Calculate enthalpy from experimental temperature changes
Use q = mcΔT and ΔH = −mcΔT/n to calculate reaction enthalpy from calorimetry data.
AS Level; Cambridge International Chemistry 9701, 2025–2027 syllabus. Report signs, states, units and significant figures consistently. Standard conditions use 298 K and 101 kPa in this syllabus. Written practice is self-checked
Before you begin
- Rearrange a formula, balance a chemical equation and use temperature differences.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
If the solution warms during an exothermic reaction, what is the sign of q for the solution?
What you will learn
- Calculate heat transfer using q = mcΔT
- Convert heat to molar reaction enthalpy
- Interpret the negative sign and the amount reacted
Temperature change estimates heat gained by the solution
Use q = mcΔT, where m is solution mass, c is specific heat capacity and ΔT is the temperature change. For water, c = 4.18 J g⁻¹ K⁻¹ (equivalently 4.18 J g⁻¹ °C⁻¹ for a temperature difference).
If the question supplies volume but not mass, use the stated density or an explicitly permitted approximation. Do not silently assume a solution's density or ignore the cup and heat loss unless the method says to do so.
Convert solution heat to reaction enthalpy per mole
The reaction and solution exchange heat. If the solution warms, it gained heat and the reaction released it, so q(reaction) = −q(solution). Divide by the amount n of reaction events or product specified by the thermochemical equation: ΔH = −mcΔT/n.
Convert joules to kilojoules if reporting kJ mol⁻¹, use the limiting amount when reactants are not in stoichiometric quantities, and preserve an appropriate number of significant figures.
Pause and explain
Why is ΔH = −mcΔT/n for heat gained by the solution?
Worked example
50.0 cm³ of 1.00 mol dm⁻³ HCl reacts with 50.0 cm³ of 1.00 mol dm⁻³ NaOH. The temperature rises 6.50 K. Assume density 1.00 g cm⁻³ and c = 4.18 J g⁻¹ K⁻¹. Find ΔHneut.
Show the worked solution
- Mass of solution = 100 g; q(solution)=100×4.18×6.50=2717 J.
- n(H₂O)=n(HCl)=0.0500 mol.
- ΔH=−2.717 kJ/0.0500 mol.
Answer ΔHneut = −54.3 kJ mol⁻¹.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A 100 g solution warms by 4.00 K. Using c = 4.18 J g⁻¹ K⁻¹, find q(solution).
Give me a hint
Use q=mcΔT and show the heat unit.
Compare my reasoning
- q = 100 × 4.18 × 4.00 J.
- Multiply mass, heat capacity and temperature difference.
- Report to three significant figures.
q(solution) = 1.67 × 10³ J = 1.67 kJ.
Look for these in your work
- Formula applied
- Temperature difference used
- Heat unit stated
0.0250 mol of a reaction releases 2.72 kJ. Calculate its molar reaction enthalpy.
Give me a hint
Released heat is negative for the reacting system; divide by reaction amount.
Compare my reasoning
- q(reaction)=−2.72 kJ.
- ΔH=−2.72/0.0250.
- Report kJ mol⁻¹.
ΔH = −109 kJ mol⁻¹.
Look for these in your work
- Sign for released heat
- Amount divided correctly
- Molar unit stated
Use the data: 50.0 cm³ of 1.00 mol dm⁻³ HCl reacts with 50.0 cm³ of 1.00 mol dm⁻³ NaOH; temperature rises 6.50 K; density is 1.00 g cm⁻³ and c=4.18 J g⁻¹ K⁻¹. Find ΔHneut.
Give me a hint
Find the mass and q of the mixed solution, then divide the reaction heat by moles of water formed.
Compare my reasoning
- Solution mass ≈100 g; q(solution)=100×4.18×6.50=2717 J.
- n(H₂O)=0.0500 mol for the 1:1 neutralisation.
- ΔHneut=−2.717/0.0500 kJ mol⁻¹.
ΔHneut ≈ −54.3 kJ mol⁻¹.
Look for these in your work
- Mass assumption applied
- Water amount from stoichiometry
- Opposite heat sign and molar division correct
Common mistakes
- Giving reaction ΔH the same sign as heat gained by solution
- Using cm³ directly as grams without a density assumption
- Dividing by total moles of acid plus alkali rather than moles of reaction
- Leaving ΔH in J when kJ mol⁻¹ is required
What can you explain now?
If the solution warms during an exothermic reaction, what is the sign of q for the solution?
Compare with the explanation
Positive
The solution gained heat from the reaction.
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Make it stick
How do the solution's heat and the reaction's molar enthalpy relate in a calorimetry experiment?
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