Enthalpy change and calorimetry

IB Chemistry Higher Level· Topic 15: Energy· 15 min read

1. 1. Key Concepts: Enthalpy Change and Reaction Classification★★☆☆☆⏱ 5 min

📘 Definition

Enthalpy Change

$Δ H$

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.

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 $Δ H < 0$ . Endothermic reactions absorb heat from the surroundings, so $Δ H > 0$ . The sign convention is always required for full marks in exams.

📐 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 $Δ H$ .

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, $Δ H > 0$

✓ Quick check

Check your understanding of sign conventions

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
Reveal answer
Negative —
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. 2. Calorimetry Calculations★★★☆☆⏱ 6 min

✓ Calculator OK

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 $Δ T = T_{f ina l} - T_{ini t ia l}$ (°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: $Δ T = 24.5 - 18.0 = 6.5$ °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
$\Delta H = -\frac{2.717}{0.050} = -54.3 \text{ kJ mol}^{-1}$

3. 3. Error Analysis for Calorimetry★★★★☆⏱ 4 min

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.

📘 Definition

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 $Δ T$ 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 tip:

Always link the error source to the direction of change in the final result for full marks.

4. Common Pitfalls

Wrong move:

Forgetting the negative sign for exothermic reactions

Why:

Examiners routinely penalize missing signs, even if the magnitude is correct

Correct move:

Always confirm if temperature increased (exothermic, ΔH negative) or decreased (endothermic, ΔH positive) before writing your final answer

Wrong move:

Using volume instead of mass in $q = m c Δ T$

Why:

Specific heat capacity is defined per unit mass, so volume gives incorrect units and wrong results

Correct move:

Convert volume of solution to mass using the given density (usually 1 g cm⁻³ for aqueous solutions) before substituting into the formula

Wrong move:

Forgetting to convert q from J to kJ

Why:

This leads to ΔH being 1000 times larger than the correct value, a common calculation error

Correct move:

Always check units: divide q by 1000 to convert joules to kilojoules before calculating molar enthalpy

Wrong move:

Citing only random measurement error when explaining results

Why:

Examiners expect you to identify systematic experimental design errors, which are the main cause of deviation from accepted values

Correct move:

Focus on systematic errors like heat loss when asked to explain differences between experimental and accepted ΔH

5. Quick Reference Cheatsheet

Concept/Formula	Key Details	Exam Notes
$q = m c Δ T$	Heat change formula	$m$ = mass (g), $c = 4.18$ J g⁻¹ °C⁻¹ for water
$Δ H$ sign convention	Exo: $Δ H < 0$ , Endo: $Δ H > 0$	Always include the sign for full marks
Molar enthalpy formula	$Δ H = - \frac{q}{n}$	$n$ = moles of limiting reactant
M	a	i	n		s	y	s	t	e	m	a	t	i	c		e	r	r	o	r
H	e	a	t		l	o	s	s		t	o		s	u	r	r	o	u	n	d	i	n	g	s
M	e	a	s	u	r	e	d		$	\|	\	D	e	l	t	a		H	\|		<	$		a	c	c	e	p	t	e	d	$	\|	\	D	e	l	t	a	H	\|	$

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · Paper 2
Calculate enthalpy of neutralization
2023 · Paper 1
Error analysis of calorimetry
2021 · Paper 2
Enthalpy of combustion calculation

Going deeper

practical guideIB Chemistry calorimetry experimental guideFor practical assessment preparation