AP Chemistry · Lesson 2

Enthalpy of reaction

Know Know it

The enthalpy change, ΔH, is the heat a reaction absorbs or releases at constant pressure. ΔH < 0 means exothermic: the products are lower in energy than the reactants, and heat goes to the surroundings. ΔH > 0 means endothermic: the products are higher in energy, and heat comes in from the surroundings.

A thermochemical equation pairs a balanced equation with its ΔH, in kJ per mole of reaction as written. So ΔH works like a coefficient: CH₄ + 2O₂ → CO₂ + 2H₂O, ΔH = −890 kJ means 890 kJ is released for every 1 mol of CH₄ or every 2 mol of O₂ that react.

To find the heat for a given amount: change grams to moles, then multiply by (ΔH ÷ the coefficient of that substance). When two reactants are given, the limiting reactant sets the heat, just as it sets the product amount.

What changes to ΔH when you change an equation
Change to the equationEffect on ΔHExample
Multiply all coefficients by nMultiply ΔH by nA + B → C, −50 kJ becomes 2A + 2B → 2C, −100 kJ
Reverse the equationChange the sign of ΔHC → A + B, +50 kJ
Change a state, such as H₂O(l) to H₂O(g)ΔH changes by the heat of that phase changeMaking water vapor releases less heat than making liquid water

Worked example Easy

Methane burns: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), ΔH = −890 kJ. How much heat is released when 4.00 g of CH₄ (16.04 g/mol) burns?

  1. 3560 kJ
  2. 444 kJ
  3. 55.5 kJ
  4. 222 kJAnswer

How to solve it

  1. Moles: 4.00 g ÷ 16.04 g/mol = 0.2494 mol CH₄.
  2. ΔH is −890 kJ per 1 mol CH₄, so heat = 0.2494 × 890 = 222 kJ.
  3. The sign of ΔH tells you the heat is released.

Why each choice is right or wrong

  • A. Incorrect. 3560 kJ multiplies the mass in grams by 890 kJ; ΔH is per mole of CH₄, so grams must be changed to moles first.
  • B. Incorrect. 444 kJ multiplies by 2, using the coefficient of O₂; the heat goes with 1 mol of CH₄.
  • C. Incorrect. 55.5 kJ divides 890 kJ by the molar mass, which is the heat per gram, not the heat for 4.00 g.
  • D. Correct. 4.00 g ÷ 16.04 g/mol = 0.249 mol CH₄, and 0.249 mol × 890 kJ/mol = 222 kJ released.

Trap ΔH goes with the equation as written

A ΔH value belongs to the coefficients shown. If you double the equation, double ΔH; if you reverse it, change the sign. Divide by the coefficient of the substance you are given before multiplying by its moles.

Explain Explain it

Task verbs: calculate, explain

Explain a heat calculation by naming each conversion: grams to moles with the molar mass, moles to kilojoules with ΔH over the coefficient, and the sign that says whether heat is released or absorbed.

Worked example Medium

The thermite reaction is 2Al(s) + Fe₂O₃(s) → Al₂O₃(s) + 2Fe(s), ΔH = −852 kJ. A mixture holds 10.0 g of Al (26.98 g/mol) and 40.0 g of Fe₂O₃ (159.70 g/mol). How much heat is released when the reaction goes to completion?

  1. 316 kJ
  2. 158 kJAnswer
  3. 213 kJ
  4. 78.9 kJ

How to solve it

  1. Moles: 10.0 ÷ 26.98 = 0.3706 mol Al; 40.0 ÷ 159.70 = 0.2505 mol Fe₂O₃.
  2. Al needs 0.3706 ÷ 2 = 0.1853 mol Fe₂O₃; there is more than that, so Al is limiting.
  3. Heat = 0.3706 mol Al × (852 kJ ÷ 2 mol Al) = 158 kJ released.

Why each choice is right or wrong

  • A. Incorrect. 316 kJ uses 852 kJ per mole of Al; the equation has 2 Al, so the heat is 852 ÷ 2 = 426 kJ per mole of Al.
  • B. Correct. Al is limiting: 0.3706 mol Al needs only 0.1853 mol Fe₂O₃ of the 0.2505 mol present, and 0.3706 ÷ 2 × 852 = 158 kJ.
  • C. Incorrect. 213 kJ treats Fe₂O₃ as limiting, but 0.2505 mol Fe₂O₃ would need 0.501 mol Al, more than the 0.371 mol present.
  • D. Incorrect. 78.9 kJ divides the moles of Al by 2 twice; ΔH is for 2 mol Al, so divide by 2 only once.

Calculate Your turn

The reaction N₂(g) + 3H₂(g) → 2NH₃(g) has ΔH = −92 kJ. Calculate ΔH for the reaction 4NH₃(g) → 2N₂(g) + 6H₂(g), and explain each change you made to the original ΔH.

Write it, then compare. Nothing you type here is saved or graded.

Compare with a model answer

A full answer does this

  • Gives ΔH = +184 kJ
  • Explains that reversing the equation changes the sign of ΔH
  • Explains that doubling the coefficients doubles the size of ΔH

Model answer

ΔH = +184 kJ. The new equation is the original one reversed, so the sign of ΔH changes from negative to positive: +92 kJ. Its coefficients are also twice the original ones (4NH₃ instead of 2NH₃), so ΔH doubles: 2 × (+92 kJ) = +184 kJ.

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