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General Chemistry I · Thermochemistry

Coffee-Cup Calorimetry (Constant-Pressure Calorimetry)

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On this page 7 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Key takeaway
  6. Study tools
  7. Sources & references

In 30 seconds

A coffee-cup calorimeter is a simple constant-pressure device: an insulated (often Styrofoam) cup with a lid, a thermometer, and usually a stirrer. Because it is open to the atmosphere, the reaction occurs at constant pressure, so the heat transferred equals the enthalpy change, ΔH = q_p. Most aqueous reactions — dissolving salts, acid–base neutralization, precipitation — are studied this way. The reaction's heat is measured indirectly: the solution (the surroundings) absorbs or releases heat, and the temperature change of that solution is converted to heat with q = mcΔT.

Why this matters

Coffee-cup calorimetry is the everyday workhorse of thermochemistry. It measures the enthalpy of dissolution (why some salts make instant cold packs and others make heat packs), neutralization reactions (relevant to titrations and acid–base chemistry), and many solution reactions whose ΔH values fill thermodynamic tables. It also gives students their first direct, hands-on link between a thermometer reading and a thermodynamic quantity.

The college version

Key Ideas

  • Constant pressure → q = ΔH. The measured heat is the enthalpy change of the reaction (with the sign flipped for the system).
  • The dilute solution behaves like water. For dilute aqueous solutions, mass = volume (density ≈ 1.00 g/mL) and c ≈ 4.184 J/(g·°C).
  • Total solution mass = mass of all reagents/solvent combined (not just water, though for dilute solutions the difference is negligible).
  • q_reaction = −q_solution. If the solution warms up, the reaction is exothermic (ΔH < 0); if the solution cools, the reaction is endothermic (ΔH > 0).
  • Molar enthalpy divides the heat by the moles of the limiting reactant to get kJ/mol.
  • Typical neutralization of a strong acid + strong base releases about −57 kJ per mole of water formed.

Equations and Variables

SymbolMeaningUnits
q_solutionHeat absorbed by the solutionJ
m_solutionTotal mass of solutiong
cSpecific heat of solution (≈ water)J/(g·°C)
ΔTT_final − T_initial of the solution°C
q_reactionHeat of the reactionJ
nMoles of limiting reactantmol
ΔHMolar enthalpy of reactionJ/mol or kJ/mol
  • q_solution = m_solution · c · ΔT
  • q_reaction = −q_solution
  • ΔH = q_reaction / n_limiting

How It Works

  1. Place a measured volume of reactant solution(s) in the insulated cup and record the initial temperature.
  2. Mix the reactants (add the second solution, or drop in the solid) and stir.
  3. Record the highest (or lowest) temperature reached — the final temperature.
  4. Compute ΔT, then q_solution using the total solution mass and c ≈ 4.184 J/(g·°C).
  5. Set q_reaction = −q_solution, then divide by moles of limiting reactant to get ΔH per mole.

The Styrofoam insulation minimizes heat exchange with the room, so essentially all the reaction's heat goes into warming (or cooling) the solution itself. Assumptions: no heat is lost to the surroundings, the solution's specific heat equals water's, and the calorimeter itself absorbs negligible heat.

Worked Example

50.0 mL of 1.00 M HCl and 50.0 mL of 1.00 M NaOH, both initially at 25.0 °C, are mixed in a coffee-cup calorimeter. The temperature rises to 31.9 °C. Calculate the molar enthalpy of neutralization.

Step 1 — Total solution volume and mass. 50.0 + 50.0 = 100.0 mL; with density 1.00 g/mL, m_solution = 100.0 g.

Step 2 — ΔT = 31.9 − 25.0 = 6.9 °C.

Step 3 — Heat absorbed by the solution:

q_solution = (100.0 g)(4.184 J/(g·°C))(6.9 °C) = 2887 J ≈ 2.89 kJ

Step 4 — Heat of the reaction (opposite sign):

q_reaction = −2.89 kJ (negative → exothermic)

Step 5 — Moles of limiting reactant. HCl: 0.0500 L × 1.00 M = 0.0500 mol; NaOH: 0.0500 mol (equal). n = 0.0500 mol.

Step 6 — Molar enthalpy:

ΔH = (−2887 J) / (0.0500 mol) = −57,740 J/mol = −57.7 kJ/mol

This matches the well-known value for strong acid–strong base neutralization (−57 to −58 kJ/mol). The negative sign confirms heat was released to the solution.

Common Confusions

  • Sign. The solution's ΔT gives q_solution. The reaction's heat has the opposite sign. Forgetting the flip is the most common error.
  • Which mass? Use the total solution mass (both solutions combined), not just one reactant's mass.
  • Molar vs. total. ΔH must be reported per mole of the limiting reactant. If the two reactants are not in stoichiometric ratio, find the limiting one first.
  • This is ΔH, not ΔE. Since it's open to the atmosphere (constant pressure), the measurement is enthalpy. The bomb calorimeter (next note) measures ΔE instead.
  • Heat lost to the cup/room. Real measurements are slightly off because some heat escapes; the simple calculation assumes perfect insulation.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Picture making a cup of hot cocoa. You pour warm milk into a Styrofoam cup — the cup keeps the heat in so your hands don't get burned and the cocoa stays hot. A coffee-cup calorimeter is the same idea, but for a chemical reaction. You mix two liquids in the insulated cup and watch the thermometer. If the thermometer goes up, the reaction is like a tiny heater — it pushed heat out into the liquid (exothermic). If it goes down, the reaction is like a tiny fridge — it pulled heat out of the liquid (endothermic). The cup is open to the air, so the pressure never changes, which is why we call this the "constant-pressure" setup. And the neat trick: we measure how much the water changed, then flip the sign to figure out what the reaction did.

Key takeaways

  • Coffee-cup = constant pressure = measures ΔH (not ΔE).
  • q_reaction = −q_solution.
  • For dilute solutions: density ≈ 1.00 g/mL, c ≈ 4.184 J/(g·°C).
  • Solution warms → exothermic (ΔH < 0); solution cools → endothermic (ΔH > 0).
  • Divide q by moles of limiting reactant to get kJ/mol.
  • Strong acid + strong base neutralization ≈ −57 kJ/mol H₂O.
  • Why does a coffee-cup calorimeter measure ΔH rather than ΔE?
  • If the solution temperature drops during a reaction, is ΔH positive or negative?
  • 25.0 mL of 1.0 M A and 25.0 mL of 1.0 M B react, warming the combined solution from 21.0 to 33.5 °C. Find q_reaction. (Assume d = 1.00 g/mL, c = 4.184 J/g·°C.)
  • In the same problem, if A is the limiting reactant, what is ΔH in kJ/mol?
  • Answers: (1) constant pressure means q = ΔH; (2) positive (endothermic); (3) m = 50.0 g, ΔT = 12.5 °C, q_solution = 50.0 × 4.184 × 12.5 = 2615 J, so q_reaction = −2.62 kJ; (4) n = 0.0250 mol, ΔH = −2615 J / 0.0250 mol = −104.6 kJ/mol.

Keep learning

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Practice General Chemistry I

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Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • Describe how a coffee-cup calorimeter works and what it measures.
  • Explain why constant-pressure calorimetry gives ΔH directly.
  • Calculate the heat of a solution reaction (dissolution, neutralization) from a measured temperature change.
  • Convert measured heat into molar enthalpy (ΔH per mole) using the limiting amount of reactant.

Sources & references

  1. OpenStax, *Chemistry 2e*, §5.2 Calorimetry (constant-pressure calorimetry).
  2. OpenStax, *Chemistry 2e*, §5.3 Enthalpy.
  3. NIST — heat capacity of water and standard reference data.

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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