Thermochemistry: Energy, Enthalpy, Hess’s Law & Applications

TAKEAWAYS:

• Energy in chemistry is measured as heat (q) in reactions, called enthalpy (ΔH).
• Exothermic reactions release heat (ΔH < 0), while **endothermic** reactions absorb heat (ΔH > 0).
• Hess’s Law lets you calculate ΔH for complex reactions using simpler steps.
• Bond energy and standard enthalpies help predict reaction energy changes.
• Calorimetry measures heat changes in labs (e.g., coffee-cup calorimeters).
• Applications include fuels, nutrition (calories), and industrial processes.

1. Thermochemistry Basics: Energy and Chemical Reactions

Chemical reactions involve energy changes. Some reactions release energy (like burning wood), while others absorb energy (like photosynthesis). Thermochemistry studies these energy changes.

Key Terms:

• System: The part of the universe we study (e.g., a reaction mixture).
• Surroundings: Everything else (e.g., air, container).
• Heat (q): Energy transferred due to temperature difference.
• Work (w): Energy used to move matter (e.g., gas expansion).
• Internal Energy (U): Total energy of a system (kinetic + potential).
• Enthalpy (H): Heat content at constant pressure (ΔH = q at constant P).

Exothermic vs. Endothermic Reactions

flowchart TD
    A["Exothermic Reaction"] -->|"ΔH < 0"| B["Releases heat\n(Feels hot)"]
    C["Endothermic Reaction"] -->|"ΔH > 0"| D["Absorbs heat\n(Feels cold)"]
    A --> E["Example: Combustion\nC + O₂ → CO₂ + heat"]
    C --> F["Example: Photosynthesis\nCO₂ + H₂O + energy → C₆H₁₂O₆"]

A simple device to measure heat changes in reactions. (Image: Community College Consortium for Bioscience Credentials, CC BY 3.0, via Wikimedia Commons)

2. Measuring Energy Changes: Calorimetry

Calorimetry measures heat (q) released or absorbed in reactions. The most common tool is the coffee-cup calorimeter.

How It Works:

1. A reaction occurs in a styrofoam cup (insulated to prevent heat loss).
2. The temperature change (ΔT) of water is measured.
3. Use the formula: $$q=m\cdot c\cdot \Delta T$$
   • $q$ = heat (J)
   • $m$ = mass of water (g)
   • $c$ = specific heat capacity of water (4.18 J/g·°C)
   • $\Delta T$ = temperature change (°C)

Example: Burning a Candle

A 0.5 g candle burns, raising 100 g of water from 20°C to 30°C. Solution: $$q=100\text{g}\times 4.18\text{J/g⋅°C}\times (30°C-20°C)=4180\text{J}$$ Since the reaction releases heat, $q=-4180\text{J}$ (exothermic).

3. Enthalpy Change (ΔH) and Standard States

• Enthalpy change (ΔH) is the heat absorbed/released at constant pressure.
• Standard enthalpy (ΔH°) is measured under:
  • 1 atm pressure
  • 25°C (298 K)
  • 1 M concentration (for solutions)

Types of Enthalpy Changes:

4. Hess’s Law: Calculating ΔH for Complex Reactions

Hess’s Law states:

The total enthalpy change for a reaction is the same, regardless of the pathway.

Steps to Use Hess’s Law:

1. Write the target reaction.
2. Find simpler reactions whose ΔH values are known.
3. Adjust coefficients to match atoms.
4. Add or subtract ΔH values.

Example: Calculate ΔH° for C + 2H₂ → CH₄

Given:

• C + O₂ → CO₂, ΔH° = -393.5 kJ
• H₂ + ½O₂ → H₂O, ΔH° = -285.8 kJ
• CH₄ + 2O₂ → CO₂ + 2H₂O, ΔH° = -890.3 kJ

Solution: Reverse the formation of CH₄ and add: $$\text{CO₂}+2\text{H₂O}\to \text{CH₄}+2\text{O₂},\Delta H°=+890.3\text{kJ}$$ Now add: $$\text{C}+\text{O₂}\to \text{CO₂},\Delta H°=-393.5\text{kJ}$$ $$2\text{H₂}+\text{O₂}\to 2\text{H₂O},\Delta H°=2\times (-285.8)=-571.6\text{kJ}$$ Total ΔH° = -393.5 + (-571.6) + 890.3 = -74.8 , \text{kJ}

5. Bond Energy and Enthalpy Changes

• Bond energy is the energy needed to break 1 mole of bonds in gas phase.
• ΔH = Σ (bond energies of bonds broken) – Σ (bond energies of bonds formed)

Example: Calculate ΔH for H₂ + Cl₂ → 2HCl

Given bond energies:

• H–H = 436 kJ/mol
• Cl–Cl = 242 kJ/mol
• H–Cl = 431 kJ/mol

Solution: $$\Delta H=[436+242]-[2\times 431]=678-862=-184\text{kJ/mol}$$

6. Applications of Thermochemistry

A. Fuels and Energy Production

• Combustion reactions release energy (e.g., gasoline, coal).
• Calorific value = heat released per gram of fuel.

B. Food and Nutrition (Calories)

• 1 Calorie (kcal) = 4.18 kJ
• Example: A 50 g chocolate bar has ~250 Calories → 250 × 4.18 = 1045 kJ.

C. Industrial Processes

• Endothermic reactions (e.g., Haber process for ammonia) require energy input.
• Exothermic reactions (e.g., cement production) release heat.

A real example of an exothermic reaction (combustion). (Image: Arthur Jan Fijałkowski, CC BY-SA 3.0, via Wikimedia Commons)

7. NEB-Style Questions and Solutions

Short Answer Questions

1. Define enthalpy of formation.

   • Answer: The heat change when 1 mole of a compound is formed from its elements in standard states.

2. Why is the enthalpy of neutralization for strong acids and bases always the same?

   • Answer: Because the reaction is always: $$\text{H⁺(aq)}+\text{OH⁻(aq)}\to \text{H₂O(l)},\Delta H°=-57.1\text{kJ/mol}$$

Numerical Problems

3. Calculate the enthalpy change for: $$2\text{SO₂(g)}+\text{O₂(g)}\to 2\text{SO₃(g)}$$ Given:

   • S + O₂ → SO₂, ΔH° = -296.8 kJ
   • 2S + 3O₂ → 2SO₃, ΔH° = -726.0 kJ

   Solution: Reverse the first equation and add: $$2\text{SO₂}\to 2\text{S}+2\text{O₂},\Delta H°=+593.6\text{kJ}$$ $$2\text{S}+3\text{O₂}\to 2\text{SO₃},\Delta H°=-726.0\text{kJ}$$ Total ΔH° = +593.6 – 726.0 = -132.4 kJ

Conceptual Questions

4. Why is ice melting an endothermic process?
   • Answer: Because it absorbs heat from surroundings to break hydrogen bonds (ΔH > 0).

Exam Tip

✅ For NEB exams:

• Memorize standard enthalpy values (e.g., ΔH°f of H₂O, CO₂).
• Practice Hess’s Law with multi-step problems.
• Label units (kJ, kJ/mol) in numerical answers.
• Understand real-world applications (fuels, food energy).
• Draw energy diagrams for exothermic/endothermic reactions.

Final Note: Thermochemistry is about energy flow in reactions. Master calorimetry, Hess’s Law, and bond energies to solve any problem! 🔥📊