Enthalpy & Calorimetry

The heat of a reaction, its sign, and how to measure it with nothing more than water and a thermometer.

High schoolIntro Gen ChemUni Year 1
⏱️ About 20 min

A hand-warmer packet gets hot on its own; an instant cold-pack turns icy the moment you snap it. Same idea, opposite direction — and a single number with a single sign captures which way a reaction's energy flows. That number is the enthalpy change, ΔH.

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The big idea: At constant pressure (an open beaker), the heat a reaction exchanges is its enthalpy change, ΔH. Exothermic reactions release heat (ΔH < 0); endothermic reactions absorb it (ΔH > 0). We measure that heat with calorimetry: q = mcΔT.
🎯 By the end, you'll be able to
  • Define enthalpy change ΔH as the heat exchanged at constant pressure
  • Assign the correct sign: exothermic ΔH < 0, endothermic ΔH > 0
  • Use q = mcΔT to calculate heat from mass, specific heat, and temperature change
  • Explain how a simple calorimeter turns a temperature rise into a measured ΔH
📎 Helpful to know first

Enthalpy: the heat of a reaction

Chemists rarely work in sealed rigid containers — we work in open flasks at the constant pressure of the atmosphere. Under those everyday conditions, the heat a reaction gives off or takes in is called the enthalpy change, written ΔH.

ΔH is the difference in stored chemical energy between products and reactants: ΔH = H(products) − H(reactants). If the products hold less energy than the reactants, the leftover energy is released as heat.

\[ \Delta H = H_{\text{products}} - H_{\text{reactants}} \;=\; q_p \]
At constant pressure, ΔH equals the heat exchanged, q_p. It's the energy of the products minus the energy of the reactants.
🔑 Exothermic vs endothermic — get the sign right
Exothermic: the reaction releases heat to the surroundings, which warm up. Products are lower in energy, so ΔH < 0 (negative). Endothermic: the reaction absorbs heat from the surroundings, which cool down. Products are higher in energy, so ΔH > 0 (positive). The cold-pack feels cold precisely because it is pulling heat out of your hand — that's endothermic, ΔH > 0.
⚠️ The sign trap
A beaker that feels hot is exothermic (ΔH negative — the system dumped heat into its surroundings). A beaker that feels cold is endothermic (ΔH positive — the system pulled heat from its surroundings). Students routinely flip these: "felt hot" does not mean "positive ΔH." Track the direction of heat flow, then read off the sign.

Measuring heat: q = mcΔT

How do we actually put a number on this heat? We let it flow into (or out of) a known mass of water and watch the thermometer. The heat needed to change a substance's temperature depends on three things: how much of it there is (mass, m), what it is (specific heat capacity, c), and how big the temperature change is (ΔT).

\[ q = m\,c\,\Delta T \]
q = heat (J); m = mass (g); c = specific heat capacity (J·g⁻¹·°C⁻¹); ΔT = T_final − T_initial (°C). For water, c = 4.18 J·g⁻¹·°C⁻¹.
✨ Specific heat, and why water rules the planet
Specific heat capacity (c) is the energy needed to raise 1 gram of a substance by 1 °C. Water's is unusually high — 4.18 J·g⁻¹·°C⁻¹ — so it soaks up a lot of heat for only a small temperature rise. That's why coastal climates are mild and why water is the go-to fluid inside a calorimeter.

The calorimeter

A calorimeter can be as simple as an insulated cup of water. Run the reaction in the water and, because the cup is insulated, essentially all the heat goes into (or comes from) the water. Measure the water's temperature change, plug it into q = mcΔT, and you've measured the reaction's heat. If the water warmed up, the reaction released heat (exothermic, ΔH < 0); if it cooled, the reaction absorbed heat (endothermic, ΔH > 0).

📝 Worked example: How much heat is needed to raise 50.0 g of water from 20.0 °C to 80.0 °C? (c_water = 4.18 J·g⁻¹·°C⁻¹)
  1. Find ΔT = T_final − T_initial = 80.0 − 20.0 = 60.0 °C.
  2. Write q = mcΔT = (50.0 g)(4.18 J·g⁻¹·°C⁻¹)(60.0 °C).
  3. Multiply: 50.0 × 4.18 = 209; then 209 × 60.0 = 12 540 J.
  4. Convert: 12 540 J = 12.54 kJ. q is positive because heat is added to the water.
✓ q = +12 540 J (12.54 kJ) absorbed by the water.
✏️ Practice: How much heat (in joules) is required to warm 250 g of water by 30.0 °C? Use c_water = 4.18 J·g⁻¹·°C⁻¹.
J
Solution
  1. q = mcΔT = (250 g)(4.18 J·g⁻¹·°C⁻¹)(30.0 °C).
  2. 250 × 4.18 = 1045.
  3. 1045 × 30.0 = 31 350 J (≈ 31.4 kJ).
✏️ Practice: Burning a snack under a calorimeter warms 500 g of water from 22.0 °C to 45.0 °C. How much heat (in joules) did the water absorb? (c_water = 4.18 J·g⁻¹·°C⁻¹)
J
Solution
  1. ΔT = 45.0 − 22.0 = 23.0 °C.
  2. q = mcΔT = (500 g)(4.18 J·g⁻¹·°C⁻¹)(23.0 °C).
  3. 500 × 4.18 = 2090; 2090 × 23.0 = 48 070 J (≈ 48.1 kJ).
  4. The water absorbed this heat, so the combustion is exothermic (ΔH < 0 for the reaction).

Check your understanding

1. An endothermic reaction has a ΔH that is…
Endothermic means the reaction absorbs heat, so the products end up higher in energy than the reactants: ΔH > 0 (positive).
2. A reaction runs in a beaker and the beaker turns noticeably cold. The reaction is…
A cold beaker means the reaction is pulling heat out of its surroundings — endothermic — so ΔH is positive. (Feeling hot would be exothermic, ΔH < 0.)
3. You add the same amount of heat to 100 g of water and to 200 g of water. Compared with the 100 g sample, the 200 g sample's temperature rise is…
From q = mcΔT with q and c fixed, ΔT ∝ 1/m. Doubling the mass halves the temperature change — more stuff to share the same energy among.
🔎 Related lessons
Previous: Energy, Heat & Work Next: Hess's Law Bond Energies
✅ Key takeaways
  • Enthalpy change ΔH is the heat a reaction exchanges at constant pressure: ΔH = H(products) − H(reactants).
  • Exothermic = releases heat, ΔH < 0. Endothermic = absorbs heat, ΔH > 0.
  • A beaker that feels hot is exothermic; one that feels cold is endothermic.
  • Heat is measured with q = mcΔT (c_water = 4.18 J·g⁻¹·°C⁻¹).
  • A calorimeter turns a water temperature change into a measured reaction heat.
➡️ Measuring ΔH directly is easy for a clean combustion — but many reactions are too slow, messy, or dangerous to run in a calorimeter. Hess's law is the clever workaround: build the ΔH you want out of reactions you can measure. That's next.
Want to test yourself on this? Try the Chemistry practice test →