Chapter: Thermochemistry

1. Introduction to Thermochemistry

Thermochemistry is the study of energy changes—particularly heat—associated with chemical reactions and physical transformations. It helps us understand how energy flows between a system and its surroundings when matter undergoes change.

Energy is a property of matter that can be converted from one form to another but cannot be created or destroyed. In chemistry, we focus primarily on thermal energy, the energy resulting from the motion of atoms and molecules.

Key Idea: Every chemical reaction involves an exchange of energy—either releasing energy into the surroundings (exothermic) or absorbing energy from the surroundings (endothermic).

2. Energy, Heat, and Work

2.1 The System and Surroundings

System: The part of the universe under study (e.g., the contents of a beaker).
Surroundings: Everything outside the system that can exchange energy with it.
Boundary: The imaginary surface separating the system from its surroundings.

Energy transfer between system and surroundings occurs as heat (q) or work (w).

2.2 Forms of Energy

Kinetic energy (KE): Energy due to motion

2.2 Forms of Energy

Kinetic energy (KE): Energy due to motion
KE = ½ mv²
Potential energy (PE): Stored energy due to position or composition.
Thermal energy: Random motion of particles, measured by temperature.

2.3 The First Law of Thermodynamics

Energy is conserved:

ΔE = q + w

where:

ΔE = change in internal energy
q = heat absorbed by the system
w = work done on the system

Sign conventions:

Quantity	Positive (+)	Negative (-)
q (heat)	Heat gained by system	Heat lost by system
w (work)	Work done on system	Work done by system

3. Heat and Enthalpy

3.1 Heat (q)

Heat is energy transferred due to a temperature difference. The relationship between heat and temperature change is:

q = mcΔT

where:

m = mass of substance
c = specific heat capacity (J·g^-1·°C^-1)
ΔT = change in temperature (°C)

3.2 Enthalpy (H)

Enthalpy (H) represents the total heat content of a system at constant pressure:

ΔH = H_products − H_reactants

Exothermic reaction: ΔH < 0 → heat released
Endothermic reaction: ΔH > 0 → heat absorbed

Examples:

Combustion of methane (exothermic):
CH₄ + 2O₂ → CO₂ + 2H₂O, ΔH = −890 kJ/mol
Photosynthesis (endothermic):
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, ΔH > 0

4. Measuring Heat Changes: Calorimetry

4.1 Principle of Calorimetry

Calorimetry measures the heat exchanged in a chemical or physical process.

If a reaction occurs in a calorimeter:

q_reaction + q_surroundings = 0

For a solution reaction at constant pressure:

q_reaction = −(m_solutionc_solutionΔT)

4.2 Types of Calorimeters

Coffee-Cup Calorimeter:
- Constant pressure
- Used for reactions in solution (e.g., acid-base neutralization)
Bomb Calorimeter:
- Constant volume
- Used for combustion reactions

In bomb calorimetry:

q_v = C_calΔT

where C_cal is the heat capacity of the calorimeter.

5. Enthalpy of Reaction and Related Quantities

5.1 Standard Conditions

Standard state: The most stable form of a substance at 1 atm pressure and 25°C (298 K).

Standard enthalpy change (ΔH°): The enthalpy change when a reaction occurs under standard conditions.

5.2 Types of Enthalpy Changes

Type	Symbol	Description
Enthalpy of formation	ΔH_f°	Heat change when 1 mol of a compound forms from its elements
Enthalpy of combustion	ΔH_c°	Heat released when 1 mol of a substance burns in oxygen
Enthalpy of fusion	ΔH_fus	Heat absorbed to melt 1 mol of solid
Enthalpy of vaporization	ΔH_vap	Heat absorbed to vaporize 1 mol of liquid

Example:

C(s) + O₂(g) → CO₂(g), ΔH_f° = −393.5 kJ/mol

6. Hess’s Law

Hess’s Law: If a reaction can be expressed as the sum of two or more steps, the overall enthalpy change equals the sum of enthalpy changes for the individual steps.

Δ H overall = \sum Δ H steps

Example:

C(s) + O₂(g) → CO₂(g), ΔH = −393.5 kJ/mol

can be derived from:

C(s) + 1/2 O₂(g) → CO(g), ΔH₁ = −110.5 kJ/mol
CO(g) + 1/2 O₂(g) → CO₂(g), ΔH₂ = −283.0 kJ/mol

Then
ΔH = ΔH₁ + ΔH₂ = −393.5 kJ/mol

7. Standard Enthalpies of Formation and Reaction

7.1 Calculations Using Standard Enthalpies

For any reaction:

ΔH°_rxn = Σ ΔH°_f(products) − Σ ΔH°_f(reactants)

Example:
For 2H₂(g) + O₂(g) → 2H₂O(l)
Given ΔH°_f(H₂O(l)) = −285.8 kJ/mol

Then:

ΔH°_rxn = [2(−285.8)] − [0 + 0] = −571.6 kJ/mol

8. Bond Enthalpies

Bond enthalpy is the energy required to break one mole of a bond in a gaseous molecule.

Average bond enthalpies can be used to estimate reaction enthalpy:

ΔH_rxn = Σ(bonds broken) − Σ(bonds formed)

Example:

For H₂(g) + Cl₂(g) → 2HCl(g)

Bond enthalpies:
H–H = 436 kJ/mol, Cl–Cl = 243 kJ/mol, H–Cl = 431 kJ/mol

ΔH = (436 + 243) − 2(431) = −183 kJ/mol

9. Energy Diagrams

Energy diagrams illustrate the difference in enthalpy between reactants and products.

Exothermic: Products have lower potential energy; energy released as heat.
Endothermic: Products have higher potential energy; energy absorbed.

10. Thermochemistry in Real Life

Combustion reactions power vehicles and generate electricity.
Metabolic reactions in living organisms release energy stored in food.
Phase changes involve enthalpy changes (melting, boiling, condensation).

Understanding thermochemistry helps in:

Designing energy-efficient processes
Estimating fuel values
Predicting reaction spontaneity (in combination with entropy and Gibbs energy)

11. Summary

Concept	Key Relationship
First law of thermodynamics	ΔE = q + w
Enthalpy change at constant pressure	ΔH = q_p
Heat-temperature relationship	q = mcΔT
Hess’s Law	ΔH_total = ΣΔH_steps
From standard formation enthalpies	ΔH_r = ΣΔH°_f(products) − ΣΔH°_f(reactants)

From bond enthalpies

ΔH_rxn = ∑ E_{bonds broken} – ∑ E_{bonds formed}

12. Practice Problems

A 50.0 g sample of water is heated from 25.0°C to 55.0°C. Calculate the heat absorbed.
(c = 4.184 J·g^-1·°C^-1)
Determine the enthalpy change for:
2SO₂(g) + O₂(g) → 2SO₃(g)
Given:
SO₂(g) + ½O₂(g) → SO₃(g), ΔH = −198 kJ/mol
Use bond enthalpies to estimate ΔH for:
CH₄ + 2O₂ → CO₂ + 2H₂O

13. Key Terms

Calorimetry
Enthalpy (H)
Endothermic / Exothermic
First Law of Thermodynamics
Heat capacity
Hess’s Law
Standard enthalpy of formation
Bond enthalpy

14. Further Reading

Zumdahl & Zumdahl, Chemistry, 11th ed., Cengage Learning
Brown, LeMay, Bursten & Murphy, Chemistry: The Central Science, Pearson
Atkins & De Paula, Physical Chemistry for the Life Sciences, Oxford University Press