# Enthalpy change and calorimetry

> IB Chemistry Higher Level · R1: What drives chemical reactions?
> Source: https://www.owlsprep.com/study/ib-chemistry-hl-u4-enthalpy-change-and-calorimetry/

This module covers core thermochemical definitions for enthalpy change, explains how simple calorimetry measures heat energy changes, and teaches you to process data and evaluate common sources of error for IB exams.

**Prerequisites:** [Introduction to thermochemistry and energy changes](https://www.owlsprep.com/study/ib-chemistry-hl-r1-introduction-to-thermochemistry/)

## Learning objectives

- Define enthalpy change ($\Delta H$) and classify reactions as exothermic or endothermic
- Process raw calorimetry data to calculate molar enthalpy change
- Evaluate systematic and random errors in calorimetry experiments

## 1. Key Concepts: Enthalpy Change and Reaction Classification

**Enthalpy Change** — The total heat energy exchanged between a chemical system and its surroundings when a reaction occurs at constant pressure, reported per mole of reaction with units kJ mol⁻¹.

*Notation:* $\Delta H$

*Example:* Combustion of 1 mole of methane has an enthalpy change of -890 kJ mol⁻¹.

By IB convention, exothermic reactions release heat to the surroundings, so $\Delta H < 0$. Endothermic reactions absorb heat from the surroundings, so $\Delta H > 0$. The sign convention is always required for full marks in exams.

> **mnemonic**
>
> Exo = Exit: Heat exits the system, so ΔH is negative. Endo = Enter: Heat enters the system, so ΔH is positive.

**Worked example:** A reaction in a calorimeter causes the temperature of the surrounding water to drop from 25 °C to 19 °C. Classify the reaction and state the sign of $\Delta H$.

1. Relate temperature change to heat flow: The temperature of the surroundings (water) decreased, so heat left the surroundings and entered the reaction system.
2. Classify the reaction: A reaction that absorbs heat from the surroundings is endothermic.
3. State the sign of ΔH: By convention, endothermic reactions have positive ΔH.
4. Final answer: Reaction is endothermic, $\Delta H > 0$

**Check your understanding**

Check your understanding of sign conventions

1. Combustion of propane heats the calorimeter water from 21 °C to 68 °C. What is the sign of ΔH for combustion?

   - Negative
   - Positive
   - Zero
   - Cannot tell

   *Why:* Temperature of the surroundings increased, so the reaction released heat (exothermic), so ΔH is negative.

> **Exam tip:** Always state the sign of ΔH even if the question doesn't explicitly ask for it.

## 2. Calorimetry Calculations

Simple constant-pressure calorimetry relies on the conservation of energy: heat lost by the reaction equals heat gained by the surroundings (usually water or aqueous solution), assuming no heat loss to the environment. The core formula for heat change is:

$$q = m \times c \times \Delta T$$

Where $q$ = heat change (J), $m$ = mass of surroundings (g), $c$ = specific heat capacity of surroundings, and $\Delta T = T_{final} - T_{initial}$ (°C or K). For IB, $c = 4.18$ J g⁻¹ °C⁻¹ for water/solutions unless stated otherwise.

**Worked example:** 50.0 cm³ of 1.00 mol dm⁻³ HCl is mixed with 50.0 cm³ of 1.00 mol dm⁻³ NaOH in a calorimeter. Initial temperature = 18.0 °C, maximum final temperature = 24.5 °C. Calculate the molar enthalpy change of neutralization. Assume density = 1.00 g cm⁻³, $c = 4.18$ J g⁻¹ °C⁻¹.

1. Calculate total mass of solution: Total volume = 100.0 cm³, so $m = 100.0$ g (density = 1 g cm⁻³)
2. Calculate temperature change: $\Delta T = 24.5 - 18.0 = 6.5$ °C
3. Calculate total heat change $q$:
4. $$q = 100.0 \times 4.18 \times 6.5 = 2717 \text{ J} = 2.717 \text{ kJ}$$
5. Calculate moles of water formed: Moles of HCl = moles of NaOH = $1.00 \times 0.050 = 0.050$ mol, so 0.050 mol of water is produced.
6. Temperature increased, so reaction is exothermic (ΔH negative). Calculate molar enthalpy:
7. $$\Delta H = -\frac{2.717}{0.050} = -54.3 \text{ kJ mol}^{-1}$$

*Calculator:* allowed

## 3. Error Analysis for Calorimetry

IB exams frequently ask you to explain why experimental enthalpy values differ from accepted data. Most errors in calorimetry are systematic, meaning they consistently shift results in one direction, rather than random.

**Systematic Error** — A consistent, repeatable error that shifts all results in the same direction, caused by flaws in experimental design rather than random measurement mistakes.

- **Heat loss to surroundings/calorimeter**: Causes measured $\Delta T$ to be smaller than true value, so magnitude of ΔH is underestimated
- **Evaporation of water**: Removes heat from the calorimeter, leading to underestimated ΔT
- Ignoring heat absorbed by the calorimeter itself: The cup/thermometer absorb heat that is not counted in calculations, so ΔT is underestimated
- Incomplete reaction: If the reaction does not go to completion, the measured heat change is smaller than expected

**Worked example:** A student obtains an experimental enthalpy of combustion of ethanol of -820 kJ mol⁻¹, while the accepted value is -1368 kJ mol⁻¹. Explain the difference, and identify the main source of error.

1. Compare values: The magnitude of the experimental ΔH (820 kJ mol⁻¹) is smaller than the accepted value (1368 kJ mol⁻¹), meaning the measured ΔT was smaller than the true value.
2. Main source of error: Significant heat loss to the surroundings and the calorimeter container in an open experimental setup.
3. Justification: Heat that is released by combustion does not all reach the water in the calorimeter, so the temperature increase is smaller than expected. This leads to a smaller calculated q, hence a lower magnitude of ΔH.

**Exam command terms**

Common command terms for calorimetry have specific IB expectations:

- **Evaluate** — Discuss how sources of error affect your final result *(State if your value is higher/lower than accepted, then justify)*

- **Calculate** — Show all working steps, including units and the correct sign for ΔH

> **Exam tip:** Always link the error source to the direction of change in the final result for full marks.

## Common pitfalls

- **Wrong:** Forgetting the negative sign for exothermic reactions
  - Why it fails: Examiners routinely penalize missing signs, even if the magnitude is correct
  - Correct: Always confirm if temperature increased (exothermic, ΔH negative) or decreased (endothermic, ΔH positive) before writing your final answer
- **Wrong:** Using volume instead of mass in $q = mc\Delta T$
  - Why it fails: Specific heat capacity is defined per unit mass, so volume gives incorrect units and wrong results
  - Correct: Convert volume of solution to mass using the given density (usually 1 g cm⁻³ for aqueous solutions) before substituting into the formula
- **Wrong:** Forgetting to convert q from J to kJ
  - Why it fails: This leads to ΔH being 1000 times larger than the correct value, a common calculation error
  - Correct: Always check units: divide q by 1000 to convert joules to kilojoules before calculating molar enthalpy
- **Wrong:** Citing only random measurement error when explaining results
  - Why it fails: Examiners expect you to identify systematic experimental design errors, which are the main cause of deviation from accepted values
  - Correct: Focus on systematic errors like heat loss when asked to explain differences between experimental and accepted ΔH

## Cheatsheet

| Concept/Formula | Key Details | Exam Notes |
| --- | --- | --- |
| $q = mc\Delta T$ | Heat change formula | $m$ = mass (g), $c = 4.18$ J g⁻¹ °C⁻¹ for water |
| $\Delta H$ sign convention | Exo: $\Delta H < 0$, Endo: $\Delta H > 0$ | Always include the sign for full marks |
| Molar enthalpy formula | $\Delta H = -\frac{q}{n}$ | $n$ = moles of limiting reactant |

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