Heat Capacity and Calorimetry
Later measurement connection: interpret a calorimeter heat balance, capacity units and systematic errors.
Before this connection: Energy transfer and enthalpy: system boundaries and heat-transfer signs.
AP Chemistry Topic 6.4 · CED printed p. 115, 116 / PDF p. 122, 123. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- System and surroundings as a chosen boundary
- Moles, balanced equations and limiting reactants
- Intermolecular versus intramolecular interactions
- Activation energy versus overall energy change
For a sample heated or cooled without phase or chemical change, , with ΔT =Tfinal−Tinitial. Use the mass of the sample whose temperature you measured and the matching specific heat capacity. Celsius differences and kelvin differences are equal in size. Positive ΔT gives positive q for that sample. In a calorimeter, temperature is an indirect energy measurement, so record initial/final temperatures and the relevant mass, not just “it got warm.”
Energy conservation sets the heat balance. In an insulated constant-pressure reaction calorimeter, . If external heat loss matters, include it; omitting a sink makes a model incomplete. Cup heat is CcupΔT with Ccup in J °C−1, not a second mass factor. A reaction and its warming surroundings must have opposite heat signs.
Specific heat capacity c states energy per gram per degree. For the same positive q and equal masses, the material with larger c has the smaller temperature rise: ΔT =q/(mc). A large temperature change can therefore reflect a small heat capacity rather than a larger energy transfer. Compare q, mass, and c together before ranking “how much heat” was exchanged.
For a sample undergoing only heating/cooling, energy entering raises its thermal energy and energy leaving lowers it. The sign follows the named sample. In a reaction experiment, the solution can heat up while the reacting species lose chemical energy. This is why substituting a positive measured ΔT directly as positive reaction heat reverses the chemistry.
Molar heat capacity Cm uses moles rather than grams: q =nCmΔT. If molar mass is Mmolar in g mol−1, then Cm =cMmolar. The whole-sample heat capacity C =mc =nCm has units J °C−1. Keep specific, molar, and whole-sample capacities distinct so an extra mass or mole factor does not slip in.
Separate three contributions when several processes occur: sensible heating/cooling, phase transition, and chemical transformation. The first uses mcΔT, the second uses nΔHtransition, and the third uses reaction amount times ΔH for the balanced equation. A temperature rise alone accounts for the thermal response of the measured surroundings, not every change in the system. Segment a heating curve or a calorimeter model before adding terms.
For dissolution data, warming of the mixture indicates an exothermic dissolution under the chosen heat-balance model; cooling indicates endothermic dissolution. Real measurements need assumptions: solution c may differ from pure water’s, the cup can absorb heat, and heat can leak during the measurement. For an exothermic trial, ignoring cup heating or heat loss typically underestimates the magnitude of released heat, giving a calculated ΔH that is less negative. Replicates improve precision but do not automatically fix these systematic omissions. A temperature-time record can support extrapolation toward the mixing time to estimate a corrected rise; method assumptions must be stated.
Let's work through it
A supplied constant-pressure trial reacts 0.0200 mol of a limiting species. The 100.0 g solution warms by 2.50 °C; c =4.184 J g−1 °C−1 and cup capacity is 20.0 J °C−1. Assume no external heat loss and one mole of limiting species per reaction unit.
- qsolution =100.0×4.184×2.50 =1046 J. qcup =20.0×2.50 =50.0 J. Both surroundings terms are positive.
- qreaction =−(1046+50.0) =−1096 J =−1.096 kJ.
- ΔH per mol reacted =−1.096/0.0200 =−54.8 kJ mol−1. Ignoring the cup would give −52.3 kJ mol−1, a smaller release magnitude.
Give 100 J to 5.00 g of sample A with c =0.500 J g⁻¹ °C⁻¹; its molar mass is 40.0 g mol⁻¹.
- Whole-sample C =5.00×0.500 =2.50 J °C⁻¹, so ΔT =100/2.50 =40.0 °C.
- Molar Cm =0.500×40.0 =20.0 J mol⁻¹ °C⁻¹; n =0.125 mol. The molar equation gives 100/(0.125×20.0) =40.0 °C too.
- A same-mass sample with twice c rises only 20.0 °C for the same energy input. Heating raises each sample’s energy without equal temperature changes.
A supplied thermal record includes warming a solid, melting it, and then reacting the liquid at constant pressure.
- Use mcΔT for warming the intact solid.
- Use nΔHfus for melting at its fixed-temperature plateau.
- Use reaction extent times ΔHreaction for the chemical transformation; add signed transfers only after specifying the same complete system and conditions.
Make the picture move
Interactive concept model
Name the system before assigning the heat sign.
Predict first. A solution warms: which sign belongs to the solution, and which belongs to the chemical reaction? Change the recorded ΔT through zero, then include the cup.
q_solution = mcΔT; q_cup = C_cupΔT; q_reaction = −(q_solution + q_cup)
On a small screen, scroll inside the graph or diagram to read its labels. The values and explanation also appear below.
The solution warms by 5.0 °C: q_solution = 2.09 kJ and q_reaction = -2.09 kJ.
Read the data and comparisons
| Quantity | Value | Meaning |
|---|---|---|
| Solution mass | 100 g | All solution, not just solute |
| Specific heat | 4.184 J g⁻¹ °C⁻¹ | Water-like constant value |
| Cup heat capacity | 0 J °C⁻¹ | Cup heat = heat capacity × ΔT |
| Tinitial / Tfinal | 20.0 °C / 25.0 °C | Constructed data record |
| Reaction extent | 0.0500 mol | Per mole of reaction as written |
| q_solution + q_cup + q_reaction | 0 kJ | Ideal energy balance |
Macroscopic / data. A thermometer measures the solution temperature change.
Particle view. Temperature reflects the distribution of particle kinetic energies; energy can transfer between the reacting system and the solution.
Symbolic view. q_solution = (100 g)(4.184 J g⁻¹ °C⁻¹)(5.0 °C); ΔH = q_reaction/(0.0500 mol).
Why it works. The solution and cup are the calorimetric surroundings and the reacting chemical process is the system. A warming solution gains heat, so the reaction loses it. Divide reaction heat by the specified reaction extent only after choosing the system and converting J to kJ. A temperature difference has the same numerical size in kelvins and degrees Celsius. Ignoring positive cup heat capacity understates the magnitude of reaction heat for a fixed measured ΔT; heat loss to the room can also reduce the observed temperature rise.
Conditions and limits. Synthetic constant-pressure coffee-cup data, negligible heat exchange with the room, cup at the same initial/final temperature as the solution, only pressure–volume work, constant water-like specific heat. The default neglects cup heat capacity; the control can include it. Solution mass includes all mixed liquid. Initial temperature is 20.0 °C; reaction extent is fixed at 0.0500 mol. The sliders explore a recorded data set, not a laboratory procedure. q at constant pressure equals the reaction enthalpy under these assumptions.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
A sample cools from 30.0 to 20.0 °C. What is ΔT and q’s sign for that sample?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
A sample cools from 30.0 to 20.0 °C. What is ΔT and q’s sign for that sample?
Worked answer and reason
ΔT =−10.0 °C; with positive m and c, q is negative.
The sample transfers heat out.
Retrieval 2
What units distinguish c, Cm, and whole-sample C?
Worked answer and reason
c: J g⁻¹ °C⁻¹; Cm: J mol⁻¹ °C⁻¹; C: J °C⁻¹. Multiply by mass, moles, or neither, respectively.
Each capacity is normalized to a different amount.
Retrieval 3
Why does ignoring cup heating bias an exothermic ΔH toward zero?
Worked answer and reason
Some released energy warmed the cup. Counting solution heat alone misses it, underestimating the total heat released.
The heat balance must include every significant recipient.
Catch the tempting mistake
- Use q =mcΔT during the entire melting plateau.
- Temperature stays constant while phase energy changes; use nΔH for that segment.
- Cup capacity needs multiplication by solution mass.
- Ccup already represents whole-cup capacity, in J per degree.
- The same temperature rise always means the same q.
- Mass and heat capacity also determine energy transfer.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 6 problem 4 · ap synthesis · multiple
- Unit 6 problem 5 · ap application · multiple
- Unit 6 problem 6 · ap synthesis · verbal
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For the teacher
- Require one heat term for each modeled recipient and units on every capacity.
- Use measured precision and an explicit systematic-error direction, not a generic “human error” statement.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 6.4.A
- Calculate the heat q absorbed or released by a system undergoing heating/cooling based on the amount of the substance, the heat capacity, and the change in temperature.
- 6.4.A.1
- The heating of a cool body by a warmer body is an important form of energy transfer between two systems. The amount of heat transferred between two bodies may be quantified by the heat transfer equation: EQN: q = mcΔT. Calorimetry experiments are used to measure the transfer of heat.
- 6.4.A.2
- The first law of thermodynamics states that energy is conserved in chemical and physical processes.
- 6.4.A.3
- The transfer of a given amount of thermal energy will not produce the same temperature change in equal masses of matter with differing specific heat capacities.
- 6.4.A.4
- Heating a system increases the energy of the system, while cooling a system decreases the energy of the system.
- 6.4.A.5
- The specific heat capacity of a substance and the molar heat capacity are both used in energy calculations.
- 6.4.A.6
- Chemical systems change their energy through three main processes: heating/cooling, phase transitions, and chemical reactions.
- 6.4.A.7
- In calorimetry experiments involving dissolution, temperature changes of the mixture within the calorimeter can be used to determine the direction of energy flow. If the temperature of the mixture increases, thermal energy is released by the dissolution process (exothermic). If the temperature of the mixture decreases, thermal energy is absorbed by the dissolution process (endothermic).
Science references for this teaching
- College Board AP Chemistry Course and Exam Description, Fall 2024 — Exact unit learning requirements and exclusions; supplied PDF is pinned by the integration catalog.
- OpenStax Chemistry 2e: Energy Basics — Scientific check: system boundaries, energy conservation, thermal transfer and heat capacities.
- OpenStax Chemistry 2e: Calorimetry — Scientific check: heat-balance equations, calorimeter heat capacity, reaction/solution signs; newly authored numerical data.
Glossary and deeper reading · 9 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Mole
A mole is an amount of substance containing exactly 6.02214076 × 10²³ specified entities. The entities can be atoms, molecules, ions, or formula units, so the counted entity must be named. For example, one mole of oxygen molecules contains two moles of oxygen atoms.
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Limiting reactant
The limiting reactant is consumed first under the specified complete-reaction model and limits the product amount. Identifying it requires comparing available amounts with the balanced equation's ratios. For example, abundant hydrogen cannot produce more water after the available oxygen has been consumed.
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Activation energy
Activation energy is the energy barrier associated with a reaction pathway in an introductory energy-profile model. It concerns the pathway and is distinct from the reactant-to-product energy change. For example, a thermodynamically favored reaction can remain slow when its activation barrier is large.
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Specific heat capacity
Specific heat capacity is the heat required per unit mass for a one-unit temperature increase under stated conditions. It connects a mass and measured temperature change to heat transfer when the model applies. For example, water requires about 4.18 joules per gram for a one-kelvin temperature rise near room temperature.
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Heat capacity
Heat capacity is the heat required to raise a specified object's temperature by one temperature unit under stated conditions. It refers to the entire object and differs from specific heat capacity, which is expressed per unit mass. For example, doubling the amount of the same material approximately doubles its heat capacity.
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Molar mass
Molar mass is the mass of one mole of a specified substance. It is commonly expressed in grams per mole and connects a sample's mass to its amount of substance. For example, water has a molar mass of approximately 18.02 grams per mole.
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Phase change
A phase change alters a substance's physical state without changing its chemical identity. It involves a change in particle arrangement and interactions and can transfer energy without raising temperature during a pure-substance transition at fixed pressure. For example, vaporizing liquid water separates water molecules into a gas.
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Mixture
A mixture contains two or more substances whose proportions can vary. Its components retain their chemical identities until a chemical reaction changes them. For example, water and ethanol can form mixtures with many different compositions.
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Exothermic process
An exothermic process transfers heat from the chosen system to its surroundings. Under constant-pressure conditions with only pressure–volume work, its enthalpy change is negative. For example, freezing water releases heat to the surroundings.