Visual walkthrough — Physical vs chemical change

Parent: Physical vs Chemical Change

The parent note told you the punchline: physical changes cost a little energy, chemical changes cost a lot. Here we build that number from nothing, in pictures. By the end you will understand why the ratio is roughly 20-to-1, not by memorising it, but by seeing what gets pulled apart in each case.

We assume you know nothing except that matter is made of tiny particles. Everything else we draw.

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Step 1 — What a molecule actually is (two kinds of "stickiness")

WHAT: Look at the figure. A single water molecule is one big oxygen ball (red) with two small hydrogen balls (blue) stuck to it. The lines inside the molecule — call them bonds — are the strong glue. The faint dotted lines between two molecules are the weak glue.

WHY draw this first: Before we can say "physical breaks the weak glue, chemical breaks the strong glue," you need to see that these are two separate things living in the same picture. Every symbol we introduce later ($\Delta H$, "bond energy") will point at one of these two glues.

PICTURE:

Hold this picture. Physical change will only ever touch the dotted lines. Chemical change reaches inside and snaps a solid line.

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Step 2 — Energy: what "kJ/mol" is really measuring

WHAT: We introduce the symbol $\Delta H$ (read "delta-H"). The Greek letter $\Delta$ (delta) just means "change in" — the difference between after and before. $H$ is the heat content of the stuff. So:

$\Delta H=H_{\text{after}}-H_{\text{before}}$

• $H_{\text{after}}$ ::: heat content after the change (glue broken).
• $H_{\text{before}}$ ::: heat content before (glue intact).
• $\Delta H>0$ ::: you had to put energy in (pulling apart costs work). This is our whole story — breaking glue always costs.

WHY this tool and not just "energy": We use $\Delta H$ — a difference — because we never care about the absolute heat content of matter (nobody can measure that). We only ever care how much the glue-breaking shifted it. A difference is measurable; an absolute is not. That is why the $\Delta$ symbol exists.

What is "per mol"? A mole (mol) is just a counting word, like "dozen" but huge: it means $6.02\times 10^{23}$ particles. We say "kJ per mole" so we can compare glues fairly — energy per identical bunch of particles.

PICTURE:

The taller the bar, the harder the pull. Keep this "bar height = pull strength" image; every number below is a bar.

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Step 3 — Physical change: pull the dotted lines only

WHAT: Watch water boil. Liquid water molecules cling by dotted hydrogen bonds. Heating gives them enough jiggle to break free into gas:

${\text{H}}_2\text{O}(l)\stackrel{\Delta H_{\text{vap}}}{\to }{\text{H}}_2\text{O}(g)$

• ${\text{H}}_2\text{O}(l)$ ::: liquid water — molecules close, dotted glue engaged.
• ${\text{H}}_2\text{O}(g)$ ::: gas water — same molecules, now flying free.
• $\Delta H_{\text{vap}}$ ::: the energy to break the dotted glue (vap = vaporisation). The solid O–H lines are untouched — notice the molecule is identical on both sides.

The measured cost:

$\Delta H_{\text{vap}}({\text{H}}_2\text{O})=40.7\text{kJ/mol}$

WHY it's this small: Each dotted hydrogen bond is worth about $20\text{kJ/mol}$, and in liquid water each molecule holds roughly two of them that must be broken to escape:

$2\times 20\text{kJ/mol}\approx 40\text{kJ/mol}✓$

• $20$ ::: strength of one hydrogen bond (a dotted line).
• $2$ ::: number of those you must cut for one molecule to leave.

Our simple picture already predicts the real number. That is the payoff of Step 1's distinction.

PICTURE:

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Step 4 — Chemical change: reach inside and snap a solid line

WHAT: Decompose water into hydrogen gas and oxygen gas:

$2{\text{H}}_2\text{O}(l)⟶2{\text{H}}_2(g)+{\text{O}}_2(g)$

• Left side (reactants): two water molecules.
• Right side (products): brand-new molecules — hydrogen gas and oxygen gas. The atoms rearranged. These are not water anymore.

To do this you must break the solid O–H bonds. The energy to break one such bond is its bond dissociation energy, symbol $D$:

$D(\text{O–H})\approx 463\text{kJ/mol}$

• $D$ ::: the pull needed to snap one solid O–H line — the strong glue from Step 1.
• $463$ ::: notice this dwarfs the $20$ of a dotted line.

Each water molecule has two O–H solid lines, so tearing one water molecule apart costs:

$2\times 463=926{\text{kJ per mole of H}}_2\text{O}$

• $2$ ::: two O–H lines inside each water molecule.
• $926$ ::: the full "reach inside" bill.

WHY so much bigger: A solid bond is two electrons shared and squeezed between the nuclei — a deep, tight grip. A dotted force is just a faint pull between the outsides of separate molecules. Deep grip ≫ faint pull.

PICTURE:

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Step 5 — The ratio: put the two bars side by side

WHAT:

$\frac{\text{Chemical}}{\text{Physical}}=\frac{926\text{kJ/mol}}{40.7\text{kJ/mol}}\approx 23$

• Numerator $926$ ::: solid-line cost (Step 4).
• Denominator $40.7$ ::: dotted-line cost (Step 3).
• $\approx 23$ ::: chemical change costs roughly twenty-plus times more.

WHY it lands near 20–100: Every physical change breaks dotted glue ($\sim$10–40 kJ/mol) and every chemical change breaks solid glue ($\sim$400–800 kJ/mol). Divide those ranges and you always get a factor of tens. The parent note's "10× to 100×" is not a coincidence — it is the ratio of the two glue strengths from Step 1.

PICTURE:

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Step 6 — Edge case: sublimation (solid straight to gas, still physical)

WHAT:

${\text{CO}}_2(s)\stackrel{\Delta H_{\text{sub}}}{\to }{\text{CO}}_2(g),\Delta H_{\text{sub}}\approx 25\text{kJ/mol}$

• ${\text{CO}}_2(s)$ and ${\text{CO}}_2(g)$ ::: same molecule both sides — the O=C=O solid lines are untouched.
• $\Delta H_{\text{sub}}$ ::: energy to break only the dotted dispersion glue between CO₂ molecules.
• $25$ ::: a small bar — clearly in dotted-line territory, not the $799\text{kJ/mol}$ it would cost to break a solid C=O bond.

WHY it's still physical: The number itself tells you which glue broke. $25$ sits with the dotted lines, so no molecule was altered → physical. This is the edge case where "a violent-looking change" is still physical — trust the energy bar, not the drama.

PICTURE:

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Step 7 — Degenerate case: zero net glue broken (dissolving sugar)

WHAT: For sucrose dissolving:

$\Delta H_{\text{soln}}\approx -5\text{ to }+5\text{kJ/mol}$

• $\Delta H_{\text{soln}}$ ::: net heat change on dissolving — the tiny leftover after old dotted glue lost and new dotted glue gained roughly balance.
• Near $0$ ::: no solid lines touched at all — sucrose (${\text{C}}_{12}{\text{H}}_{22}{\text{O}}_{11}$) leaves the water exactly as it entered.

WHY it matters: This is the "$\Delta H\approx 0$" degenerate case. Even no net energy change is still physical, because the criterion is did a solid line break? — and here none did. Evaporate the water and identical sugar crystals return.

PICTURE:

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The one-picture summary

One flowchart, one rule: which glue broke?

Recall Feynman retelling — say it back in plain words

Matter has two kinds of glue. One is dotted: a weak pull holding whole molecules to their neighbours. The other is solid: a strong grip holding atoms inside a single molecule. When you melt, boil, sublimate, or dissolve, you only ever tug the dotted glue apart — the molecules survive intact, so it's a physical change, and it's cheap: tens of kilojoules per mole. When you burn, rust, or bake, you reach inside a molecule and snap a solid line — atoms rearrange into brand-new molecules, so it's a chemical change, and it's expensive: hundreds of kilojoules per mole. Divide the two prices and you get a factor of about twenty. That single factor is the whole difference between "changed its shape" and "changed what it is."

Recall Quick self-check

The dotted line is the intramolecular bond. True or false? ::: False — the dotted line is the intermolecular force (between molecules). The solid line is the intramolecular bond. Sublimation of dry ice costs 25 kJ/mol. Physical or chemical? ::: Physical — 25 kJ/mol is dotted-glue territory; the C=O solid bonds (799 kJ/mol) stay intact. Why is the chemical/physical energy ratio always tens, not just 2? ::: Because solid bonds (~400–800) are inherently tens of times stronger than dotted forces (~10–40); dividing those ranges always lands in the tens.

Related vault notes: States of Matter · Chemical Reactions · Energy in Chemistry · Conservation of Mass · Molecular Structure · Identification of Substances