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Heat capacity and calorimetry

To turn a thermometer reading into an amount of energy, you need two more things: how much stuff there is and how hard it is to heat. That is q = mcΔT, the workhorse of calorimetry.

§1

Heat from a temperature change.

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The heat absorbed or released by a substance is q = mcΔT: its mass (m), its specific heat capacity (c, how much energy raises one gram by one degree), and its temperature change (ΔT). All three are needed — a temperature change alone is not a heat.

Calorimetry uses this to measure a reaction's heat. In a coffee-cup calorimeter, the reaction's heat is transferred to the surrounding solution, and by conservation qrxn = −qsolution.

So you measure the solution's temperature change, compute q = mcΔT for the solution, and the reaction's heat is the negative of that. Heat released by the reaction warms the solution, and vice versa.

UNIT 6 TOPIC 6.4 • HEAT CAPACITY AND CALORIMETRY CALORIMETRY LAB COFFEE-CUP CALORIMETRY solution mass = m specific heat = c temperature change = ΔT HEAT CALCULATION qsolution = mcΔT qrxn = −qsolution Heat released by the reaction is absorbed by the solution, and vice versa. HEAT CAPACITY q = mcΔT same q and same m: larger c → smaller ΔT smaller c → larger ΔT water: c = 4.18 J·g⁻¹·°C⁻¹ specific heat: J/(g·°C) molar heat capacity: J/(mol·°C) CED ANCHOR Energy is conserved (first law). A calorimeter tracks where energy moves by measuring temperature change. TAKEAWAY Use q = mcΔT for temperature changes and qrxn = −qsolution for the reaction inside the cup. AP Chemistry · Unit 6 · Thermodynamics
Fig. 6.4.1 Calorimetry measures heat from a temperature change: q = mcΔT, using mass, specific heat, and temperature change. In a coffee-cup calorimeter, the heat released by the reaction equals the negative of the heat gained by the solution.
§2

Doing a calorimetry calculation.

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Use all three factors and the sign convention.

  1. Gather m, c, and ΔT. You need the mass, specific heat, and temperature change; a temperature change alone is insufficient.
  2. Compute q for the solution. q = mcΔT gives the heat absorbed by the solution.
  3. Apply the sign convention. The reaction's heat is the negative of the solution's: q_rxn = −q_solution.
  4. Interpret the sign. If the solution warmed, the reaction released heat (exothermic, q_rxn < 0).
§3

The pieces you'll meet.

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A short glossary for calorimetry.

q
Heat
Energy transferred; q = mcΔT.
m
Mass
How much substance; a factor in q.
c
Specific heat
Energy to raise one gram by one degree.
ΔT
Temperature change
Final minus initial temperature.
calorimeter
Calorimeter
Device measuring heat via temperature change.
q_rxn
Reaction heat
Equals −q_solution by conservation.
§4

Worked example: heat of a reaction.

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Data. A reaction in a coffee-cup calorimeter warms 100. g of solution (c ≈ 4.18 J/g·°C) by 5.0 °C.

Solution heat. q_solution = mcΔT = (100.)(4.18)(5.0) = 2090 J absorbed by the solution.

Reaction heat. q_rxn = −q_solution = −2090 J.

Interpret. The negative sign means the reaction released heat (exothermic), which is why the solution warmed. Note you needed the mass and specific heat, not just the 5.0 °C rise.

§5

Mistakes that cost real points.

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Pitfall · 01

"A temperature change tells you the heat directly."

Heat depends on mass and specific heat as well as the temperature change: q = mcΔT. The same temperature rise in different amounts or substances corresponds to different heats. A temperature change alone is not a quantity of heat.

Fix. Always use all three factors — mass, specific heat, and ΔT — to get the heat from a temperature change.

Pitfall · 02

"Heat and temperature are interchangeable in calorimetry."

They are not. The thermometer reads temperature; the heat is computed from it via q = mcΔT. Two substances can reach the same temperature having absorbed very different amounts of heat.

Fix. Distinguish the measured temperature change from the calculated heat; convert with q = mcΔT.

Pitfall · 03

"The reaction heat and the solution heat have the same sign."

They are equal and opposite: q_rxn = −q_solution. If the solution absorbs heat (warms, positive q), the reaction released it (negative q). Mixing up the sign gives the wrong endo/exothermic conclusion.

Fix. Apply q_rxn = −q_solution: the reaction's heat is the negative of the solution's.

§6

Skill Check.

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