdle the molecules must jump, and every valley is a resting place. If you can read the map, you can predict the behavior of the chemistry Simple, but easy to overlook. Simple as that..
