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 Most people skip this — try not to. Still holds 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 Most people skip this — try not to..
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. Think about it: 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.
Quick note before moving on Simple, but easy to overlook..
The vertical axis is Gibbs free energy, usually in kJ/mol or kcal/mol. Consider this: lower is more stable. Higher is less stable It's one of those things that adds up..
Reactants sit on the left. Day to day, 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 Easy to understand, harder to ignore..
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 The details matter here..
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 Most people skip this — try not to. Surprisingly effective..
Single-step vs. multi-step
A one-step reaction has one peak. Two steps? Two peaks and one intermediate valley. Three steps? Three peaks, two valleys. The number of peaks equals the number of elementary steps Which is the point..
This is where a lot of students get tripped up. " Nope. They see a diagram with two humps and think "two transition states, so two rate-determining steps.Only the highest transition state relative to the starting material determines the overall rate. The others matter for other reasons — selectivity, intermediate buildup, catalyst design — but not for the overall rate constant Small thing, real impact..
Quick note before moving on.
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. Consider this: kinetics tells you how fast. ** And free energy diagrams show you both on the same plot Took long enough..
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.
Diamond turning into graphite has a negative ΔG°. It's thermodynamically favorable. But the activation barrier is enormous. 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 Turns out it matters..
Catalysts only lower peaks
A catalyst provides an alternative pathway with lower activation barriers. On the diagram, you see new peaks that are lower than the uncatalyzed ones. Day to day, the reactants and products stay at the same energy. ΔG° doesn't change. Day to day, the equilibrium constant doesn't change. Only the rate changes.
This is why enzymes are so powerful. So 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.
Selectivity lives in the differences
Two competing pathways from the same intermediate? On top of that, lower barrier = major product. The diagram shows you exactly which product forms faster. Even if the other product is more stable (lower on the diagram), if its barrier is higher, you get kinetic control Practical, not theoretical..
This is why reaction conditions matter. Low temperature, short reaction time — you trap the kinetic product. Which means high temperature, long time — the system equilibrates to the thermodynamic product. The diagram doesn't change. Your position on it does.
How to Read One Like a Pro
Don't just look at the shape. Think about it: ask questions. Every feature on that graph answers something.
Start with the endpoints
Where are reactants? Also, what's ΔG°? By how much? In real terms, a ΔG° of -5 kJ/mol is barely favorable. On the flip side, is it negative? That said, where are products? Worth adding: -50 kJ/mol is strongly favorable. The magnitude matters for equilibrium position Most people skip this — try not to..
Count the peaks
Each peak = one elementary step. If you're proposing a mechanism, your diagram must match the number of steps. In practice, three peaks but you only wrote two steps? Your mechanism is wrong And that's really what it comes down to. Less friction, more output..
Find the highest transition state
Measure from the starting reactants to each peak. 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.
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. Consider this: step 2 is rate-determining. The diagram makes this obvious if you measure from the bottom left.
Check for intermediates
Are there valleys? A shallow valley means a short-lived intermediate. How deep? A deep valley means a stable intermediate that might accumulate, be isolated, or cause side reactions Took long enough..
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. On top of that, if a step is highly exergonic, its reverse barrier is huge. On the flip side, 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 a transition state sitting in a valley. You cannot have an intermediate at a peak. Intermediates are minima. 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. On the flip side, 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. Here's the thing — 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.
Quick note before moving on The details matter here..
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. That's why 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 And it works..
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 It's one of those things that adds up..
