Intuition The one core ideaA chemical reaction is nothing but pulling old bonds apart (which always costs energy) and snapping new bonds together (which always gives energy back). If the snapping gives back more than the pulling took, the leftover energy escapes as heat — and the whole topic is just carefully counting those two piles of energy.
This page assumes nothing . Before you touch the parent topic , every squiggle, arrow, and Greek letter it uses is built here from the ground up. Read top to bottom; each block earns the tools the next one needs.
Definition A bond = two atoms held togetherA bond is a link between two atoms that keeps them stuck to each other. On paper we draw it as a line between the atom letters: H − H C − H O = O
one line − single bond (one shared connection)
two lines = double bond (a stronger, tighter grip)
Think of two magnets stuck together. To separate them you must pull , and pulling takes effort. To let them snap back together, they do the work for you and you feel the click. That "effort to pull apart" vs "click when they snap" is the entire physics of this topic.
Intuition Why lines carry energyEvery line you draw is a little reservoir of stored energy. A double line (= −
Definition Heat given out or taken inWhen a reaction happens, energy either leaves (the beaker gets warm) or enters (the beaker gets cold). The amount of that heat, measured per one "batch" of the reaction, is what we are chasing.
We need a symbol for it. Chemists write it as Δ H
Δ H
The letter H enthalpy — think of it simply as the heat-energy content of the chemicals at constant pressure (the everyday open-beaker situation).
The triangle Δ "change in" — specifically (after) minus (before) .
So Δ H "the change in heat content" = −
Now the sign of that number tells a story:
Δ H
Δ H < 0 negative ): the products hold less energy than the reactants, so the leftover energy escaped as heat . The surroundings warm up. We call this exothermic (Greek exo = "out").Δ H > 0 positive ): the products hold more energy, so energy had to be pulled in from the surroundings, which cool down. We call this endothermic (endo = "in").
Recall Why the minus sign means "energy out"Energy leaving ::: the products keep less than the reactants had, so H products < H reactants Δ H = H final − H initial
See Exothermic vs Endothermic Reactions and Enthalpy and the First Law of Thermodynamics for the deeper story of H
A subscript is just a label hanging on Δ H which enthalpy change we mean. The parent note uses three:
Definition Reading the subscripts
Δ H r x n r x n reaction . So Δ H r x n the whole reaction . This is the prize we compute. Δ H X − Y specific bond (X bonded to Y). So Δ H C − H bond enthalpy (built in §4).Δ H f ∘ f formation and the little circle ∘ standard conditions (a fixed reference: 1 bar pressure, usually 298 K). This is a rival, more accurate method covered in Standard Enthalpy of Formation .
Common mistake Don't confuseΔ H r x n Δ H X − Y Δ H r x n Δ H X − Y always positive — see §4. They look similar but play opposite roles.
Definition What "mole" and "kJ/mol" mean
A mole is just a counting word for a fixed huge number of particles (like "dozen" means 12, "mole" means 6.02 × 1 0 23 per mole so the number doesn't depend on how big a scoop we took.
kJ = kilojoule = 1000 joules, the standard energy unit. So kJ/mol reads "kilojoules of energy per one mole of the thing."
Every bond value in the parent — C–H = 413, O=O = 498 — carries the hidden unit kJ/mol . It means: "break one mole of these bonds and you must supply this many kilojoules."
Common mistake Bare percent and unitsIn LaTeX always write energies with \text{kJ/mol} and never a bare percent sign — write ± 10% ± 10%
Now we can finally define the central quantity the parent leans on.
The bond enthalpy Δ H X − Y break one mole of the X − Y , with everything in the gas phase , splitting the molecule into free floating atoms:
X − Y ( g ) ⟶ X ( g ) + Y ( g ) , Δ H X − Y > 0
Let's unpack every piece of that line:
⟶ reaction arrow : "turns into." Left side = start, right side = end.( g ) phase label : this species is a gas . (Other labels: ( l ) ( s ) ( a q ) only defined for gases, because in liquids/solids extra sticking forces would muddy the number.The result is two separate atoms with no line between them — the bond is gone.
Intuition Why bond enthalpy is ALWAYS positiveBreaking a bond is like pulling those two magnets apart — you always have to put effort in . You never get energy for free by snapping something. So Δ H X − Y
Definition Why the tables say "average"A C–H bond in methane isn't identical to a C–H bond in ethanol — the neighbours tug slightly differently. So tables list an average over many molecules (C–H ≈ 413 kJ/mol). This is the root of why the whole method is only an estimate , good to about ± 10 40 Lewis Structures , and the leftover error partly from Resonance Energy .
The master equation stacks many bond energies together. To write that compactly we borrow one symbol.
Definition The sigma symbol∑ ∑ S ("sigma"), standing for Sum . It means "add up every item in the list that follows."
∑ Δ H bonds broken = ( first bond ) + ( second bond ) + ⋯ "the sum of all the bond enthalpies of bonds broken." Nothing fancier — it's just a instruction to total a column.
∑ ∑ Δ H broken = 4 × 413 = 1652 kJ/mol ∑
The parent takes a bold shortcut: it pretends every reaction first rips all reactants into loose atoms, then rebuilds the products. Real reactions don't do that — so why is the answer still right?
Definition State function (plain words)A quantity is a state function if its change depends only on where you start and where you finish , never on the route between. Enthalpy H
Intuition The mountain-height pictureYour altitude is a state function. Climb straight up or spiral around the mountain — the height gained is identical, because it only cares about start and end elevation. Δ H Δ H
Because enthalpy is a state function, the total Δ H Δ H This is Hess's Law , and it is the permission slip for the whole atomic-path trick.
So the plan:
Break everything in the reactants → cost + ∑ Δ H broken Build everything in the products → payback − ∑ Δ H formed Add the two — Hess's law guarantees this equals the real Δ H r x n
That is precisely the parent's master equation :
Δ H r x n = ∑ Δ H bonds broken − ∑ Δ H bonds formed
Alphabetical: B before F = the order you subtract. Breaking costs (comes first, positive); forming pays back (subtracted).
A bond = line between atoms
Double bond grips harder than single
Bond enthalpy delta H X-Y always positive gas phase
Delta means final minus initial
delta H = heat change of reaction
Negative exothermic Positive endothermic
Mole and kJ per mol units
Sigma means add up the list
Master equation broken minus formed
Enthalpy is a state function
Hess law any path allowed
Estimating delta H rxn from bond energies
Test yourself — cover the right side and answer out loud before revealing.
What does the triangle Δ "Change in" = final minus initial.
What does H The heat-energy content of the chemicals at constant pressure.
A negative Δ H Exothermic — energy leaves, surroundings warm up.
A positive Δ H Endothermic — energy is absorbed, surroundings cool.
What is a bond enthalpy Δ H X − Y The energy to break one mole of that bond, in the gas phase, into free atoms.
Why is bond enthalpy always positive? Breaking a bond always requires putting energy in — you never get energy free from breaking.
What phase label must all species carry for bond enthalpies to apply? Gas phase, ( g )
What does the symbol ∑ Add up every item in the list that follows.
What is a state function? A quantity whose change depends only on start and end, not the path taken.
Which law lets us use an imaginary atomic path? Hess's law (because enthalpy is a state function).
State the master equation in words. Δ H r x n
What does "kJ/mol" mean? Kilojoules of energy per one mole of the bond or reaction.
Why are tabulated bond enthalpies only averages? The same bond differs slightly between molecules, so tables average over many.
