IB DP Chemistry Reactivity 1.1: Measuring enthalpy changes

This study guide teaches IB DP Chemistry Reactivity 1.1, “Measuring enthalpy changes”, starting from nothing. It is written against the IB Diploma Programme Chemistry guide (first assessment 2025, published February 2023), whose understandings Reactivity 1.1.1 to 1.1.4 each get a worked example here. The sub-topic has no additional higher level (AHL) content, so SL and HL learn identical material.

Afterwards, the revision notes give a one-sitting summary and the practice questions check your understanding. Temperature and particle kinetic energy belong to Structure 1, covered in the Structure 1 study guide. Plan your revision from the course hub and topic checklist, and spot weak areas with a free diagnostic.

Coverage at a glance

Understanding	You should be able to	SL / HL
Reactivity 1.1.1	Describe a reaction as energy moving between system and surroundings, with no energy created or destroyed; explain how heat differs from temperature	Both
Reactivity 1.1.2	Call a reaction exothermic or endothermic and predict whether the temperature goes up or down	Both
Reactivity 1.1.3	Use the relative stability of reactants and products to explain the sign of ΔH; sketch and read energy profiles	Both
Reactivity 1.1.4	Say what ΔH⦵ means; calculate ΔH from a temperature change using Q = mcΔT and ΔH = −Q/n	Both

Reactivity 1.1.1 Energy transfer, heat and temperature

Drawing the boundary

Chemists divide any change into two parts.

• The system is the set of chemicals taking part: the reactants as they turn into products.
• The surroundings are everything outside that: the solvent water, the cup, the thermometer, the bench and the air.

Energy can cross the boundary either way but is never created or lost: if the system gives out 3 kJ, the surroundings take in exactly 3 kJ.

Two different quantities

	Temperature	Heat
What it is	An indicator of how fast the particles move on average (their mean kinetic energy)	Energy that flows from hotter to cooler because of a temperature difference
Depends on amount of substance?	No	Yes
Unit	kelvin, K (or °C)	joule, J, or kilojoule, kJ

A bucket and a single drop of water, both at 30 °C, share one temperature, yet the bucket can give out far more heat as it cools because it has far more particles.

A change in temperature has the same number in kelvin and in degrees Celsius, since the two scales have the same step size. Warming from 16.0 °C to 21.5 °C is ΔT = 5.5 K. Only absolute temperatures need converting: T/K = t/°C + 273.15.

Worked example 1: one heat input, two temperature rises

Exactly 2.09 kJ of heat goes into 50.0 g of water. The same amount goes into a separate 250 g of water. Using c = 4.18 J g⁻¹ K⁻¹, find each ΔT.

Rearrange Q = mcΔT:   ΔT = Q / (m × c)

50.0 g:   ΔT = 2090 / (50.0 × 4.18) = 10.0 K
250 g:    ΔT = 2090 / (250 × 4.18)  = 2.00 K

Five times the mass gives one fifth of the rise, so equal heat need not mean equal temperature change.

Reactivity 1.1.2 Exothermic and endothermic reactions

The label depends only on which way energy crosses the boundary.

	Exothermic	Endothermic
Direction of energy transfer	From system to surroundings	From surroundings to system
Sign of ΔH	−	+
What the thermometer shows	Temperature goes up	Temperature goes down
Familiar cases	Burning fuels, acid + alkali, metals in acid	Heating calcium carbonate, dissolving ammonium nitrate, photosynthesis

The thermometer sits in the surroundings (usually the water). Energy released by the system warms the water; energy absorbed by the system comes from the water, which cools.

In practice, an exothermic mixture feels warm; an endothermic one feels cold and may gather condensation on the outside of the container.

Worked example 2: classifying from readings

Two mixtures each start at 19.5 °C. Dissolving solid X in water ends at 12.8 °C. Adding solid Y to dilute acid ends at 27.1 °C. Classify each and give the sign of ΔH.

X: ΔT = 12.8 − 19.5 = −6.7 K   water cooled → energy into system → endothermic, ΔH > 0
Y: ΔT = 27.1 − 19.5 = +7.6 K   water warmed → energy out of system → exothermic, ΔH < 0

ΔT and ΔH always have opposite signs.

Reactivity 1.1.3 Stability and energy profiles

Why some reactions give out energy

Whether a reaction is exothermic or endothermic comes down to the relative stability of reactants and products. The lower a substance’s potential energy (the chemical energy held in its bonds and structure), the more stable it is.

• Products more stable (lower potential energy) than reactants: the difference is given out, so the reaction is exothermic (ΔH < 0).
• Products less stable (higher potential energy): the difference must be taken in, so the reaction is endothermic (ΔH > 0).

The guide connects this to bonding with a puzzle: if most combustions release energy, why does nitrogen take in energy when it reacts with oxygen? The triple bond in N₂ is exceptionally strong, which makes N₂ very stable. The nitrogen oxide product therefore lies above the starting gases in potential energy.

Sketching an energy profile

An energy profile follows potential energy as reactants turn into products. The guide asks for the horizontal axis to be labelled reaction coordinate and the vertical axis potential energy.

Feature	Exothermic	Endothermic
Where the products sit	Lower than the reactants	Higher than the reactants
ΔH arrow	Downwards, reactants → products	Upwards, reactants → products
Ea arrow	Reactant level → peak	Reactant level → peak
Which side is more stable	Products	Reactants

A complete sketch shows:

1. both axes labelled as above;
2. a labelled reactant level and a labelled product level at the right relative heights;
3. one smooth curve rising to a peak (the transition state) between them;
4. a vertical ΔH arrow between the two levels, pointing from reactants to products;
5. a vertical activation energy, Ea, arrow starting at the reactant level and ending at the peak.

Worked example 3: taking values off a profile

On a profile, the reactant level is 40 kJ mol⁻¹, the peak is 125 kJ mol⁻¹ and the product level is 95 kJ mol⁻¹ (relative potential energies). Find ΔH and Ea and say which side is more stable.

ΔH = E(products) − E(reactants) = 95 − 40  = +55 kJ mol⁻¹  → endothermic
Ea = E(peak) − E(reactants)     = 125 − 40 = 85 kJ mol⁻¹

The reactants have the lower potential energy, so they are more stable.

Reactivity 1.1.4 Standard enthalpy change and calorimetry

Defining ΔH⦵

The enthalpy change, ΔH, of a reaction is the heat transferred between system and surroundings when the reaction happens at constant pressure. The standard enthalpy change, ΔH⦵, is the value for standard conditions, with each substance in its standard state. Standard pressure is 100 kPa, and tabulated values usually refer to 298 K. ΔH⦵ is given in kJ mol⁻¹, meaning per mole of the reaction as written in the balanced equation.

From temperature change to ΔH

Enthalpy cannot be read off an instrument. Instead, the reaction exchanges energy with a weighed amount of a pure substance (normally water), whose temperature change you measure. Then:

Q  = m × c × ΔT     Q in J; m = mass of water or solution (g);
                    c in J g⁻¹ K⁻¹; ΔT in K
ΔH = −Q / n         Q converted to kJ; n = moles of limiting
                    reactant (or of fuel burned)

According to the guide, both Q = mcΔT and the specific heat capacity of water appear in the data booklet. The standard value of c for water is 4.18 J g⁻¹ K⁻¹. A dilute aqueous solution is treated as if it were water: 1.00 cm³ weighs 1.00 g and has the same c.

Watch the minus sign. Q is the energy the water gains. A rise in temperature gives a positive Q, which is energy the system lost, so ΔH comes out negative.

Worked example 4: a metal reacting with acid

Into an insulated cup go 45.0 cm³ of 1.00 mol dm⁻³ hydrochloric acid and then 0.150 g of magnesium. The temperature climbs by 14.8 K at most. The reaction is Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g); the relative atomic mass of magnesium is 24.31. Find ΔH.

Which reactant runs out?
  n(Mg)  = 0.150 / 24.31     = 6.170 × 10⁻³ mol
  n(HCl) = 0.0450 dm³ × 1.00 = 0.0450 mol
  HCl required = 2 × 6.170 × 10⁻³ = 0.01234 mol  (< 0.0450)
  → magnesium is limiting

Q  = 45.0 g × 4.18 × 14.8 = 2784 J = 2.784 kJ
ΔH = −2.784 / (6.170 × 10⁻³) = −451 kJ mol⁻¹

Here m is the 45.0 g of solution, not the 0.150 g of metal.

Investigating combustion of fuels and foods

The guide suggests measuring combustion enthalpies of substances such as alcohols or foods. A liquid fuel burns in a spirit burner and a food sample on a mounted needle, each beneath a metal can of water. Weigh the burner (lid on) before and after, record the water’s mass and starting temperature, stir while heating, and note the highest temperature reached.

Worked example 5: methanol in a spirit burner

A burner loses 0.412 g of methanol, CH₃OH, while warming 150.0 g of water by 11.6 K. Find the enthalpy change of combustion and compare it with a data value of −726 kJ mol⁻¹.

M(CH₃OH) = 12.01 + 4(1.01) + 16.00 = 32.05 g mol⁻¹
n        = 0.412 / 32.05 = 0.01285 mol

Q  = 150.0 × 4.18 × 11.6 = 7273 J = 7.273 kJ
ΔH = −7.273 / 0.01285   = −566 kJ mol⁻¹

difference = (726 − 566) / 726 × 100 = 22 %

As usual, the measured value is less exothermic than the data value.

Why the temperature change is smaller than expected

The guide asks why calorimetry usually records a smaller ΔT than theory predicts. The main causes:

• energy escapes to the air instead of reaching the water, worst of all with an open flame;
• the can or cup and the thermometer warm up too, and that energy is left out of Q;
• the fuel burns incompletely, giving out less energy and leaving soot on the can;
• some fuel evaporates from the wick, so the mass loss overstates the fuel actually burned;
• products are not in their standard states (for example, water leaves as steam).

Allowing for heat loss with a graph

For a reaction in solution, read the thermometer every 30 seconds, starting a few minutes before mixing and carrying on for several minutes after. On the graph, the slow decline after the peak is fitted with a straight line, which is then extended back to the mixing time. Where it meets that time is the best estimate of the peak with no losses.

Suppose the start is 20.4 °C, the highest reading 26.8 °C and the extended line reaches 27.5 °C at the time of mixing. Use ΔT = 7.1 K rather than 6.4 K. The recorded value would make Q roughly 10 % too small.

Common errors

• Putting the mass of the metal, salt or fuel into Q = mcΔT. Use the mass of liquid that changed temperature.
• Dividing by the moles of a reactant in excess; the limiting reactant fixes the energy released.
• Dividing joules by moles, which makes ΔH a thousand times too big when the unit is kJ mol⁻¹.
• Leaving off the minus sign on an exothermic answer, or adding one when the water cooled.
• Labelling a profile’s axes “time” and “energy” instead of reaction coordinate and potential energy.

Where next

Lock in the definitions and methods with the revision notes, then work the practice set. Reactivity 1.2 then uses bond enthalpies and Hess’s law for reactions that cannot be measured directly. For exam technique across the course, read the exam preparation guide.

Official syllabus

International Baccalaureate Organization, Diploma Programme Chemistry guide, first assessment 2025 (published February 2023). Material on this page: Reactivity 1.1 (Measuring enthalpy changes).