Lessons · Thermochemistry

How much heat? Burning methane and the energy ledger

Machine-checked — balanced, charge-conserved, extent-verified by ChemKernel Formation enthalpies data-sourced (openstax-chemistry-2e) 4 modeling assumptions (disclosed)

A burner burns 0.80215 g of methane (CH₄) in 3.83976 g of oxygen. The reaction goes to completion, and the heat released is measured. Which reactant runs out first, and how much heat does this burn actually release?

Heat of reaction q exothermic

-44.5 kJ

q = ΔH_rxn × ξ · q < 0 ⇒ heat released

Limiting reagent

CH₄

Left over

O₂ 20 mmol

Reaction enthalpy — model-exact (Hess's law) ΔH_f° sourced (openstax-chemistry-2e) each ΔH_f° is a sourced measurement; ΔH_rxn is their ν-weighted sum, and the heat scales with the extent

Species	signed ν	ΔH_f° (kJ/mol)	ν·ΔH_f°
$\mathrm{CH_{4}}$ (g) reactant	−1	-74.6	74.6
$\mathrm{O_{2}}$ (g) reactant	−2	0 (element → 0)	0
$\mathrm{CO_{2}}$ (g) product	+1	-393.51	-393.51
$\mathrm{H_{2}O}$ (l) product	+2	-285.83	-571.66
ΔH_rxn = Σ ν·ΔH_f° (products − reactants)			-890.57

-890.57 kJ/molΔH_rxn, per mole of reaction

0.05 molextent ξ (capped by CH₄)

-44.5 kJq, the heat of reaction

ΔH_rxn is per mole of reaction (one "run" of the balanced equation). This burn advances only ξ = 0.05 mol before the limiting reagent runs out, so q = -44.5 kJ — it releases 44.5 kJ, not 890.57 kJ. Elements in their standard state have ΔH_f° = 0 (they are the reference level, not zero energy).

Molecular equation — what you combine

\mathrm{CH_{4}}\,\text{(g)} + 2\,\mathrm{O_{2}}\,\text{(g)} \rightarrow \mathrm{CO_{2}}\,\text{(g)} + 2\,\mathrm{H_{2}O}\,\text{(l)}

There are no ions in solution here — every species is molecular (or a free element), so the complete-ionic and net-ionic equations would just repeat the molecular one. A reaction only has an ionic equation when strong electrolytes dissolve into ions.

Verification Every claim below was proven at build time — not asserted.

✓ Atoms balance across the equation [conservation matrix]
✓ Charge balances (net ionic re-verified) [charge row]
✓ Units cancel through the dimensional chain [units engine]
✓ No amount goes negative — extent is physical [nonnegative-extent guard]

✗ Common misconception: “ΔH_rxn for burning methane is −890.57 kJ/mol, so this burn releases 890.57 kJ of heat.”

ΔH_rxn = -890.57 kJ/mol is the heat per mole of reaction — for exactly one "run" of the balanced equation. The actual heat is q = ΔH_rxn × ξ, and the extent ξ = 0.05 mol is capped by the limiting reagent (CH₄). So this burn releases -44.5 kJ, not 890.57 kJ. The energy tracks the extent, exactly as the species amounts do — it is the ledger's other column.

Modeling assumptions — author-asserted, disclosed not discharged

model The combustion goes to completion — every mole of the limiting reagent that can react, does.
model Enthalpy is a state function, so ΔH_rxn depends only on the substances, not the path — this is Hess's law, and it lets ΔH_rxn be built from standard enthalpies of formation.
model The standard enthalpies of formation apply at these conditions (298.15 K, constant pressure) and are treated as temperature-independent over the range.
model The water product is liquid (its ΔH_f° = −285.83 kJ/mol); if it left as vapor the reaction would release less heat.

Concepts in this lesson

Linked into the Chemical Atlas where an entry exists; the rest fill in as the Atlas grows.

Practice this

The lesson goes deep on one scenario; the gym builds fluency by repetition. Drill these:

Calorimetry: q = m·c·ΔT →