# Introduction to Enthalpy of Reaction

> AP Chemistry · AP Chemistry CED Unit 6
> Source: https://www.owlsprep.com/study/ap-chemistry-u6-introduction-to-enthalpy-of-reaction/

This core study guide aligns with AP Chemistry CED Unit 6, covering definitions of enthalpy and enthalpy of reaction, sign conventions, thermochemical equation interpretation, and stoichiometric scaling of ΔH.

**Prerequisites:** First law of thermodynamics; Heat transfer and temperature relationships; Balanced chemical reaction stoichiometry; [AP Chemistry Unit 6 Overview](https://www.owlsprep.com/study/ap-chemistry-u6-overview/)

## Learning objectives

- Define enthalpy and enthalpy of reaction, and explain ΔHᵣₓₙ = qₚ at constant pressure
- Apply correct sign conventions for endothermic and exothermic reactions from the system perspective
- Interpret thermochemical equations, including scaling ΔH and reversing reactions
- Calculate total heat transfer for reactions using stoichiometric proportionality of ΔH

## Core Definitions of Enthalpy and Enthalpy of Reaction

Enthalpy of reaction (abbreviated $\Delta H_{rxn}$) 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 foundational for all thermodynamic calculations in AP Chemistry Unit 6, which makes up 19-20% of total AP exam score.

**Enthalpy of Reaction** — The change in enthalpy of a system when a reaction proceeds to completion at constant pressure, equal to the heat gained or lost by the system.

*Notation:* $\Delta H_{rxn}$

*Example:* The enthalpy of reaction for combustion of 1 mol propane is -2220 kJ.

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. We can derive the key relationship used for all enthalpy of reaction calculations:

**Derivation:** Prove $\Delta H_{rxn} = q_p$ at constant pressure

*Starting from:* Definition of enthalpy and first law of thermodynamics

1. The change in enthalpy for any process is:

   $$\Delta H = \Delta U + \Delta(PV)$$
2. At constant pressure, $\Delta(PV) = P\Delta V$, so this simplifies to:

   $$\Delta H = \Delta U + P\Delta V$$
3. From first law, $\Delta U = q + w$, and pressure-volume work $w = -P\Delta V$. Substitute into the expression:

   $$\Delta H = (q - P\Delta V) + P\Delta V = q$$
4. At constant pressure, $q = q_p$, the heat of the process at constant pressure.

*Conclusion:* At constant pressure, $\Delta H_{rxn} = q_p$, meaning enthalpy change directly equals the heat transferred to or from the system.

> **Exam tip:** $\Delta H$ is only equal to $q$ at constant pressure, which is the standard condition for all enthalpy of reaction measurements tested on the AP exam.

## Sign Conventions for Endothermic/Exothermic Reactions

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 $\Delta H$ 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 $\Delta H$ corresponds to an exothermic process.

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

## Thermochemical Equations and Standard Enthalpy

**Thermochemical Equation** — A balanced chemical equation that includes the full reaction stoichiometry and the associated enthalpy of reaction for the reaction proceeding exactly as written.

When $\Delta H$ 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 $\Delta H^\circ_{rxn}$. Key AP-tested rules for working with thermochemical equations:

- $\Delta H$ is proportional to moles of reactant: if you multiply the entire balanced equation by a factor $n$, multiply $\Delta H$ by the same factor $n$
- If you reverse the reaction (swap products and reactants), reverse the sign of $\Delta H$; the magnitude remains identical
- $\Delta H$ 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: $\text{C}_3\text{H}_8(g) + 5\text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(l) \quad \Delta H^\circ_{rxn} = -2220 \text{ kJ/mol-rxn}$. What is $\Delta H^\circ$ for the combustion of 0.350 mol of propane, and what is $\Delta H^\circ$ for the reverse reaction (decomposition of CO₂ and water to form 1 mol of propane)?

1. The given $\Delta H^\circ$ is for 1 mol of propane reacting, as written. For 0.350 mol, multiply $\Delta H$ 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 $\Delta H$ and keep the magnitude the same for 1 mol of propane produced.
3. $\Delta H$ for the reverse 1 mol-rxn is $+2220 \text{ kJ/mol-rxn}$.

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

## Stoichiometric Calculations of Total Heat Transfer

The proportionality of $\Delta H_{rxn}$ 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 AP 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. 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: $\text{C}_3\text{H}_8(g) + 5\text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(l) \quad \Delta H^\circ_{rxn} = -2220 \text{ kJ/mol-rxn}$. 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 $\Delta H$ 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.

**Check your understanding**

Test your understanding of sign conventions:

1. 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 $\Delta H$ for this process (from the system perspective, the dissolution of NH₄NO₃) and what type of process is it?

   - ΔH < 0, exothermic
   - ΔH > 0, exothermic
   - ΔH < 0, endothermic
   - ΔH > 0, endothermic

   *Answer:* ΔH > 0, endothermic

   *Why:* 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, $\Delta H$ (equal to $q_p$ for the system at constant pressure) is positive. A positive $\Delta H$ is defined as an endothermic process.

> **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 $\Delta H$ if the question explicitly asks for the enthalpy change of the process.

## Common pitfalls

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

## Cheatsheet

| Category | Formula/Rule | Notes |
| --- | --- | --- |
| Enthalpy definition | $H = U + PV$ | State function; only changes in enthalpy (ΔH) are measured, absolute enthalpy cannot be measured |
| ΔH at constant pressure | $\Delta H_{rxn} = q_p$ | Only valid for constant pressure, the standard condition for most open reaction systems |
| Exothermic ΔH sign | $\Delta H < 0$ | System releases heat to surroundings; temperature of surroundings increases |
| Endothermic ΔH sign | $\Delta H > 0$ | System absorbs heat from surroundings; temperature of surroundings decreases |
| Scale ΔH with reaction size | $\Delta H_{\text{total}} = n \times \frac{\Delta H_{rxn}}{\text{coefficient}}$ | ΔH scales proportionally with moles of reactant or product consumed/formed |
| ΔH for reverse reaction | $\Delta H_{\text{reverse}} = -\Delta H_{\text{forward}}$ | Magnitude of ΔH stays identical, only sign changes when reversing a reaction |
| Standard enthalpy of reaction | $\Delta H^\circ_{rxn}$ | Measured at 1 atm pressure, 1 M concentration, 298 K (standard state conditions) |

## What's next

This topic 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 equilibrium and Gibbs free energy, where enthalpy change is required to calculate reaction favorability and spontaneous direction.

- [Bond Enthalpy](https://www.owlsprep.com/study/ap-chemistry-u6-bond-enthalpy/)
- [Enthalpy of Formation](https://www.owlsprep.com/study/ap-chemistry-u6-enthalpy-of-formation/)
- [Hess's Law](https://www.owlsprep.com/study/ap-chemistry-u6-hess-s-law/)

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