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I-12: Calorimetry and thermochemical energy

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Module I-12 · Recommended before: Before heat and reaction enthalpy

Calorimetry and thermochemical energy

Heat calculations combine a temperature difference with mass and specific heat. Signs distinguish heat entering and leaving a system.

Learn the method

q = m c ΔT; ΔE = q + w

  1. Find final temperature minus initial temperature.
  2. Compute q = mcΔT.
  3. Report energy in J or kJ.
  4. For calorimetry, use conservation of energy to relate system and surroundings.
  5. Apply the proper sign convention.

Common mistake: A positive temperature change gives positive heat for the warmed water; the reacting system may have the opposite sign.

Worked example

Problem: Find q for 50.0 g water warming from 20.0 to 30.0 °C; c = 4.184 J/(g·°C).

Step-by-step solution: q = (50.0)(4.184)(10.0) = 2.09 × 10³ J absorbed by the water.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Expansion work

A gas expands by 2.00 L against 1.00 atm: w = −PextΔV = −2.00 L·atm ≈ −203 J, using 101.325 J per L·atm.

Hess’s law

Reversing a reaction changes the sign of ΔH; multiplying its balanced equation by 2 doubles ΔH. Add the transformed enthalpies after cancellation.

Enthalpy of formation

Calculate ΔH°rxn by adding coefficient-weighted standard enthalpies of formation for products and subtracting the analogous reactant total. Retain signs and kJ/mol units.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. Calculate heat for 50 g water warming by 25 °C; c=4.184 J/(g·°C).
Hint for question 1

Heat uses the temperature change, not the final temperature.

Question 2. Calculate heat for 60 g water warming by 5 °C; c=4.184 J/(g·°C).
Hint for question 2

Heat uses the temperature change, not the final temperature.

Question 3. Calculate heat for 70 g water warming by 10 °C; c=4.184 J/(g·°C).
Hint for question 3

Heat uses the temperature change, not the final temperature.

Question 4. Calculate heat for 80 g water warming by 15 °C; c=4.184 J/(g·°C).
Hint for question 4

Heat uses the temperature change, not the final temperature.

Question 5. Calculate heat for 90 g water warming by 20 °C; c=4.184 J/(g·°C).
Hint for question 5

Heat uses the temperature change, not the final temperature.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

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