Difficulty: Intermediate | Prerequisites: The mole and molar mass (Ch. 3)
Chapter 5 asks: how much energy does a chemical or physical process release or absorb? You will measure heat changes with calorimeters and calculate them with the q = mcΔT equation. The sign of q tells you the direction of energy flow, and converting between kJ/g and kJ/mol ties thermochemistry back to the mole concept from Chapter 3.
Thermochemistry measures the heat absorbed or released during chemical and physical changes. The core equation is q = mcΔT (heat = mass × specific heat × temperature change). Calorimeters capture that heat so you can calculate it: a coffee-cup calorimeter measures heat at constant pressure, and a bomb calorimeter measures heat at constant volume. Negative q means the process releases heat (exothermic); positive q means it absorbs heat (endothermic).
Heat (q)
Energy transferred between a system and its surroundings because of a temperature difference. Measured in joules (J) or kilojoules (kJ). In simple terms, heat is what flows from hot to cold.
Specific heat capacity (c)
The amount of heat needed to raise the temperature of 1 gram of a substance by 1 °C (units: J/g°C). Water's specific heat is 4.184 J/g°C, which is unusually high. Think of it as a measure of how stubborn a substance is about changing temperature.
Heat capacity (C, capital)
The amount of heat needed to raise the temperature of an entire object or calorimeter by 1 °C (units: kJ/°C or J/°C). Unlike specific heat, it applies to the whole apparatus, not per gram.
Calorimetry
The experimental measurement of heat changes using a calorimeter. The central principle: heat lost by one part of the system equals heat gained by another (conservation of energy).
Coffee-cup calorimeter
A simple, constant-pressure calorimeter (typically two nested styrofoam cups) used for reactions in solution. The heat gained by the solution equals the heat lost by the reaction: q_cal = -q_sys.
Bomb calorimeter
A rigid, sealed, constant-volume calorimeter used to measure heats of combustion. The calorimeter absorbs the heat released by the reaction: q_bomb = C_bomb × ΔT, and q_rxn = -q_bomb.
Exothermic process
A process that releases heat to the surroundings. q is negative for the system, and the surroundings warm up.
Endothermic process
A process that absorbs heat from the surroundings. q is positive for the system, and the surroundings cool down.
Enthalpy of combustion
The heat released when one mole (or one gram) of a substance burns completely in oxygen. Reported as kJ/mol or kJ/g, always negative (combustion is exothermic).
This is the workhorse of thermochemistry. Every variable:
q = heat transferred (J)
m = mass of the substance (g)
c = specific heat capacity (J/g°C)
ΔT = T_final - T_initial (°C)
The sign of ΔT determines the sign of q. If the substance cools down, ΔT is negative, so q is negative (heat released). If it warms up, ΔT is positive, so q is positive (heat absorbed).
Worked example: Cooling a piece of nickel
A 4.85 g piece of Ni at 75.0 °C is cooled to 25.0 °C. Specific heat of Ni = 0.444 J/g°C.
q = (4.85 g)(0.444 J/g°C)(25.0 °C - 75.0 °C)
q = (4.85)(0.444)(-50.0) = -107.7 J
The negative sign confirms the nickel released heat as it cooled.
Principle: the heat released by the process (system) is absorbed by the surrounding solution (calorimeter), so q_cal = -q_sys.
You measure the temperature change of the solution and use q = mcΔT for the solution to find q_cal, then flip the sign to get q_sys.
Worked example: Melting ice in a calorimeter
25.8 g of ice is placed in a calorimeter with 100.0 g of water at 35.4 °C. After the ice melts, the water temperature is 18.1 °C. Specific heat of water = 4.184 J/g°C.
The total mass of solution used for q_cal is 100.0 g + 25.8 g = 125.8 g (the melted ice becomes part of the solution).
q_cal = (125.8 g)(4.184 J/g°C)(18.1 °C - 35.4 °C)
q_cal = (125.8)(4.184)(-17.3) = -9106 J
q_sys = +9106 J (the ice absorbed this much energy to melt)
Per gram of ice: 9106 J / 25.8 g = 353 J/g = 0.353 kJ/g
Per mole of ice: 9106 J / (25.8 g ÷ 18.02 g/mol) = 9106 / 1.43 mol = 6370 J/mol = 6.37 kJ/mol
A bomb calorimeter has a known heat capacity (C_bomb, in kJ/°C) for the entire apparatus. The formula simplifies:
q_bomb = C_bomb × ΔT
q_rxn = -q_bomb
Worked example: Combustion of quinone (C₆H₄O₂)
0.194 g of quinone is combusted. C_bomb = 1.56 kJ/°C. Temperature rises by 3.2 °C.
q_bomb = (1.56 kJ/°C)(3.2 °C) = 4.992 kJ
q_rxn = -4.992 kJ
Per gram: -4.992 kJ / 0.194 g = -25.7 kJ/g
Molar mass of C₆H₄O₂ = 6(12.01) + 4(1.008) + 2(16.00) = 108.09 g/mol
Moles: 0.194 g / 108.09 g/mol = 0.00179 mol
Per mole: -4.992 kJ / 0.00179 mol = -2782 kJ/mol
q = mc\Delta THeat equals mass times specific heat times temperature change.
q_{\text{cal}} = -q_{\text{sys}}In a coffee-cup calorimeter, the heat gained by the solution is equal and opposite to the heat of the process.
q_{\text{bomb}} = C_{\text{bomb}} \times \Delta TIn a bomb calorimeter, the heat absorbed by the calorimeter equals its heat capacity times the temperature rise.
To convert from kJ to kJ/g: divide q_rxn by the mass of the sample.
To convert from kJ/g to kJ/mol: multiply kJ/g by the molar mass (g/mol).
Students often mix up the sign of q. Remember: ΔT = T_final - T_initial. If the substance cools, ΔT is negative and q is negative. A negative q for the system means it released heat (exothermic).
Students confuse specific heat capacity (c, lowercase, J/g°C, per gram) with heat capacity (C, uppercase, kJ/°C, for the whole calorimeter). The bomb calorimeter formula uses heat capacity, not specific heat.
In coffee-cup calorimetry, students sometimes forget that the ice (once melted) adds to the total mass of solution. The mass in q = mcΔT is the mass of all the liquid in the calorimeter.
When converting q_rxn to kJ/mol, students sometimes divide by the mass instead of dividing by the number of moles. The correct sequence is: q_rxn (kJ) ÷ mass (g) = kJ/g, then kJ/g × molar mass (g/mol) = kJ/mol. Or directly: q_rxn ÷ moles = kJ/mol.
⚠️ q = mcΔT is guaranteed on the final. Know what every variable is and watch the sign of ΔT.
⚠️ Calorimetry problems may ask for q in J, kJ/g or kJ/mol. You need all three conversions.
⚠️ Bomb calorimeter problems use the calorimeter's total heat capacity (C_bomb), not a specific heat. Read the problem carefully to see which value is given.
⚠️ The relationship q_cal = -q_sys is fundamental. The sign flip is where many students lose marks.
True or False: If ΔT is negative, the process is endothermic. (False, negative ΔT means the substance cooled, so it released heat, exothermic)
Fill in the blank: The specific heat capacity of liquid water is ____ J/g°C. (4.184)
True or False: In a bomb calorimeter, q_rxn = q_bomb. (False, q_rxn = -q_bomb)
Fill in the blank: To convert heat of combustion from kJ/g to kJ/mol, multiply by the ____. (molar mass)
Q: A 10.0 g sample of copper (c = 0.385 J/g°C) is heated from 20.0 °C to 80.0 °C. How much heat was absorbed?
A: q = (10.0 g)(0.385 J/g°C)(80.0 - 20.0 °C) = (10.0)(0.385)(60.0) = 231 J
Q: In a coffee-cup calorimeter, 50.0 g of solution at 22.0 °C rises to 28.5 °C after a salt dissolves. What is q_rxn? (Use c = 4.184 J/g°C.)
A: q_cal = (50.0)(4.184)(28.5 - 22.0) = (50.0)(4.184)(6.5) = 1360 J. q_rxn = -1360 J (the dissolving released heat).
Q: A 0.500 g sample of naphthalene (C₁₀H₈, molar mass 128.17 g/mol) is burned in a bomb calorimeter (C_bomb = 5.00 kJ/°C). The temperature rises by 1.58 °C. What is the heat of combustion in kJ/mol?
A: q_bomb = (5.00)(1.58) = 7.90 kJ. q_rxn = -7.90 kJ. Moles = 0.500 / 128.17 = 0.00390 mol. Heat of combustion = -7.90 / 0.00390 = -2026 kJ/mol.
Q: Explain why q_cal = -q_sys in a coffee-cup calorimeter.
A: Conservation of energy. The heat released by the reaction (system) is absorbed by the surrounding solution (calorimeter). They are equal in magnitude but opposite in sign.
Thermochemistry connects directly to enthalpy (ΔH) and Hess's law in later chapters, where you combine heats of reaction to find ΔH for a new reaction. The mole concept from Chapter 3 is essential for converting between kJ and kJ/mol. Calorimetry also appears in later topics such as bond energies and heats of formation.
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