AP Chemistry: Calorimetry and Heat Transfer (q = mcΔT)

AP Chemistry – Calorimetry and Heat Transfer (q = mcΔT)

AP Chemistry Study Guide: Calorimetry and Heat Transfer (q = mcΔT)

What This Is

Calorimetry is the science of measuring heat transfer during physical or chemical changes. On the AP exam, you’ll use q = mcΔT to calculate heat absorbed or released by a substance, often in lab-based scenarios (e.g., coffee-cup calorimetry). This concept is critical for understanding thermodynamics, reaction enthalpies, and energy flow in systems. Real-world example: A historical use of calorimetry was Antoine Lavoisier’s 18th-century experiments measuring heat from animal respiration (using guinea pigs in an ice calorimeter!) to study metabolism—proving that respiration is a form of combustion.

Key Terms & Concepts

• Heat (q): Energy transferred between objects due to a temperature difference. Measured in joules (J) or calories (cal).
• Specific heat capacity (c): The amount of heat required to raise 1 g of a substance by 1°C. Units: J/(g·°C) or J/(g·K).
• Example: Water has a high specific heat (4.18 J/g·°C), which is why oceans regulate Earth’s climate.
• q = mcΔT: The formula for heat transfer.
• q = heat (J)
• m = mass (g)
• c = specific heat capacity (J/g·°C)
• ΔT = temperature change (°C or K) = T_final – T_initial
• Calorimeter: A device that measures heat transfer (e.g., coffee-cup calorimeter for solution reactions, bomb calorimeter for combustion).
• System vs. Surroundings:
• System: The part of the universe being studied (e.g., a reaction in a calorimeter).
• Surroundings: Everything else (e.g., the water in a coffee-cup calorimeter).
• Exothermic process: Releases heat (q < 0, system loses energy).
• Endothermic process: Absorbs heat (q > 0, system gains energy).
• Enthalpy (ΔH): Heat transferred at constant pressure (for AP, ΔH ≈ q in coffee-cup calorimetry).
• Law of Conservation of Energy: Heat lost by one part of a system = heat gained by another (q_system = –q_surroundings).
• Molar heat capacity: Heat required to raise 1 mole of a substance by 1°C (units: J/mol·°C). Not the same as specific heat!
• Thermal equilibrium: When two objects in contact reach the same temperature (no net heat transfer).

Step-by-Step: Solving Calorimetry Problems

1. Identify the system and surroundings.
2. Example: In a coffee-cup calorimeter, the system is the reaction, and the surroundings are the water and calorimeter.

3. Lab tip: If the calorimeter absorbs heat, include its heat capacity (often given as C_calorimeter).

4. Write the heat transfer equation for each part.

5. For the surroundings (water): q_water = m_water × c_water × ΔT_water

6. For the system (reaction): q_reaction = –q_water (because heat lost by reaction = heat gained by water).

7. Calculate ΔT.

8. ΔT = T_final – T_initial (use °C or K—the scale doesn’t matter for ΔT!).

9. Trick: If the temperature increases, the process is exothermic (q < 0 for the system).

10. Plug in values and solve for q.

11. Use q = mcΔT for the surroundings, then flip the sign for the system.

12. Example: If 50.0 g of water warms from 22.0°C to 28.5°C, q_water = (50.0 g)(4.18 J/g·°C)(6.5°C) = +1.36 kJ. Thus, q_reaction = –1.36 kJ (exothermic).

13. Scale to moles (if needed).

14. For ΔH per mole, divide q_reaction by moles of limiting reactant.

15. Example: If 0.050 mol of a compound releases –1.36 kJ, ΔH = –1.36 kJ / 0.050 mol = –27.2 kJ/mol.

16. Check units and significant figures.

17. Common units: J, kJ (1 kJ = 1000 J).
18. Sig figs: Match the least precise measurement (e.g., if mass is 50.0 g and ΔT is 6.5°C, use 2 sig figs).

Common Mistakes

• Mistake: Forgetting the negative sign for exothermic reactions.

• Correction: If the surroundings gain heat, the system loses heat (q_system = –q_surroundings).

• Mistake: Using the wrong specific heat (e.g., using water’s c for a metal).

• Correction: Memorize c_water = 4.18 J/g·°C and look up others (e.g., c_aluminum = 0.897 J/g·°C).

• Mistake: Confusing ΔT with T_final or T_initial.

• Correction: ΔT = T_final – T_initial, not the other way around.

• Mistake: Ignoring the calorimeter’s heat capacity.

• Correction: If given C_calorimeter, include q_calorimeter = C_calorimeter × ΔT in your calculations.

• Mistake: Mixing up specific heat (c) and molar heat capacity.

• Correction: Specific heat is per gram; molar heat capacity is per mole.

AP Exam Insights

1. FRQs often combine calorimetry with stoichiometry.
2. Example: A reaction’s ΔH is measured via calorimetry, then used to find the heat released for a given mass of reactant.

3. Trap: Forgetting to convert grams to moles before scaling q to ΔH.

4. Multiple-choice questions test sign conventions.

5. Example: “A reaction causes the temperature of the surroundings to decrease. Is the reaction endothermic or exothermic?”

6. Answer: Endothermic (q > 0 for the system).

7. Lab-based questions may ask about experimental errors.

8. Example: “If the calorimeter is not insulated, how would the measured ΔH compare to the true value?”

9. Answer: ΔH would be less negative (for exothermic reactions) because heat is lost to the environment.

10. Tricky distinction: q vs. ΔH.

11. q = heat at any conditions.
12. ΔH = heat at constant pressure (for AP, assume ΔH ≈ q in coffee-cup calorimetry).

Quick Check Questions

1. A 25.0 g sample of metal at 100.0°C is placed in 50.0 g of water at 22.0°C. The final temperature is 25.5°C. What is the specific heat of the metal? (c_water = 4.18 J/g·°C)
2. A) 0.128 J/g·°C
3. B) 0.444 J/g·°C
4. C) 0.897 J/g·°C
5. D) 1.25 J/g·°C

6. Answer: B) 0.444 J/g·°C.
   Explanation: Heat lost by metal = heat gained by water (q_metal = –q_water). Solve for c_metal using m_metal × c_metal × ΔT_metal = –m_water × c_water × ΔT_water.

7. In a coffee-cup calorimeter, 50.0 mL of 1.0 M HCl reacts with 50.0 mL of 1.0 M NaOH. The temperature increases from 22.0°C to 28.5°C. Calculate ΔH for the reaction (in kJ/mol). Assume the density of the solution is 1.0 g/mL and c_solution = 4.18 J/g·°C.

8. Answer: –54.4 kJ/mol.
   Explanation: Total mass = 100 g (50 mL + 50 mL). q_solution = (100 g)(4.18 J/g·°C)(6.5°C) = 2.72 kJ. Moles of HCl/NaOH = 0.050 mol. ΔH = –2.72 kJ / 0.050 mol = –54.4 kJ/mol.

9. True or False: If a reaction is exothermic, the temperature of the surroundings must increase.

10. Answer: True.
    Explanation: Exothermic reactions release heat, which is absorbed by the surroundings, raising their temperature.

Last-Minute Cram Sheet

1. q = mcΔT → Heat = mass × specific heat × temperature change.
2. ΔT = T_final – T_initial (use °C or K—same difference!).
3. q_system = –q_surroundings (conservation of energy).
4. c_water = 4.18 J/g·°C (memorize this!).
5. Exothermic: q < 0 (system loses heat); Endothermic: q > 0 (system gains heat).
6. Coffee-cup calorimeter: Measures ΔH ≈ q at constant pressure.
7. Bomb calorimeter: Measures q at constant volume (not ΔH).
8. ⚠️ Units matter! J vs. kJ (1 kJ = 1000 J), grams vs. moles.
9. ⚠️ Sign errors: If surroundings gain heat, system loses heat (q_system = –q_surroundings).
10. ⚠️ Don’t forget the calorimeter’s heat capacity if given! (q_total = q_water + q_calorimeter).