Introduction to enthalpy of reaction — AP Chemistry Study Guide

For: AP Chemistry candidates sitting AP Chemistry.

Covers: Definition of enthalpy (H), enthalpy of reaction (ΔHᵣₓₙ), sign conventions for endothermic/exothermic reactions, ΔH = qₚ at constant pressure, thermochemical equation interpretation, and stoichiometric scaling of reaction enthalpy. Aligns with AP Chemistry CED Unit 6.

You should already know: First law of thermodynamics. Heat transfer (q) and temperature relationships. Balanced reaction stoichiometry.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Chemistry style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Introduction to enthalpy of reaction?

Enthalpy of reaction (abbreviated ΔHᵣₓₙ) is the change in enthalpy, a state function related to heat transfer, that occurs when a chemical reaction proceeds to completion under constant pressure — the most common reaction condition in open labs and biological systems. This topic is the foundational entry point for all thermodynamic calculations in AP Chemistry Unit 6, which makes up 19-20% of the total AP exam weight per the official CED. Enthalpy of reaction questions appear in both multiple-choice (MCQ) and free-response (FRQ) sections: MCQ typically test conceptual understanding and sign conventions, while FRQ require stoichiometric calculations and conceptual interpretation. Synonyms for enthalpy of reaction include heat of reaction and reaction enthalpy; it is called standard enthalpy of reaction when measured at standard state conditions. Unlike internal energy change ΔU, which accounts for both heat and pressure-volume work, ΔH directly gives the heat absorbed or released by the system at constant pressure, making it far more useful for most routine chemistry applications. This topic builds on first law basics and connects to all subsequent enthalpy calculation methods.

2. Enthalpy and Sign Conventions for Endothermic/Exothermic Reactions

Enthalpy (symbol $H$) is a state function defined as $H=U+PV$, where $U$ is internal energy, $P$ is pressure, and $V$ is volume of the system. The change in enthalpy for any process is therefore: $$\Delta H=\Delta U+\Delta (PV)$$ At constant pressure (the standard condition for enthalpy of reaction measurements, for reactions run in open containers), this simplifies to $\Delta H=\Delta U+P\Delta V$. From the first law of thermodynamics, $\Delta U=q+w$, and pressure-volume work $w=-P\Delta V$. Substituting gives the key relationship you must memorize: at constant pressure, the change in enthalpy of a reaction equals the heat gained or lost by the system ($\Delta H_{rxn}=q_p$).

By universal AP Chemistry convention, we always measure enthalpy change from the perspective of the system (the reaction itself), not the surroundings. This gives the standard sign rules:

• If $\Delta H_{rxn}<0$ (negative): the system releases heat to the surroundings = exothermic reaction.
• If $\Delta H_{rxn}>0$ (positive): the system absorbs heat from the surroundings = endothermic reaction.

Worked Example

When 1 mol of solid sodium hydroxide dissolves in water, the temperature of the water solution increases from 21.0 °C to 38.8 °C. From the perspective of the system (the dissolved NaOH), what is the sign of ΔH for this dissolution process, and is the process endothermic or exothermic?

1. The temperature change is measured in the surroundings (the water solution). The temperature increased, so the surroundings gained heat.
2. By conservation of energy, heat gained by the surroundings must have been released by the system (the NaOH dissolution process).
3. Since the system released heat, $\Delta H=q_p$ is negative for the system.
4. A negative ΔH corresponds to an exothermic process.

Final answer: ΔH is negative, process is exothermic.

Exam tip: Always double-check which perspective the question asks for. If the question asks for ΔH of the reaction (system), never reverse the sign even if the question focuses on temperature change of the surroundings.

3. Thermochemical Equations and Standard Enthalpy of Reaction

A thermochemical equation is a balanced chemical equation that includes the full stoichiometry of the reaction and the associated enthalpy of reaction for the reaction proceeding exactly as written. ΔHᵣₓₙ scales directly with the number of moles of reactants consumed, per the reaction stoichiometry. When ΔH is reported at standard state conditions (1 atm pressure, 1 M concentration for solutions, pure solids/liquids, typically 298 K), it is called the standard enthalpy of reaction, written $\Delta H_{rxn}^{\circ }$.

Key rules for working with thermochemical equations that are frequently tested on the AP exam:

1. ΔH is proportional to moles of reactant: if you multiply the entire balanced equation by a factor $n$, multiply ΔH by the same factor $n$.
2. If you reverse the reaction (swap products and reactants), reverse the sign of ΔH; the magnitude remains identical.
3. ΔH depends on the physical state of reactants and products, so you must always include $(s),(l),(g),(aq)$ phase notation for all species.

Worked Example

Given the thermochemical equation for combustion of propane: $${\text{C}}_3{\text{H}}_8(g)+5{\text{O}}_2(g)\to 3{\text{CO}}_2(g)+4{\text{H}}_2\text{O}(l)\Delta H_{rxn}^{\circ }=-2220\text{ kJ/mol-rxn}$$ What is ΔH° for the combustion of 0.350 mol of propane, and what is ΔH° for the reverse reaction (decomposition of CO₂ and water to form 1 mol of propane)?

1. The given ΔH° is for 1 mol of propane reacting, as written. For 0.350 mol, multiply ΔH by the mole factor: $\Delta H=0.350\text{ mol}\times (-2220\text{ kJ/mol})=-777\text{ kJ}$.
2. For the reverse reaction, reverse the sign of ΔH and keep the magnitude the same for 1 mol of propane produced.
3. ΔH for the reverse 1 mol-rxn is $+2220\text{ kJ/mol-rxn}$.

Final answers: ΔH for 0.350 mol combustion = -777 kJ; ΔH for reverse 1 mol-rxn = +2220 kJ.

Exam tip: Always confirm the physical states of all species when interpreting a thermochemical equation. Changing H₂O from liquid to gas changes the ΔH value for combustion reactions by more than 10%, so AP questions explicitly test recognition of mismatched states.

4. Stoichiometric Calculations of Total Heat Transfer

The proportionality of ΔHᵣₓₙ to moles of reactant or product allows us to calculate the total heat absorbed or released for any measured amount of reactant consumed, a common calculation on both MCQ and FRQ sections. The general formula for total heat $q$ is: $$q=n\times \frac{\Delta H_{rxn}}{\text{coefficient of the substance in the balanced equation}}$$ Where $n$ is the number of moles of the substance you are given. ΔHᵣₓₙ is reported per reaction event, as written in the balanced equation, so the coefficient accounts for how many moles of the substance are in that one reaction event. For problems that give mass of reactant instead of moles, first convert mass to moles using the substance's molar mass before applying the formula.

Worked Example

Using the propane combustion reaction: ${\text{C}}_3{\text{H}}_8(g)+5{\text{O}}_2(g)\to 3{\text{CO}}_2(g)+4{\text{H}}_2\text{O}(l)\Delta H_{rxn}^{\circ }=-2220\text{ kJ/mol-rxn}$. Calculate the total heat released when 10.0 g of propane is completely combusted. Molar mass of C₃H₈ is 44.1 g/mol.

1. Convert the given mass of propane to moles: $n_{{\text{C}}_3{\text{H}}_8}=\frac{10.0\text{ g}}{44.1\text{ g/mol}}=0.227\text{ mol}$.
2. In the balanced equation, the coefficient of C₃H₈ is 1, so each 1 mol of C₃H₈ corresponds to a ΔH of -2220 kJ.
3. Calculate total q: $q=0.227\text{ mol}\times \frac{-2220\text{ kJ}}{1\text{ mol}}=-504\text{ kJ}$.
4. The negative sign confirms heat is released by the system, so the total heat released is 504 kJ.

Final answer: 504 kJ of heat is released, $q=-504\text{ kJ}$.

Exam tip: If a question asks "how much heat is released", they expect a positive value for the magnitude, but always keep the correct negative sign for ΔH if the question explicitly asks for the enthalpy change of the process.

5. Common Pitfalls (and how to avoid them)

• Wrong move: Reversing the sign of ΔH because the question mentions the surroundings got hotter. Why: Students confuse system vs surroundings perspective; ΔH is always defined for the system by convention, not the surroundings. Correct move: Always assign sign based on the system: if heat leaves the system, ΔH is negative, regardless of what happens to the surroundings.
• Wrong move: Forgetting to change ΔH when multiplying a thermochemical equation to scale for a target amount of reactant. Why: Students treat ΔH as an invariant property of the reaction, not a proportional quantity that scales with moles. Correct move: Every time you multiply the entire equation by a factor, multiply ΔH by the exact same factor before using it in any calculation.
• Wrong move: Ignoring the physical states of reactants/products when using ΔH values. Why: Students assume ΔH is the same regardless of state, but enthalpy is different for solid, liquid, and gas phases of the same substance. Correct move: Always confirm every species has the correct phase notation in the thermochemical equation before using its ΔH value.
• Wrong move: Using ΔH given per 1 mol-rxn directly as the answer for a problem that gives a different mass/amount of reactant. Why: Students mix up ΔH per reaction event vs total heat for the given amount of reactant. Correct move: Always add an extra check: "Is my given amount of reactant equal to the coefficient in the balanced equation? If not, scale ΔH accordingly."
• Wrong move: Assigning a positive ΔH to combustion reactions because "burning produces heat". Why: Students associate "heat produced" with positive numbers, forgetting the convention is based on the system's energy change. Correct move: Memorize that all combustion reactions are exothermic, so ΔH is always negative for combustion.

6. Practice Questions (AP Chemistry Style)

Question 1 (Multiple Choice)

The dissolution of ammonium nitrate in water is the process used in instant cold packs for first aid. When ammonium nitrate dissolves, the temperature of the resulting solution drops significantly. What is the sign of ΔH for this process (from the system perspective, the dissolution of NH₄NO₃) and what type of process is it? A) ΔH < 0, exothermic B) ΔH > 0, exothermic C) ΔH < 0, endothermic D) ΔH > 0, endothermic

Worked Solution: The temperature of the solution (surroundings) decreases, meaning the surroundings lose heat. By conservation of energy, heat lost by the surroundings is gained by the system (the dissolution process). Since the system gains heat, ΔH (equal to qₚ for the system at constant pressure) is positive. A positive ΔH is defined as an endothermic process. This matches option D. Correct answer: D.

Question 2 (Free Response)

Iron reacts with chlorine gas to form iron(III) chloride according to the balanced thermochemical equation below: $$2\text{Fe}(s)+3{\text{Cl}}_2(g)\to 2{\text{FeCl}}_3(s)\Delta H_{rxn}^{\circ }=-399\text{ kJ/mol-rxn}$$ (a) A chemist reacts 5.00 g of solid Fe with excess Cl₂. Calculate the total enthalpy change for this reaction. Show your working. (b) Write the thermochemical equation for the formation of 1 mol of FeCl₃(s) from Fe(s) and Cl₂(g), and give the ΔH° for this reaction. (c) A student claims that the decomposition of 2 mol of FeCl₃(s) into Fe(s) and Cl₂(g) releases 399 kJ of heat. Is the student correct? Justify your answer.

Worked Solution: (a) Molar mass of Fe = 55.85 g/mol. Moles of Fe: $n_{\text{Fe}}=\frac{5.00\text{ g}}{55.85\text{ g/mol}}=0.0895\text{ mol Fe}$. From the balanced equation, 2 mol Fe gives ΔH = -399 kJ. Total ΔH: $\Delta H=0.0895\text{ mol Fe}\times \frac{-399\text{ kJ}}{2\text{ mol Fe}}=-17.9\text{ kJ}$. Final (a): $\Delta H=-17.9\text{ kJ}$

(b) Divide all coefficients and ΔH by 2 to get 1 mol of FeCl₃: $$\text{Fe}(s)+\frac{3}{2}{\text{Cl}}_2(g)\to {\text{FeCl}}_3(s)\Delta H^{\circ }=-199.5\approx -200\text{ kJ/mol}$$

(c) The student is incorrect. Decomposition is the reverse of the given formation reaction. For the reverse reaction, ΔH = +399 kJ, meaning the system absorbs 399 kJ of heat (it does not release heat). The student incorrectly kept the negative sign from the forward reaction for the reverse process.

Question 3 (Application / Real-World Style)

Burning methane from natural gas is the primary method of home heating in many regions. The thermochemical equation for complete combustion of methane is: $${\text{CH}}_4(g)+2{\text{O}}_2(g)\to {\text{CO}}_2(g)+2{\text{H}}_2\text{O}(l)\Delta H_{rxn}^{\circ }=-890\text{ kJ/mol}$$ An average-sized home requires 45,000 kJ of heat during a cold winter day. Assuming all heat from combustion is captured for heating (no energy losses), what mass of methane (in grams) must be burned to provide this amount of heat? Molar mass of CH₄ is 16.04 g/mol.

Worked Solution: Each mole of CH₄ releases 890 kJ of heat. Calculate moles of CH₄ required: $$n_{{\text{CH}}_4}=\frac{\text{Total heat required}}{{\text{Heat per mole CH}}_4}=\frac{45000\text{ kJ}}{890\text{ kJ/mol}}=50.56\text{ mol}$$ Convert moles to mass: $${\text{Mass CH}}_4=50.56\text{ mol}\times 16.04\text{ g/mol}=811\text{ g}$$ This result means approximately 0.8 kg (1.8 lbs) of methane is needed to heat an average home for one cold day, which aligns with real-world energy usage data.

7. Quick Reference Cheatsheet

8. What's Next

This chapter is the foundational prerequisite for all subsequent enthalpy calculation topics in AP Chemistry Unit 6. Without mastering sign conventions, proportional scaling, and thermochemical equation interpretation, you will not be able to correctly apply Hess’s law, calculate enthalpy from bond energies, or use standard enthalpies of formation to solve problems. Enthalpy of reaction is also the core concept that connects thermodynamics to later topics in Unit 7 (equilibrium) and Unit 9 (Gibbs free energy), where enthalpy change is required to calculate reaction favorability and spontaneous direction. Next you will learn specific methods to calculate ΔHᵣₓₙ for reactions that cannot be measured directly. Hess's Law and enthalpy cycles Bond enthalpy calculation of ΔHᵣₓₙ Standard enthalpies of formation Gibbs free energy and spontaneity