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Enthalpy of formation

Formation enthalpies turn ΔH into simple arithmetic: look up a number for each compound, subtract reactants from products. The two things people forget are that elements count as zero and that the order is products minus reactants.

§1

Building compounds from elements.

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The standard enthalpy of formation, ΔHf°, is the enthalpy change when one mole of a compound forms from its elements in their standard states.

A key consequence: an element in its standard state has ΔHf° = 0 (forming it from itself requires no change). Only compounds have nonzero formation enthalpies.

A reaction's enthalpy then comes from a table of these values: ΔH = Σ ΔHf°(products) − Σ ΔHf°(reactants), with each term weighted by its coefficient. Products minus reactants — in that order.

UNIT 6 TOPIC 6.8 • ENTHALPY OF FORMATION FORMATION FROM ELEMENTS DEFINITION ΔH°f enthalpy change when 1 mole of a compound forms from its elements in their standard states An element in its standard state: ΔH°f = 0 REACTION CALCULATION ΔH°rxn = Σ nΔH°f(products) − Σ nΔH°f(reactants) Use the balanced coefficients as multipliers. Example — a formation reaction forms exactly 1 mole of the compound H₂(g) + ½O₂(g) → H₂O(l) ΔH°f [H₂O(l)] = −285.83 kJ/mol STANDARD STATE ≈ 1 bar, usually 25 °C — the pure substance in its most stable form at those conditions (e.g. O₂ gas, C as graphite). CED ANCHOR ENE-3 — Tabulated ΔH°f give a common zero baseline, so ΔH°rxn is found from products − reactants. TAKEAWAY Formation enthalpies (element ΔH°f = 0) let any reaction's ΔH° be computed as Σ products − Σ reactants, each scaled by its coefficient. AP Chemistry · Unit 6 · Thermodynamics
Fig. 6.8.1 The standard enthalpy of formation (ΔHf°) is the enthalpy change to form one mole of a compound from its elements in their standard states. Elements in their standard states have ΔHf° = 0. A reaction's ΔH is Σ ΔHf°(products) − Σ ΔHf°(reactants).
§2

Using formation enthalpies.

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Sum products, sum reactants, subtract in order.

  1. Look up each ΔH_f°. Find the formation enthalpy of each compound; elements in standard states are 0.
  2. Weight by coefficients. Multiply each ΔH_f° by its coefficient in the balanced equation.
  3. Sum products and reactants. Add the weighted values on each side.
  4. Subtract in order. ΔH = Σ products − Σ reactants (never the reverse).
§3

The pieces you'll meet.

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Elements are zero; products minus reactants.

ΔHf°
Formation enthalpy
Forming 1 mol of a compound from its elements.
elements
Elements = 0
Elements in standard states have ΔHf° = 0.
products − reactants
The formula
ΔH = Σ ΔHf°(products) − Σ ΔHf°(reactants).
coefficient
Coefficient weight
Each ΔHf° is scaled by its coefficient.
standard state
Standard state
The element's most stable form under standard conditions.
one mole
One mole
ΔHf° is defined per mole of compound formed.
§4

Worked example: use formation enthalpies.

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Reaction. Suppose products have ΔH_f° values summing (with coefficients) to −600 kJ, and reactants to −450 kJ. (Any element among them contributes 0.)

Apply the formula. ΔH = Σ products − Σ reactants = (−600) − (−450) = −150 kJ.

Order matters. Reversing to reactants − products would give +150 kJ — the wrong sign. Products minus reactants is the rule.

Elements. If O₂ or another element appeared, its ΔH_f° is 0 and it simply drops out of the sum.

§5

Mistakes that cost real points.

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Pitfall · 01

"Elements in their standard states have nonzero formation enthalpies."

By definition, an element in its standard state has ΔH_f° = 0 — forming it from itself involves no change. Assigning elements a nonzero value adds phantom energy and corrupts the reaction enthalpy.

Fix. Set every element in its standard state to ΔH_f° = 0; only compounds carry nonzero values.

Pitfall · 02

"ΔH = reactants − products."

The correct order is products minus reactants: ΔH = Σ ΔH_f°(products) − Σ ΔH_f°(reactants). Reversing the order flips the sign, turning an exothermic result endothermic and vice versa.

Fix. Always compute products minus reactants; do not reverse the order.

Pitfall · 03

"You can ignore the coefficients when summing formation enthalpies."

Each ΔH_f° must be multiplied by its coefficient in the balanced equation, because ΔH scales with amount. Two moles of a product contribute twice its formation enthalpy. Ignoring coefficients undercounts the energy.

Fix. Weight each formation enthalpy by its stoichiometric coefficient before summing.

§6

Skill Check.

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